A livestock population can be characterized by different population genetic parameters, such as linkage disequilibrium and recombination rate between pairs of genetic markers. The population structure, which may be caused by family stratification, has an influence on the estimates of these parameters. An expectation maximization algorithm has been proposed for estimating these parameters in half-sibs without phasing the progeny. It, however, overlooks the fact that the underlying likelihood function may have two maxima. The magnitudes of the maxima depend on the maternal allele frequencies at the investigated marker pair. Which maximum the algorithm converges to depends on the chosen start values. We present a stepwise procedure in which the relationship between the two modes is exploited. The expectation maximization algorithm for the parameter estimation is applied twice using different start values, followed by a decision process to assess the most likely estimate. This approach was validated using simulated genotypes of half-sibs. It was also applied to a dairy cattle dataset consisting of multiple half-sib families and 39,780 marker genotypes, leading to estimates for 12,759,713 intrachromosomal marker pairs. Furthermore, the proper order of markers was verified by studying the mean of estimated recombination rates in a window adjacent to the investigated locus as well as in a window at its most distant chromosome end. Putatively misplaced markers or marker clusters were detected by comparing the results with the revised bovine genome assembly UMD 3.1.1. In total, 40 markers were identified as candidates of misplacement. This outcome may help improving the physical order of markers which is also required for refining the bovine genetic map. Population genetic parameters, such as linkage disequilibrium (LD) and recombination rate, are relevant parameters for characterizing a livestock population. Methods for genomic selection  are of particular interest, for instance, to map QTL in such breeds. Neglecting the population structure may lead to biased parameter estimates.The estimation of recombination rate requires genotypic and pedigree information—most often parent-offspring data are used. Different approaches are available enabling the parameter estimation based on phased  algorithm. However, a special characteristic of the underlying likelihood function (LF) is its bimodality  is employed to find the most probable final estimate when the LF has two modes.At first, the LF for estimating θ and nAA, AB. It is assumed that paternal linkage phases are known without error, and only those loci at which a sire is heterozygous are considered. Otherwise a recombination rate cannot be inferred. The sire haplotypes are denoted as A-A and B-B in the coupling phase as well as A-B and B-A in the repulsion phase. Hence the frequency of the paternal A allele is 0.5 among offspring.The SNP genotypes of progeny are used to estimate the unknown parameters; SNP alleles are denoted as A and B. The observed genotype frequencies at two loci, e.g., AA and AB, are denoted as Based on the multinomial distribution and considering a full model, in which the maternal haplotype frequencies and θ are the unknown parameters, the logarithmic LF can be expressed similarly to Gomez-Raya  as:i, k is the probability of the two-locus genotype i, k∈{AA, AB, BB}. For instance, LF depends on the frequency of maternal gametes  and θ. It is now reparametrized and written in terms of LD of maternal and paternal gametes, Dsire = ±(1−2θ)/4 (the positive sign corresponds to the coupling phase), respectively, to better investigate the relationship between these parameters. Indices are used at frequencies (p1 and p2) of the maternal A allele to distinguish between the loci. Hence, using the computer algebra system Maple™ :where πLF depends on the maternal allele frequencies at the two loci: they affect the number (one or two) and height of the modes. Plotting this function also reveals its characteristics, see Figure Dsire∈ and L1 = max{−p1p2, −(1−p1)(1−p2)} and L2 = min{p1(1−p2), (1−p1)p2}  estimation is not straightforward, see e.g., Hill  and dominance effects covdom  require the paternal and maternal LD, and a system of two equations is achieved:The theoretical derivations of Bonk et al.  can be aDdam and Dsire (indices I and II) can be obtained. Given one solution, the other solution is derived as:Then two solutions for p1 = p2 = 0.5, maternal and paternal LD are mutually exchangeable.In the particular case of Dsire = 0.25 (θ = 0) and Ddam = 0. Start values for the maternal haplotype frequencies are received from Ddam and ML estimates of the maternal A allele at the investigated loci, i.e., nAA and nBB denote the number of offspring with AA and BB genotypes, respectively. Start values for the second run are obtained after using the EM estimates of the first run and employing the complementary relationship in Equation (2). If this relationship leads to start values outside the parameter space, we conclude that the underlying likelihood is unimodal and skip a second EM run. Otherwise, this “educated guess” shall lead the EM algorithm to the second mode.For the first run of EM, default start values are used: LF can either be unimodal or bimodal with modes of different height when p1 and p2 differ from 0.5. Then, the most likely estimate of Ddam and θ can be identified from comparing the value of logLF at the two proposals. It is obvious to select the estimates of parameter values constituting the higher value of logLF. Because logLF can be rather flat  was modified mildly by combining genotype frequencies. In a family with few progeny, not all genotype combinations may have been observed, i.e., some cells remained empty in a genotype-count table, and haplotype frequencies were then estimated to be close to zero. To level the influence of zero or almost-zero haplotype frequencies on the likelihood function, the none-observed genotypes and the least-observed genotype were combined into one cell. The corresponding set of index pairs was set up as 0 = {i, k∈{AA, AB, BB}|ni, k = 0} collects the indices from the empty cells, and In view of the empirical data analysis, the logwith parameters as above. Thus, compared to a strategy of leaving empty cells out, the probability of the least observed genotype is marginally increased.LF* was applied to all locus pairs with allele frequencies outside the critical range.The DP based on the value of logp1, p2∈, it is expected that the modes of logLF have almost equal height, and a decision about the final estimates is actually not possible. Only additional information about the physical position and estimates of θ in the neighborhood might allow selecting the most appropriate set of parameter estimates. If SNP i and k had estimates of allele frequency in the critical range, i.e., i, k∈{1, …, mc}, i<k; mc denotes the number of SNPs on a particular chromosomec. Then the estimated recombination rates ,– EMDP: θ = 0 and Ddam = 0,– EMT0: θ = 0 and Ddam = 0.– EMT05: θ = 0.5 and i∈{1, …, mc} as the average of the nearby s markers:The estimation of recombination rates based on empirical bovine data enables the identification of SNPs with wrong placement in the underlying genome assembly. SNPs revealing high estimates of θ with SNPs in close neighborhood or low estimates with distant SNPs are candidates for misplaced SNPs. In order to trace such SNPs, a statistic for unusually high estimates was calculated for each locus s = 30; this choice will be discussed later. Similarly, for investigating the pattern of unusually low estimates, a statistic was computed for a window at the most distant chromosome end:The number of SNPs considered in a local environment of the target SNP was i = 1, …, mc; c = 1,.., 29) were taken as thresholds, and SNPs with The 99% quantile of N = 100 or N = 1, 000 progeny) were simulated at two loci. The sire was double-heterozygous in coupling phase, and the paternal haplotypes of progeny were determined considering a random recombination event during meiosis. The maternal haplotypes of progeny were drawn by chance from a dam population with a given LD between the two loci.In order to validate the influence of start values on the parameter estimates, genotype data of a single half-sib family ; Ddam = 0.05,I) Small θ: Dsire = 0.15 (θ = 0.20); Ddam = 0.05,II) Medium θ: Dsire = 0.05 (θ = 0.40); Ddam = 0.15.III) Large θ: p1 = p2 = 0.5; (b) p1 = p2 = 0.4; (c) p1 = 0.4, p2 = 0.6; and (d) p1 = p2 = 0.8. Scenarios II (a) and III (a) are complementary settings. A balanced design, i.e., Dsire = Ddam, leads to a unimodal logLF and is not considered here. As only a single SNP pair was simulated, the DP was reduced to comparing the logLF* values only.Different maternal allele frequencies were considered for each scenario: (a) N = 100 or N = 1, 000 half-sibs and 1,000 replicates were simulated. Separate runs of the simulation were executed with fixed allele frequency at the first locus, p1 = 0.4 or p1 = 0.5, but varying frequency at the second locus: p2 was randomly drawn from a uniform distribution on the interval . In each run Ddam was fixed at 0.05 or 0.10. Hence, 8 scenarios were studied in total.In a second simulation study, θ was varied in a range from zero to 0.5 with step size 0.005. For each value, genotypes of R  to BTA4  as well as to a SNP cluster from BTA1 (index positions 411–420) to BTA4 (index positions 411–420).The empirical data are provided in Files N = 100 half-sibs were considered. In such cases, EMDP was the second-best choice. If N = 1, 000, bias and MSE reduced for all approaches and EMDP performed best overall in terms of MSE  or two proposals (EMDP) influenced the estimates of disequilibrium in sires and dams. The first simulation study showed that EMT0 and EMDP performed equally well for the small-θ setting in terms of bias and MSE of E Tables , 2 when E Tables , S2. FurN = 100, EMDP had the least bias of Ddam = 0.05 , BTA13  and BTA20 . Smaller regions of high LD were also observed outside the center, e.g., on BTA14 , BTA23 , and BTA29 . Such regions may indicate the presence of cold spots.The estimated Among all SNP pairs, 37,040 (0.3%) estimates of θ followed the rules of the DP for critical maternal allele frequencies: the most appropriate LF at the two proposals yielded the final estimate of genetic parameters. The decision was in favor of the first proposal, which was derived from default start values θ = 0 and Ddam = 0, in 72.13% regarding all chromosomes. On the other hand, in 27.87% of pairwise investigations, the proposal obtained from the complementary relationship (Equation 2) yielded the larger logLF; this makes EMDP superior to EMT0. Either way, the smaller In 99.7% of pairwise investigations, a comparison of logBos taurus assembly UMD 3.1.1. The aforementioned SNP cluster on BTA5 had the same chromosome assignment but the base pair position now ranged from 103.47 to 104.23 Mb based on UMD 3.1.1. The order of SNPs within this cluster remained. A second SNP cluster was found on BTA3  which was now assigned to BTA2 based on UMD 3.1.1. Furthermore, the order of SNPs within this cluster was reversed. The rsID of a single SNP on BTA2  was unavailable. The DNA sequence of this SNP derived from Btau 4.2 was mapped to the sequence based on UMD 3.1.1 using Bowtie 2 . This outcome might be explained by the algorithm-internal step-width regularization. To circumvent this, the two local maxima can be sought via grid search. This procedure is feasible in the reduced LF case but not recommended for a search in the whole parameter space considering not only θ and Ddam but also the allele frequencies as unknown parameters .Assuming that the maternal allele frequencies are known, the recombination rate and maternal LD can also be inferred from the reduced LF where θ and For various species it is known that the recombination rate varies between males and females . Such a large window could be counteractive: it would definitely detect candidates being putatively placed on another chromosome but might fail to detect candidates which have a different position on the same chromosome.The physical order of SNPs has been updated regularly, and misplacements have been corrected successively . Those candidates that cannot be matched may be further explored based on information about the raw data used for the current assembly. As, for instance, not only coverage but also read lengths of contigs and mate-pair distances have an impact on the quality of the genome build  is available –(S16) in the File A more formal approach of identifying misplacements is testing the mean of see File , an asymquations 0–(S16) iNot only does the investigation of a et al.  detecteda et al.  even idea et al.  though tThe proposed method is applicable not only to paternal but also to maternal half-sib families as they appear, for instance, in insects (Milne and Friars, Ddam. In such families, there is no means to estimate θ, and haplotype frequencies can be estimated using simplified equations (Gomez-Raya, Half-sib families of dairy cattle typically contain many offspring. For instance, on average 828 offspring were reported for German Holstein bulls (median 172.5, minimum 12.0 and maximum 25,590; Vereinigte Informationssysteme Tierhaltung, Dsire∈ in the coupling phase. The extent of genetic and chromatid interference shall be studied in more depth in future. It may help fitting a mapping function to the estimated θ's and improving the corresponding genetic map.In some cases, the smoothing curve adopts The theoretical consideration of the likelihood function shows that the maternal allele frequencies have an influence on the position and height of its maxima. We employed an expectation maximization algorithm with two sets of start values to estimate recombination rate and maternal linkage disequilibrium near the two modes. Knowing the two modes gave a competitive edge on the parameter estimates, particularly if the maternal allele frequencies at the investigated SNP pair were about 0.5. In this case, a decision rule was proposed for selecting the most suitable proposal based on estimates in the neighborhood and the corresponding physical position. This study also showed that half-sib families can be used for the identification of misplaced SNPs in the genome assembly due to the information provided from linkage analyses and linkage disequilibrium coming from maternal contribution. A correct physical order is helpful for further investigating the genetic distance between SNPs and refining the bovine genetic map.Animal Care and Use Committee approval was not obtained for this study because the blood samples were collected during a veterinary routine examination in 2009.AH implemented the theory, developed the simulation design, analyzed the data and drafted the manuscript. FT raised the initial question, contributed to the theoretical investigations and to the discussion of the results. LG-R contributed to the theoretical investigations and suggested improvements to the manuscript. MD contributed to the investigations of the likelihood function. DW supervised the project and contributed to the theoretical derivations, data analysis, discussion of results, and writing of the manuscript. All of the authors have read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


DNA m.3243A>G mutation is associated with a wide range of clinical features, making disease prognosis extremely difficult to predict. We aimed to understand the cause of this heterogeneity.The pathogenic mitochondrial UK MRC Mitochondrial Disease Patient Cohort using the Newcastle Mitochondrial Disease Adult Scale. We modeled the role of risk factors for the development of specific phenotypes using proportional odds logistic regression. As mitochondria are under the dual control of their own and the nuclear genome, we examined the role of additive nuclear genetic factors in the development of these phenotypes within 46 pedigrees from the cohort.We examined the phenotypic profile of 238 adult m.3243A>G carriers (patients and asymptomatic carriers) from the R2 values are low (0.14–0.17). We found a high heritability estimate for psychiatric involvement  and moderate estimates for cognition , ataxia , migraine , and hearing impairment .Seizures and stroke‐like episodes affect 25% and 17% of patients, respectively; more common features include hearing impairment, gastrointestinal disturbance, psychiatric involvement, and ataxia. Age, age‐adjusted blood heteroplasmy levels, and sex are poor predictors of phenotypic severity. Hearing impairment, diabetes, and encephalopathy show the strongest associations, but pseudo‐Our results provide good evidence for the presence of nuclear genetic factors influencing clinical outcomes in m.3234A>G‐related disease, paving the way for future work identifying these through large‐scale genetic linkage and association studies, increasing our understanding of the pathogenicity of m.3243A>G and providing improved estimates of prognosis. Mitochondria, essential organelles responsible for oxidative phosphorylation (OXPHOS), are under the dual control of their own and the nuclear genome. Mitochondrial DNA (mtDNA) encodes 13 subunits of the OXPHOS system, along with 22 mitochondrial tRNAs and two mitoribosomal subunits.MT‐TL1 ), which represents the most common heteroplasmic mtDNA disease genotype.To explore the cause of this heterogeneity, we studied the pathogenic m.3243A>G mtDNA variant within Heteroplasmy describes the coexistence of mutant and wild‐type mtDNA molecules within the same cell. mtDNA mutant levels can vary dramatically between different individuals and tissues; postmitotic tissues such as muscle have higher levels, whilst levels in blood decrease significantly over time.Such unexplained heterogeneity suggests that unidentified factors influence phenotype; the nuclear genome is a strong candidate given the interaction between the two genomes. Nuclear background has been shown to influence mitochondrial function, with a mouse model showing decreased fitness and lifespan when mitochondrial and nuclear mutations are combined.The extent to which genetic factors contribute to a phenotype can be assessed using familial relationships to estimate heritability.We aimed to model the development of specific m.3243A>G‐related phenotypes within a large UK patient cohort to allow the prediction of disease prognosis in patients. We examined the role of age, heteroplasmy, and sex as risk factors and evaluated the potential role of additive nuclear genetic factors by exploiting familial relationships to generate estimates of heritability.These studies were undertaken using data from 238 m.3243A>G carriers from the MRC Mitochondrial Disease Patient Cohort UK.N = 175), the median follow‐up time was 3.60 years  with a median of 4 assessments per patient .The median age at last assessment was 43.4 years , and only two individuals were <18 years old. For the patients with multiple NMDAS assessments ; 157 of these were from families with multiple members within the cohort, comprising 46 familial lineages with multiple members, and 62 individuals who had no relatives in the cohort. Pedigrees range in size from two to seven individuals , and span 2–4 generations.Ethical approval was granted by the Newcastle and North Tyneside Research Ethics Committee (13/NE/0326), and written informed consent from patients was obtained prior to study inclusion. All clinical investigations were evaluated according to the Declaration of Helsinki.http://www.newcastle-mitochondria.com/clinical-professional-home-page/clinical-publications/nmdas/) were considered. Section I of NMDAS scores current function according to patients and/or caregiver interview and relates to the preceding 4 weeks. Most questions from this NMDAS section were omitted from these analyses due to their subjective nature. The exception was hearing impairment which was included as it is one of the common symptoms for m.3243A>G‐related disease, and is the only question that captures information about hearing. All questions are independently assessed; therefore, the exclusion of questions does not affect the validity of the sections that were retained in the study. Section II scores system specific involvement according to patients and/or caregiver interview and consultation with medical notes and relates to the preceding 12‐month period and section III scores current clinical assessment according to an examination performed at the time of assessment; both are likely to be more objective and so all were included. Some traits, such as stroke‐like episodes, can be stochastic in nature; individuals can score very low on one assessment despite historically high scores. Therefore, to ensure we captured these historical events, a single independent point for each trait and each individual was determined by the maximal NMDAS score and the youngest age at which that score was attained. For asymptomatic individuals, the age at the most recent assessment was used.Nineteen questions from the NMDAS . Given this exponential decline, m.3243A>G levels were corrected for age using the following formula: Age‐adjusted blood level = Blood heteroplasmy/0.977(age+12) The median age‐adjusted blood heteroplasmy level was 60.1% .In blood, the m.3243A>G heteroplasmy level progressively declines by ~2.3% yearPearson correlations between traits and significance levels were calculated using the rcorr function in the Hmisc package in R.P = 0.05, determined by maximum likelihood testing) was not reached. This was the case for all phenotypes except ptosis, myopathy, and gastrointestinal disturbance. NMDAS scores were re‐categorized as asymptomatic/mild (NMDAS = 0–1), moderate (2–3), and severe (4–5) to ensure sufficient patients in each group for statistical modeling.Specific phenotypic feature analysis used proportional odds multiple logistic regression, with age, age‐adjusted mean blood heteroplasmy, and sex as predictors, using clm from the ordinal package in R.P = 0.05. Encephalopathy did not meet the assumption of proportional odds so was considered as a binary trait using threshold scores determined a priori based on the NMDAS clinical descriptors,Assumptions of the proportional odds model were tested by comparing fitted models with models where the effects were modeled as nominal rather than ordinal, using a likelihood ratio test and a significance threshold of R2 values,c)/log(Lnull), where Lc is the maximum likelihood of the fitted model and Lnull is the maximum likelihood of the null.We report McFadden's pseudo‐Odds ratios (relating to decades for age and 10% change in level for heteroplasmy) were calculated by taking exponentials of the coefficients estimated by the model. They represent the odds that an individual will move from one category to the next (asymptomatic/mild to moderate or moderate to severe) given an increase of a decade (age) or 10% (heteroplasmy) in the predictor variables, compared to the odds in the absence of an increase.P values as for reasons well documented in the literature, Bonferroni correction would be too conservative, particularly as we are testing a priori hypotheses with variables that are not all independent.Unless otherwise stated, we report unadjusted h2) is the proportion of the total population variance of a trait (σp2) that can be attributed to additive nuclear genetic effects (σa2), expressed as a ratio (h2=σa2/σp2). Heritability was estimated using variance components methods and significance levels obtained using likelihood ratio tests, as implemented in the SOLAR software package (SOLAR Eclipse version 8.1.1).Heritability in the narrow sense . The square root of trait score was used for cerebellar ataxia, neuropathy, dysphonia–dysarthria, encephalopathy, stroke‐like episodes, visual acuity, and chronic progressive external ophthalmoplegia (CPEO), in order to ensure normality of the residuals (kurtosis <0.8). After this transformation, only stroke‐like episodes and encephalopathy showed residual kurtosis outside of the acceptable range, and this is likely to be due to the small number of affected individuals for these traits. Pyramidal and extrapyramidal involvements were excluded from the heritability analysis due to low numbers of affected individuals.To produce heritability estimates which excluded the variation due to known factors such as age and heteroplasmy level, we included these factors as covariates in these analyses. Sex was included where it was shown to have an effect at the h2), standard error (SE), P values, and Kullback‐Leibler R2, as calculated in SOLAR.For binary trait analysis, individuals with a score greater than or equal to a threshold score Table  were codTo determine whether common genetic factors influence pairs of traits, bivariate heritability analysis was performed. SOLAR calculates the estimated genetic correlation (rhoG), a measure of the shared genetic variance between traits (pleiotropy). Significant (determined by likelihood ratio test) genetic correlations suggest the presence of common genetic factors (one or more genes) that influence both traits.First, we examined the range of clinical phenotypes observed in our patient cohort, as assessed by the NMDAS. The most common phenotypic traits associated with the pathogenic m.3243A>G variant are hearing impairment  and gastrointestinal disturbance (76%), followed by psychiatric involvement (69%) and cerebellar ataxia (66%) . Hearing impairment and diabetes are moderately correlated (r ~ 0.45), confirming a well‐reported association between these two traits.r ~ 0.52–0.59). Cerebellar ataxia is correlated with a number of traits, notably myopathy (r ~ 0.76), hearing impairment (r ~ 0.63), and dysphonia–dysarthria (r ~ 0.68).We then asked whether traits commonly observed in association with the pathogenic m.3243A>G variant are correlated with each other, which would provide evidence of a common underlying etiology .Interestingly, both migraine and diabetes are only correlated with a small number of other traits. Migraine is, however, moderately correlated with gastrointestinal disturbance (P = 1.5 × 10−8), hearing impairment , cerebellar ataxia , and neuropathy  are most strongly associated with increasing age, consistent with the clinical picture of a progressive disease. Almost all features were significantly associated with higher heteroplasmy, the most strongly associated being hearing impairment , dysphonia–dysarthria , diabetes , stroke‐like episodes , cerebellar ataxia , myopathy , cardiovascular involvement , and encephalopathy . Although McFadden's pseudo‐R2 values indicate that hearing impairment , diabetes , and cerebellar ataxia  show the strongest association between higher phenotypic severity, higher age‐adjusted blood heteroplasmy, and increasing age, pseudo‐R2 values are low, highlighting the limited predictive power of these covariates.Next, we explored the impact of age, heteroplasmy level, and sex on the severity of specific phenotypic features using proportional odds logistic regression Fig. . Odds raSeveral key features of the MELAS phenotype, including stroke‐like episodes, seizures, and encephalopathy, were not associated with age, only with heteroplasmy. This is consistent with clinical observations.males = 3.02, P = 2.6 × 10−3 and myopathy; ORmales = 0.43, P = 7.9 × 10−3). Although more males  were affected by stroke‐like episodes than females , this did not reach significance .For two phenotypes, the effect of sex was significant  of NMDAS traits using the information contained within pedigree structures.As low pseudo‐h2=0.76, P = 0.0003) and moderate estimates for cognition , cerebellar ataxia , migraine , and hearing impairment  (Table P < 0.08). These results, which take age‐adjusted blood heteroplasmy, age, and sex into account, provide good evidence for the presence of nuclear genetic factors influencing several clinical outcomes in m.3234A>G‐related disease.We found a significant, high heritability estimate for psychiatric involvement , and for migraine  and encephalopathy , the estimates are greater for the binary trait. This may be due to a stricter definition of the phenotypes, with milder cases coded as unaffected in the binary model. Heritability estimates for cerebellar ataxia, cognition, and hearing impairment are no longer significant, but this is not surprising given the loss of information due to converting NMDAS scores to binary traits and may be due to incorrectly assigning milder individuals an unaffected status.The variance component methods implemented in SOLAR assume normally distributed quantitative trait data. A limitation of our study is that the trait data are ordered categorical variables and do not all follow a normal distribution. To address this issue, we also calculated heritabilities considering the traits as binary variables Table . The herP = 0.0081), cerebellar ataxia and migraine , encephalopathy and migraine , and cognition and hearing . This implies that these traits share a genetic etiology; that is, they may be influenced by variations in the same genes and is not surprising, given the role of the nervous system in these traits and the increasing evidence of pleiotropy in complex traitsTo determine the extent to which the heritability of traits is caused by shared genetic factors, a bivariate model was used to calculate the estimated genetic correlation between traits. There is significant genetic correlation between cerebellar ataxia and psychiatric involvement  to 0.17 (hearing impairment), leaving a considerable amount of variance unexplained. Notably, pseudo‐R2 values for traits characteristic of the MELAS phenotype lie between 0.14  and 0.07 (stroke‐like episodes and seizures). Thus, predicting which patients are likely to develop severe disease using these risk factors is almost impossible.The underlying cause of the extensive clinical heterogeneity associated with m.3243A>G‐related mitochondrial disease remains poorly understood. Given the heteroplasmic nature of this pathogenic variant and the progressive nature of disease, it was not unreasonable to hypothesize that heteroplasmy level and age explain some of this variance, although previous studies have only explained a small proportion.h2 range = 0.40–0.76). This is good evidence for the presence of nuclear factors influencing the clinical phenotype in m.3243A>G‐related disease. Pedigrees containing m.3243A>G carriers with similar phenotypic presentations have been previously described, suggesting the presence of a heritable factor influencing phenotype.Using a pedigree‐based study design, we have shown that additive genetic factors play a much larger role in determining the phenotypic outcome in m.3243A>G carriers than heteroplasmy level, age, and sex. Moderate to large estimates of heritability were observed for psychiatric involvement, cerebellar ataxia, migraine, cognition, and hearing impairment  are strongly correlated and a moderate correlation is seen between hearing and deafness, features of maternally inherited diabetes and deafness (MIDD).r ~ 0.24–0.34) were also intriguing. Upon further investigation, we discovered that of the 22 patients in our cohort who have both encephalopathy and moderate to severe psychiatric disturbance (NMDAS≥3), 19 have evidence of encephalopathy documented before or within the same 12‐month period as the onset of these psychiatric symptoms. Therefore, psychosis may be linked to dysfunctional brain and such a hypothesis is supported by the well‐documented existence of postictal psychosis in epilepsy patients.The correlations between psychiatric disturbance and seizures, encephalopathy, and stroke‐like episodes . Continued pedigree recruitment and long‐term follow‐up is needed to produce more accurate estimates.Although we estimate low heritabilities for stroke‐like episodes and seizures, we cannot exclude the possibility that nuclear factors are involved in these severe phenotypes. A number of our pedigrees were identified due to a diagnosis of MELAS in one family member, but many of these could not be recruited to the study due to the often fatal nature of MELAS, limiting our ability to measure heritability for these traits. Within this context, it is interesting to note that encephalopathy, a sign of substantial brain disease, is heritable when considered as a binary trait . The mechanisms involved in the establishment of the tissue distribution of heteroplasmy levels and mtDNA copy number levels are poorly understood, although nuclear factors may play a role and could represent one mechanism by which nuclear variation modifies phenotype.Second, we have used the NMDAS to define m.3243A>G‐related traits and this should be considered when interpreting our results. For instance, psychiatric disturbance can range from mild  to severe , and is likely to represent a number of different conditions with different aetiologies. Similarly, the NMDAS migrainous question does not distinguish between different types of migrainous headache and impairment of visual acuity could represent a number of different pathologies, including pigmentary retinopathy and optic atrophy. Therefore, the underlying genetic architecture influencing these traits is also likely to be heterogeneous. In addition, the NMDAS scale for cognition primarily assesses processing speed and pre‐morbid IQ, known to decline in patients with mitochondrial disease, and we have not corrected this for confounders such as educational attainment. However, the NMDAS is clinically validated and widely used and is the only currently available tool for this type of analysis. In further support of its use, our heritability estimates fall within population‐based estimates for migraine (28–65%),CFH contributing to age‐related macular degeneration, and rare variants with higher penetrance and could be detected using a family‐based approach.Finally, although the variance component methods implemented in SOLAR estimate the proportion of variance due to additive genetic factors using the degree of relatedness between individuals, heritability estimates may be inflated due to increased shared environment between more closely related individuals. Even with high heritabilities, the nuclear genetic factors may not be easy to identify. Our patient cohort is large and well characterized for such a rare disease, but sample size could be a limitation. Most genetic associations in common disease confer a relatively small effect on phenotype with odds ratios of 1.2–1.5, their detection requiring large sample sizes.This study identifies nuclear variation as a key contributor to the vast clinical heterogeneity seen in m.3243A>G‐related disease, opening up the possibility of identifying these factors and improving our understanding of this complex mitochondrial disease. It also highlights the benefits of pedigree tracing, not only to improve patient care and the rate of diagnosis but also to better understand disease etiology. The molecular mechanisms underlying m.3243A>G‐associated traits are likely to involve a complex interplay between m.3243A>G mutant load, mtDNA copy number, nuclear genetic factors, epigenetics, and environmental exposures. The next challenge is to identify these nuclear risk factors in order to better understand the cellular and tissue‐specific effects in m.3243A>G‐related disease and provide improved estimates of disease prognosis and counseling to patients.We declare no conflict of interests.Conception and design of the study: SJP, JPG, RMcF, RWT, DMT, HJC, IJW; Acquisition and analysis of data: SJP, JPG, YSN, AMS, GSG; Drafting the manuscript: SJP; Critical review of the manuscript: RWT, JPG, YSN, DMT, HJC, IJW, GSG, RMcF.


Ne), i.e. when individuals are closely related. For example, with the sample size of discovery set N = 3000, heritability h2 = 0.5 and population prevalence K = 0.1, AUC value approached to 0.9 and the top percentile of the estimated genetic profile scores had 23 times higher proportion of cases than the general population. This suggests that there is considerable room to increase prediction accuracy by using a design that does not exclude closer relationships.Genomic prediction shows promise for personalised medicine in which diagnosis and treatment are tailored to individuals based on their genetic profiles for complex diseases. We present a theoretical framework to demonstrate that prediction accuracy can be improved by targeting more informative individuals in the data set used to generate the predictors (“discovery sample”) to include those with genetically close relationships with the subjects put forward for risk prediction. Increase of prediction accuracy from closer relationships is achieved under an additive model and does not rely on any family or interaction effects. Using theory, simulations and real data analyses, we show that the predictive accuracy or the area under the receiver operating characteristic curve (AUC) increased exponentially with decreasing effective size ( The genomics era has demonstrated the polygenic nature of complex genetic traits, and genomic prediction shows much promise for personalised medicine in which diagnosis and treatment are tailored to individuals based on the profiles recorded in their genome. This creates the opportunity for ‘stratified medicine’A key feature of risk predictors is that their use does not necessarily require an understanding of the aetiology of diseaseGenomic prediction has recently been tested and shown to be promising for diseases of which genetic variance is largely explained by a number of major genes2356781011121415171820212021Ne) and effective number of chromosome segments (Me) to prediction accuracy, assuming that trained individuals and predicted subjects are from the same homogenous population. We use simulated as well as real data to demonstrate that prediction accuracy can be increased when predicting from more related subjects. We extend this work to a case-control data set, which is a typical design for human diseases, so that the outcomes of this study are applicable to a clinical program for human diseases.In this study, we revisit the theory on genomic prediction accuracy as presented previously2021Me, the effective number of chromosome segments segregating in a population. Intuitively, this makes sense, as fewer independent chromosomal segments require fewer independent parameters to be estimated from the same data. We show that Me depends on effective population size Ne, the number of chromosomes and the length of genomic region . The expected Me Me, the eomosomes . We valifrom eqs  or (11),Me, the eMe from the genomic relationships  was close to the expected Me from eqs Me from tfrom eqs .Me. We theoretically quantified prediction accuracy. Using the theory  and N = 3000 (number of records for the discovery sample) that mimics a typical GWAS. It is noted that 23 chromosomes each with L = 1.3 Morgan  gave similar values (result not shown). Ne was smaller, the correlation between the estimated genetic profile scores and phenotypes for the target samples was increased, approaching the square root of the heritability. With Ne = 10,000, this correlation was only 0.18, but the accuracy became larger rapidly with smaller Ne. For example, the correlation was 0.65 with Ne = 100.Accuracy of the genomic prediction is determined by the genetic variance, the number of phenotypic observations and ory  an anMe. Weory (eqs ), the prK = 0.1 and a proportion of cases in the sample of P = 0.5 was used. With these parameters, we obtained the expected values for AUC . The discovery set had an average of 3394 individuals and the target set had an average of 849 individuals over 100 cross-validation replicates . In 100 cross-validation replicates, the real data was randomly divided into two sets - one for discovery and the other for target, where sampling was either family wise to create a larger plicates . The est080 from  when genh2 = 0.82324h2 = 0.4526h2 = 0.8 and Me = 4,434, the expected accuracy of genomic prediction was 0.551 , and 11.1% of the remaining 90% of phenotypes were chosen to be controls. Therefore, the case-control ratio was 1:1 (i.e. P = 0.5). The two sampling strategies used in cross-validation for the quantitative traits, were also used for the case-control data generating higher and lower variance of relationships between discovery and target sets . The discovery set had an average of 680 individuals and the target set had an average of 170 individuals over 100 cross-validation replicates  and simulating phenotypes with the total variance fully or partly explained by the SNPs in order to support the results from the real data analysis  cohort. When using the GERA dataset that does not have a clear family structure, the prediction accuracy for hypertension phenotypes is significantly higher for 25% of the target sample with the highest variance of pair-wise relationships with the discovery sample . The preMe . These ranalysis  and 7 byanalysis .We also analysed dyslipidemia phenotypes and found a consistent result showing that the prediction accuracy was significantly increased for 25% of the target sample with the highest variance of pair-wise relationships with the discovery sample , and thaIn this study, we have shown, by theory, simulations and analyses of real data that genomic prediction based on a discovery set that includes individuals with close relationships to the predicted subjects leads to higher prediction accuracy, assuming that reference sample and predicted subjects are from the same homogenous population. The accuracy can be predicted from the variation in relationships of the target individual with the individuals in the discovery data set. The variation in relationship can be linked back to the number of effective chromosome segments to be estimated, which in turn is a result of a certain effective population size, i.e. the size of a homogeneous unstructured population where the amount of chromosome segment sharing is similar, leading to the same accuracy of prediction. We showed that there is merit in designing the discovery population such that variation of genetic relationships is maximized.Ne values of more than a few thousand and a resulting Me across the genome in the tens of thousands, even when predictions are just within populations of pure European descent. The effective number of chromosome segments is a key parameter on which prediction accuracy depends2021Me. Note that this is similar to predicting in a population with a smaller Ne, in other words, including closer relatives in the discovery set has the same effect as predicting in a population with a smaller Ne. It was shown that the prediction accuracy (AUC and ORs) increased with a design of a smaller Ne, compared to that with a larger Ne, using theory, simulations and real data analyses. Note that the term ‘effective population size’ is used here not as a property of the population at large, but rather the term refers to the effective information that arises from the relatedness between the discovery set and the subject(s) to be predicted.Current studies for polygenic diseases or disorders have reported that the accuracy of genomic prediction is not useful for actual clinical practice5678Ne, and even when using a moderate sample size in the discovery set  and a heritability of 0.5 , or 176-fold with a higher heritability (h2 = 0.8) (Ne) are a valuable resource for genomic prediction that can be used in stratified medicine. This is an important implication because currently the information on relatives is often discarded in predicting human complex traits and diseases based on genome-wide SNP data.The utility of genomic prediction was illustrated with an example where the top percentile of the estimated genetic profile scores had a substantially higher proportion of cases than a random population sample (23-fold) especially when using a design that includes closer relatives, which effectively leads to a smaller y of 0.5 . This co2 = 0.8) . This deMe and Ne). This may have important implications when only considering population-based samples in genomic risk prediction for human complex traits and diseases where higher relationships are subject to be excluded.Even for a data set of unrelated individuals based on a random population sample, such as the case in the GERA data set, when using the discovery individuals that are more related to the target individuals, the genomic prediction accuracy increased , becauseOne challenge with this approach is that a large number of records or samples needs to be collected within a local community or from extended families. However, increasingly databases are built with phenotypic and genotypic information from closer relatives2931323334In many previous studies, it was observed that family-based estimates are considerably higher than population-based estimates of heritability2325171819In the near future, hundreds of thousands or more records on genotype and phenotype of people will be available for a reference sample to predict genetic risk for a target individual, e.g. all newborn babies could be genotyped and there are improved data bases for recording phenotypes, consisting of one large reference panel that can be generally applied to a nation-wide genomic prediction. Using eqs Practically, the genotypic and phenotypic information of a subject’s relatives  can be used effectively as a part of the unified reference panel that also include a large number of individuals that are not related to the predicted subject to improve the accuracy further as illustrated in Me was slightly reduced . This work is also extended to case-control data analyses so that the outcomes of this study are applicable to a clinical program for human diseases. It is argued that there is considerable room to increase prediction accuracy for polygenic phenotypes so that genomic prediction can be useful for clinical applications in the near future.In this study, we present a theoretical framework, simulation and real data analyses to demonstrate that prediction accuracy can be improved by targeting more informative individuals in a discovery set with closer relationships with the subjects, making prediction more similar to those in populations with small effective size . The accuracy of the genomic prediction depends on the captured genetic variance as a proportion of the total variance, the number of phenotypic observations and the number of independent genomic regions expressed as the effective number of chromosome segments202122h2 is the heritability of the trait, Me is the effective number of chromosome segments, N is the number of phenotypic observations and b is the proportion of genetic variance captured by observed variants (e.g. SNPs) that can be written as202122where M is the number of observed variants. Owing to dense SNP genotypes or sequence data being available, b is often close to unity. Therefore, with dense markers, the genomic prediction accuracy can be simplified aswhere The correlation coefficient between phenotypes and estimated genetic profile scores in a target data set isWhen using case-control studies for human diseases, the correlation coefficient between true and estimated genetic profile scores can be written as4142u is a genetic profile score on the 0, 1 disease scale41K is the population prevalence for the disease, P is the proportion of cases in the total sample N of cases and controls, and z is the density at the threshold on the normal distribution in the liability threshold model. The AUC as a measure of the accuracy of genomic prediction in a target data set for case-control studies is4445where i is the mean liability for cases, i2 is the mean liability for controls, t is the threshold on the normal distribution that truncates the proportion of disease prevalence K and Φ is the cumulative density function of the normal distribution. Another approach to assess the predictive utility of a continuous risk score of diseases, which is common in epidemiology studies, is to stratify individuals into percentiles according to ranked values of the genetic profile scores and estimate the odds ratio of case-control status by contrasting the top percentile with the bottom percentilewhere where the probability of being a case in the top/bottom percentile isanditop and ibottom are the mean genetic profile scores for the top and bottom percentiles, respectively, ttop and tbottom are the thresholds on the normal distribution that truncates the proportion of the top and bottom percentiles  is a key parameter for determining the accuracy of the genomic prediction as fewer segments require fewer independent parameters to be estimated from the same data, i.e. a higher accuracy. Me depends on the effective population size (Ne) and the length of genomic region (L)2021Me based on population parameters but there are some inconsistencies between these2021Me as a function of Ne and L, using the theory of a squared correlation matrix between all SNPsThe effective number of chromosome segments r2 = 1/(1 + 4Ne × c) where Ne is the effective population size and c is the distance in Morgan between each pair of SNPs under a standard neutral model without mutationS are all zero, the effective number of SNPs (or chromosome segments) is less than M. In order to obtain the effective number of SNPs, each SNP can be weighted and the weights can be obtained as46Considering a genomic region spanning 1 Morgan with andw is an M vector of SNP weights derived from the correlation structure among the SNPs and e is a vector of length M with all elements equal to one. In fact, the effective number of chromosome segments is calculated from the sum of the SNP weights aswhere M can be written asThe underlying linear system of order ith and jth SNPs in the matrix S. This linear system can be simplified aswhere where t and w is usually small, it can be approximated asAs the covariance between Me, resulting inFrom This agrees with Goddard 2009)0920 who S because of the SNPs being equally distributed. For example, the values for It is noted that the pattern of the same values is repeated in the matrix r2 based on the distance, and the second part refers to the frequency of SNP pairs with such an r2 value. When scaling the equation by M2, this can be rewritten aswhere the first part of each term refers to the estimated M approaching infinity, the expression can be approximately transformed to a function of x with infinity data points ranging from 0 to 1, which can be written asFor the right hand side with f(x) in the variable x ranging from 0 to 1 is defined by an integration. Therefore the denominator in The sum of the function L rather than 1 Morgan , When accounting for mutationThe equivalence between eqs  and (7),Ne)2 and that of having one parent in common  is 4/Ne − (2/Ne)2. This generates a variance of the relationships among the pairs, which can be analytically approximated as 1/(4Ne). For the previous generations, the variance is 1/(16Ne), 1/(32Ne), 1/(64Ne) and so on. Summing all these variances gives 1/(3Ne), therefore, the covariance of the pairwise relationships between two chromosomes is 1/(3Ne).Equations 20212021Assuming there are multiple chromosomes having an equal genomic length, the chromosome covariance matrix  can be written asMe) can be obtained from eqs Ne)) is the covariance of the pairwise relationships between two chromosomes. As in Meacross the multiple chromosomes can be obtained such that all elements in the covariance matrix should be averaged. Hence, eqs where the diagonal  between true and estimated genetic profile scores (GBLUP) in the target data set.Using the genotype data of the discovery data set, a GRM was constructed and K = 0.1). In the discovery data set, cases were over-sampled such that the ratio of cases and controls was equal (P = 0.5), mimicking a typical case-control design. The total number of samples in the discovery set was N = 3000. We simulated Me independent SNPs, the effects of which were normally distributed, and a residual effect such that the heritability on the liability scale was h2 = 0.5. We used 5 different values for Me = 254, 1188, 4506, 10891 and 21248, reflecting the expected values for Ne = 100, 500, 2000, 5000 and 10000, respectively when using a genomic length of 30 Morgan (30 chromosomes each with 1 Morgan long) and the coalescence formula 1/(2 + 4Ne × c)  . SNP effeory eqs .Publicly available data from the Framingham heart study (phs000007.v26.p10.c1)575858Ne(and Me) values, two kinds of cross-validation schemes were implemented. For a design with larger Ne, 80% of the 628 families were selected as the discovery data set, with the remaining 20% of families used as the target data set. Therefore, the discovery and target sample shared distant common ancestors, hence a larger Ne and Me. In contrast, for a design with smaller Ne, each member in every family was assigned an 80% chance to be a discovery sample and the rest was in the target sample. Therefore, the discovery and target sample shared recent common ancestors, hence a smaller Ne and Me.In order to contrast designs with smaller and larger Me was estimated from Using the real genotype data, the genomic relationships between the discovery and target sample were constructed, and As a second real data set, we used genetic data from the European ancestry participants of the Kaiser Permanente genetic epidemiology research on adult health and aging (GERA) cohort (phs000674.v1.p1)5758N = 36,800) and a target data set , respectively, in 100 cross-validation replicates. We calculated the variance of pair-wise relationships with the individuals in the discovery data set for each individual in the target data set, and identified the top 25% of the target individuals with the highest variance of the relationships. Then, we tested if the prediction accuracy for the top group  was higher than that for the entire target sample, to show if a larger variance, hence smaller Me, resulted in a higher prediction accuracy even when using a population-based sample without a substantial family structure. In addition, we obtained the prediction accuracy from a subset of the sample that excluded higher relationships (>0.025). We first applied the relatedness cut-off to all individuals, and then selected 46,000 individuals that were subsequently divided into the discovery  and target data sets . It is noted that for each target individual, the variance of pair-wise relationships  in order to have the same power and for fair comparisons.Unlike the Framingham data, GERA does not have an explicit family structure, i.e. the proportion of pair-wise relationship more than 0.2 was only 0.0002%. Therefore, the family-wise cross-validation schemes used in the Framingham data could not be used. Instead, we randomly selected 46,000 individuals, and randomly assigned 80% and 20% to a discovery data set (ionships  with theWe used publicly available data. Accession codes are in the following. The Framingham heart study (phs000007.v26.p10.c1). The European ancestry participants of the Kaiser Permanente genetic epidemiology research on adult health and aging (GERA) cohort (phs000674.v1.p1).https://sites.google.com/site/honglee0707/mtg2.Theory, simulation models and GBLUP used in this study have been fully implemented in publicly available software, MTG2. The source code, executive binary file, manual and examples are readily available to use, and can be downloaded from How to cite this article: Lee, S. H. et al. Using information of relatives in genomic prediction to apply effective stratified medicine. Sci. Rep.7, 42091; doi: 10.1038/srep42091 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


A plethora of genetic association analyses have identified several genetic risk loci. Technological and statistical advancements have now led to the identification of not only common genetic variants, but also low-frequency variants, structural variants, and environmental factors, as well as multi-omics variations that affect the phenotypic variance of complex traits in a population, thus referred to as complex trait architecture. The concept of heritability, or the proportion of phenotypic variance due to genetic inheritance, has been studied for several decades, but its application is mainly in addressing the narrow sense heritability (or additive genetic component) from Genome-Wide Association Studies (GWAS). In this commentary, we reflect on our perspective on the complexity of understanding heritability for human traits in comparison to model organisms, highlighting another round of clues beyond GWAS and an alternative approach, investigating these clues comprehensively to help in elucidating the genetic architecture of complex traits. CFH for age-related macular degeneration (odds ratio 1.25–20.28) [ANGPTL4 associated with Coronary Artery Disease (odds ratio 0.32–0.81) [Elucidating the genetic underpinnings of diseases that occur frequently in the population, such as obesity, type 2 diabetes, hypertension, and cancer, are essential research foci among researchers in the human genetics community. The underlying genetic etiologies behind these common human traits are inherently complex due to the effects of multiple genes on the phenotype in comparison to diseases such as cystic fibrosis which follow a Mendelian pattern of inheritance . Remarka5–20.28) ,4, while32–0.81) ,7. GWAS are mainly performed using retrospective study designs from sample populations collected from either academic medical centers/healthcare provider organizations  ,9,10 or Despite the success of association analyses among heritable complex diseases, a meager proportion of phenotypic variance has been explained ,15,16. MHeritability of a disease trait refers to the proportion of variance that can be explained by genetic factors. Estimation of heritability is usually done by observing patterns of inheritance among samples either in family based studies or in population based studies. In family based studies, patterns among a pedigree of family members or among monozygotic and dizygotic twins are estimated. In these studies, environmental factors are assumed to be constant. Whereas in population based studies, patterns of inheritance among the population are observed in non-stationery environmental conditions. In this commentary, we highlight studies aimed towards understanding the heritability of complex traits in the realm of sifting through the stack of clues to uncover the mystery of complex trait genetic architecture. We will also emphasize the validation of association analyses from model organisms where available and challenges in interpreting these validated associations.How much closer do we get to explaining heritability as estimated by family and twin studies by exploiting genetic variations in population based studies?How much of the phenotypic variance is additive ? This is referred to as narrow sense heritability.How much of variance cannot be explained merely by adding all variations in a single model?Genetic association studies are founded on the bedrock of the concept of heritability. Significant challenges for association studies arise in the realm of answering the following fundamental questions:2FAM (family based estimate of heritability) [2SNP (SNP-based estimate of heritability), whereas complex traits such as obesity, type 2 diabetes, and neurological disorders among others are also estimated to be highly heritable  [Clue: The Classic Mystery Game” . In this classic board game, the goal is to identify who committed a crime, with what weapon the crime was committed, and where the crime took place. A similar analogy has been used in the area of genome sequencing to solve the medical mystery of a drug resistant bacterial spread [Answers to these questions vary from one phenotype to another phenotype. For example, a trait such as height is highly heritable (>90% hability) ; offsprictively) ,34. Howectively) ,35,36. Cctively) ,39 whichctively) . That sal spread . This anl spread ; we expaFTO gene to be associated with obesity and studies in mouse models also suggest a lean body type when these genetic variations are present [CFH with AMD progression and pharmacological progress has been made regarding the design of a drug targeting CFH for AMD patients [Over the past decade, studies to correlate common genetic variations with phenotypic effects have become a standard part of genetic association studies. Among the most popular tools/weapons for investigating common variants are GWAS where single nucleotide polymorphisms (SNPs) obtained via genotyping chips and/or imputed data are tested for association with a phenotype of interest. GWAS have identified over 50 K SNP-trait associations ,45,46. G present . Ortholo present . DespiteDrosophila melanogaster and Saccharomyces cerevisiae [, but the role and validation of epistasis for most  complex human diseases are still hidden due to numerous challenges in discovery and replication of epistatic effects. These challenges are out of the scope of this review but have been discussed previously by many [Biological processes are complex, and they arise due to the integration of many genes that interact in a pathway to complete a cellular process. Thus, exploiting the interactive effects of common variants is a natural extension in elucidating the complexity of common diseases. Analyses of the non-linear genetic effects of common variants are referred to as epistasis ,38,56,57revisiae ,60,61,62 by many ,37,63. WIFIH1 with type 2 diabetes [PCSK9 with low density lipoproteins (LDL) levels [PCSK9 in designing lipid-lowering medications has been implicated in mouse model testing [Genetic variants that are less frequent in the population could have potentially large effects on complex diseases, as illustrated in common-disease-rare-variant (CDRV) hypothesis. The CDRV model is not captured by common variant GWAS designs . Analyzidiabetes  and the ) levels ,71. The  testing ,73. LargSingle nucleotide variants (SNVs) as explained in the previous two sections are of great importance in understanding the link between genotype and phenotypes, but large structural variations such as insertions, deletions, translocations, and inversions  also pla2) of complex diseases can be estimated from both genetic and environmental factors. Heterogeneity in association results could be due to the effects of phenotype interactions with exposure or the interaction of genotypes with exposure. Thus, studying the effect of environment is crucial in understanding biological pathways and mechanisms behind complex traits. Studying the effects of environmental exposures on phenotypes is referred to as environment-wide association study (EWAS) [The broad sense heritability (Hy (EWAS) ,81 and ty (EWAS) ,83,84. Ey (EWAS) ,85 have y (EWAS) . We hypoSpecific regions of the genome consist of genetic variations that lead to highly heritable variability of gene expression . These rGene expression data have also been utilized in multi-omics integrative approaches. For example, LaCriox et al.  proposedAnother popular approach to leverage gene expression data to identify how gene expression mediates the effect of genetic variants on diseases and trait is Transcriptome Wide Association Study (TWAS). Gusev et al.  showed tThe genetic underpinning of disease phenotypes can be better understood better if we can pinpoint the agitations in normal cellular functions that lead to the disease process. The approaches as mentioned above to identify how DNA variations predispose individuals to disease are important, but they do not get us very close to identifying the underlying mechanisms affecting the phenotype unless the specific causal variants are tested. Amino acid changes can lead to the disruptions of proteins in biological pathways. Testing for the effect of protein variability on human diseases could have potential implications for identifying drug targets, susceptibility to diseases, and also in developing preventive care measures. The effect of proteins can be tested in many different ways: analyzing the effect of protein–protein interactions, the impact of protein complexes, and the effect of metabolites. The field of study to link proteins and their functions to diseases is referred to as proteomics. Biomarkers identified by proteomics are used in developing diagnostic measures for early detection of various types of cancers such as prostate cancer ,97, as wGermline genetic variations in DNA of an individual do not change significantly during the life course, but the chemical changes in DNA such as methylation and histone modification do change ,103. ManIn the previous section, we introduced the lineup suspects (or “WHO?”) in the still uncovered mystery of complex trait architecture. These suspects are responsible for influencing disease risk. Another important aspect is to identify which weapons (or “HOW?” the independent variables are modeled) can be used for studying the behaviors of suspects discussed above. Weapons here refer to the tools that can be used by researchers in identifying underlying biological mechanisms. Multiple analysis tools exist in the literature to focus on one or more factors that can contribute towards the susceptibility of complex traits. These weapons or modeling tools are listed in A key conclusion from analyzing all of these weapons is that there is likely no one single weapon that can investigate all variations (“omics”) together simultaneously. Meta-dimensional approaches aim to explore not only genomic features but also proteomic and epigenetic features by integrating the effects of all variations in ingenious ways ,166. HowEvery suspect (“variations” as described in previous sections) may alter different tissue types in various biological processes. DNA variations are primarily obtained from blood or serum plasma samples, but it is essential to know which pathway, tissue, or cell type that the risk locus affects. The GTEx database is a powerful resource where the link between gene and the tissue that is affected is investigated . SimilarIn the search for undercover heritability, many suggestions have been made. Genotyping and sequencing technologies rely on the collection of blood samples from study population. Thus, the tissue investigated remains constant in majority of the studies. The common variant common diseases hypothesis (CDCV) suggests that many common variants are the suspects, an additive genetic model is the weapon, and the disease risk manifests in the blood (where the SNPs are measured). Likewise, the rare variant common disease (RVCD) hypothesis suggests that rare variants are the suspects, either burden or distribution of multiple rare variants are the weapons, and blood is the location where the variation is measured. All of these suggestions are tested in one study or the another, but in reality, it seems that we should consider both rare and common variants in multiple possible genetic models for complex diseases. In addition, in elucidating the etiologies of complex traits, the “murder” (or undercover heritability) can take place any location, where location refers to the tissue that is affected by the risk loci. Hence, the secret of this game to identify undercover heritability is to be more open-minded and evaluate each new study with the broad set of data types, tools, and tissues where possible.Family and Twin studies: In family and twin studies, a set of related individuals and their phenotypic traits are analyzed to identify how heritable the phenotypic trait is in families and in sets of identical twins respectively. Family study estimates are usually lower than twin study estimates. For example, family studies for BMI estimate that BMI is 24–81% heritable whereas twin studies estimate BMI to be 47–90% heritable [eritable . The estPopulation based studies: Genomic heritability mainly refers to the proportion of trait variance that can be attributable to genetic factors such as common variants and low frequency or rare variations. Many methods and tools exist in the literature to measure heritability among a set of unrelated individuals. These include mixed model approaches  [K, etc.) ,176, BayK, etc.) , LD baseK, etc.) , and macK, etc.) ,180. AllK, etc.)  determinK, etc.) . Recent K, etc.)  showed hK, etc.)  proposedThe measure of heritability that explains the degree to which a trait is inherited from one generation to another refers to how the heritability values are quantified. The process in which heritability is studied can take place in several different designs as explained below: Arabidopsis thaliana, but its application on big, large-scale human datasets is still to be explored.Methods described above refer to the narrow sense heritability as estimated from GWAS studies which reflects only the additive variance component. With the advent of sequencing technologies, new methods analyzing the effects of rare variants and genetic and gene–environment interactions are also necessary. Heritability estimates for rare variants can be obtained from single variants as well as collapsed regions containing information on the burden of rare variants. To determine unbiased estimates of heritability for gene-based rare variants, Liu et al.  proposedAddressing a phenotype of interest and analyzing an accurate representation of the phenotype is of great importance. Association analyses are often conducted as retrospective studies, for example by utilizing electronic health record datasets , epidemiIn this era of rapid molecular technological advancements, we expect to see future studies not looking at the relevance of one omics dataset at a time, but instead considering the combinatorial effects (including additive and interactive) of all possible omics datasets. The field is moving in the direction of integrative modeling approaches  , and, thClue”. We allow for some variations to classic game of “Clue” for one or team of the suspects, weapons, and locations to be the accurate solutions to the crime (disease risk) in question. Another extension to consider in this game is that, in studying the underlying genetic underpinnings of complex traits, we should consider investigating series of crimes and not a single crime. This refers to the concept of phenotypic heterogeneity where many sub-phenotypes (multiple crimes) could be leading to a complex phenotype in investigation. Our ability to explore the different types of omics variation, using different underlying genetic architectures and modeling methods, will be critical to achieving our maximal understanding of the genomics of common, complex diseases and traits.However, future studies will likely involve the development of methods to integrate all types of omics variations in identifying models affecting disease traits. Methods should also focus on dealing with the sparsity of data because it is highly unlikely to have all of the different data types variations collected on large enough sample sizes. Still, our challenge will be to initiate each new investigation as we would a new round of the board game “


Genome-wide association studies have enabled identification of thousands of loci for hundreds of traits. Yet, for most human traits a substantial part of the estimated heritability is unexplained. This and recent advances in technology to produce high-dimensional data cost-effectively have led to method development beyond standard common variant analysis, including single-phenotype rare variant and multi-phenotype common variant analysis, with the latter increasing power for locus discovery and providing suggestions of pleiotropic effects. However, there are currently no optimal methods and tools for the combined analysis of rare variants and multiple phenotypes.APOA5 and ZNF259, and at ZNF259 provides stronger support for association (PTG+FI = 1.8 × 10−9) than observed in single phenotype rare variant analyses (PTG = 6.5 × 10−8 and PFI = 0.27).We propose a user-friendly software tool MARV for Multi-phenotype Analysis of Rare Variants. The tool is based on a method that collapses rare variants within a genomic region and models the proportion of minor alleles in the rare variants on a linear combination of multiple phenotypes. MARV provides analyses of all phenotype combinations within one run and calculates the Bayesian Information Criterion to facilitate model selection. The running time increases with the size of the genetic data while the number of phenotypes to analyse has little effect both on running time and required memory. We illustrate the use of MARV with analysis of triglycerides (TG), fasting insulin (FI) and waist-to-hip ratio (WHR) in 4,721 individuals from the Northern Finland Birth Cohort 1966. The analysis suggests novel multi-phenotype effects for these metabolic traits at MARV is a computationally efficient, flexible and user-friendly software tool allowing rapid identification of rare variant effects on multiple phenotypes, thus paving the way for novel discoveries and insights into biology of complex traits.The online version of this article (doi:10.1186/s12859-017-1530-2) contains supplementary material, which is available to authorized users. In the past decade, genetic locus discovery for human traits and diseases has been advanced via genome-wide association studies (GWAS). Recent improvements in technology to produce genotype data in a very cost- and time-effective manner and powerful easy-to-use software tools have played a major role in these advances, facilitating fast analysis of constantly increasing amounts of data. Clearly, the next advances in the field of genomics will be based on large-scale sequencing and other high-dimensional omics data. A key challenge for successful utilisation of these data lies, once again, in the availability of powerful methods and user-friendly software tools, thus enabling researchers to make rapid discoveries .Large-scale sequencing efforts, such as the 1000 Genomes Project  or more There has also been increasing interest in addressing analysis of high-dimensional phenotypic and omic data, such as metabolomics, in relation to human genome variation. Multi-phenotype analysis (MPA), i.e. joint analysis of multiple phenotypes, is an example of recent developments in the field. Several methods and related software for single-variant MPA, including Bayesian and frequentist approaches, have recently been published . The MPAWe propose a novel tool MARV for RV MPA, which enables joint analysis of both large-scale high-dimensional genomic and phenotypic data. It extends the burden test for RVs to high-dimensional phenotypic data by applying the MPA approach. Recently, methods designed for MPA of RVs have been proposed –16, but The method on which MARV is based is briefly introduced in Methods, and is extensively described, including power simulations, elsewhere  , corresponsing to a column name in the sample file, and the method to use for the analysis, i.e. whether to analyse the genotype dosages derived by the software from the imputation probabilities (--method expected) or whether to use the thresholded genotypes based on a pre-defined cut-off  Fig. . Additiopheno_a and pheno_b, three different models for the proportion are fitted with the following predictor combinations: 1) pheno_a + pheno_b, 2) pheno_a, 3) pheno_b. MARV calculates the Bayesian Information Criterion (BIC) for each model to help the user in identifying the best fitting phenotype combination.MARV works across the genome by going through the specified gene regions one by one. Based on the gene boundaries and desired rare variant cut-off, it calculates, for each individual, the proportion of minor alleles at rare variants within the region . After tP-value for each model. We note that the P-value is uncorrected for any multiple testing. If the user is interested in the effect estimates and their standard errors for each of the model members, i.e. phenotypes included in the fitted model, a separate.betas file can be requested (--betas)  Figs.  and 2. AN = 12,068 live-born children) [To illustrate the use of MARV across the genome, we have applied it to data from the Northern Finland Birth Cohort 1966 (NFBC1966), which covers over 96% of all births in the two northernmost provinces of Finland in 1966 (hildren) . We inclMotivation for the selection of the traits comes from a common variant single-trait GWAS, which has shown an enrichment of FI associations among SNPs preselected on Metabochip for TG and waist phenotypes . For theDNA was extracted from blood samples drawn after overnight fasting at the 31 year clinical examination. Genotyping was performed with the Illumina HumanCNV370DUO Analysis BeadChip platform at the Broad Institute, USA, with Beadstudio algorithm being used for genotype calling. Detailed genotyping and sample quality control (QC) of the first set of data have been reported before . Additio−6 was adopted based on a Bonferroni correction for 30,000 genes. We analysed all variants irrespective of their annotation across autosomal chromosomes using the following cut-offs: MAF < 5% and imputation quality > 0.4.We analysed the transformed residuals in MARV with the method “threshold” (option -m threshold), i.e. genotypes with probability of 0.95 or higher were considered called, whilst all others were considered missing. The gene list from the University of California Santa Cruz   was usedFI_TG = 0.37, RFI_WHR = 0.18, RTG_WHR = 0.19). The multi-phenotype analysis of the three phenotypes revealed genome-wide significant associations covering two gene regions on chromosome 11: at APOA5 (apolipoprotein A-V) and at ZNF259  genes , while at ZNF259, the model with FI and TG provided the lowest BIC and hence support for the best fit (P = 1.8 × 10−9) , suggesting that at least the association with FI would have been missed in univariate analyses. The effects of TG and FI on the rare allele load were in opposite directions: while the increase in TG levels was associated with a greater proportion of minor alleles within ZNF259, the opposite was true for FI. This was true also for the univariate models  individuals with complete data on eight continuous phenotypes. We analysed a combination of two, four and eight continuous phenotypes and used 1000 Genomes imputed chromosomes 1 and 22 data for the association analyses. All analyses were run and their performance data were collected using Imperial College HPC Cluster. Compute nodes were equipped with Intel(R) Xeon(R) CPU E5-2620 v2 @ 2.10GHz machine.The results are summarised in Table The memory usage of MARV is more related to the size of the genetic data and number of individuals to analyse rather than the number of phenotypes to analyse. In our example, the peak memory usage was almost constant for all chromosome 1 and 22 analyses when the sample size remained the same, independent of the number of phenotypes in the model , ơ2 being a covariance matrix. Weighted linear regression is applied to allow for weighting by the number of successfully genotyped or imputed RVs within the region of interest. The significance testing is based on a likelihood ratio test which compares the weighted likelihoods of the fitted model against a null model where β = 0. The likelihood ratio test statistic has an approximate χ2 distribution with K degrees of freedom.MARV is based on a so-called “reverse regression” approach, i.e. as compared to the standard GWAS in which the phenotype is the outcome and the genotype the predictor, this scenario is reversed in MARV. By using the genetic data as the outcome, we enable assessment of associations with multiple phenotypes simultaneously through the use of simple linear regression. While the “reverse regression” approach has been proposed for single genetic variants with the risk allele count or allele dosage being the outcome , 37, MARThe type I error rate and power of the method have been tested under various scenarios with simulated phenotype and genotype data, and the results from these analyses are described in detail elsewhere .Project name: MARVProject home page:https://github.com/ImperialStatGen/MARVOperating system(s): UNIXProgramming language: C++Other requirements: Standard Linux/UNIX build tools to compile the program.License: BSD 3-Clause LicenseAny restrictions to use by non-academics: None


However, except for values close to the maximum, most of the response surface shows little difference between the methods. We also determined that the conditions resulting in the greatest prediction accuracy for BLUP occurred when genetic architecture consists solely of additive effects, and heritability is equal to one.An epistatic genetic architecture can have a significant impact on prediction accuracies of genomic prediction (GP) methods. Machine learning methods predict traits comprised of epistatic genetic architectures more accurately than statistical methods based on additive mixed linear models. The differences between these types of GP methods suggest a diagnostic for revealing genetic architectures underlying traits of interest. In addition to genetic architecture, the performance of GP methods may be influenced by the sample size of the training population, the number of QTL, and the proportion of phenotypic variability due to genotypic variability (heritability). Possible values for these factors and the number of combinations of the factor levels that influence the performance of GP methods can be large. Thus, efficient methods for identifying combinations of factor levels that produce most accurate GPs is needed. Herein, we employ response surface methods (RSMs) to find the experimental conditions that produce the most accurate GPs. We illustrate RSM with an example of simulated doubled haploid populations and identify the combination of factors that maximize the difference between prediction accuracies of best linear unbiased prediction (BLUP) and support vector machine (SVM) GP methods. The greatest impact on the response is due to the genetic architecture of the population, heritability of the trait, and the sample size. When epistasis is responsible for all of the genotypic variance and heritability is equal to one and the sample size of the training population is large, the advantage of using the SVM method  Using simulation models, these attributes can be varied and their impact on prediction accuracies has been evaluated.Genomic selection (GS) is an approach for improving quantitative traits through the use of genomic prediction (GP) techniques which use information provided by phenotypic values and genotypic information for individuals, lines, varieties, or hybrids in a training set to predict phenotypic values of individuals, lines, varieties, or hybrids with only genotypic information . GS can In a previous publication . Further, it is possible that interactions among the factors influence GP. Our objective herein is to report a strategy for identifying conditions under which the diagnostic could be employed. We determined this by constructing the response surface for accuracies of linear-model and machine learning GP methods as determined by sample size, number of markers, number of QTL, degree of epistasis, and heritability. We chose ridge regression BLUP and support vector machine (SVM) as representatives of linear-model and machine learning GP methods because Before communicating the methods and results for the diagnostic we provide background information on RSMs. Next, we describe how the response surface for GP accuracies was simulated, and last, we illustrate how the steepest ascent RSM can be applied to efficiently determine the specific combination of factors that maximize estimated prediction accuracies of GP.y and a set of design variables  and the code can be found in Supplemental Material, File S1.To illustrate the response surface for two variables, we simulated hypothetical yield data which are influenced by temperature and drought. Average daily temperature is simulated to be between For these simulated data it is clear that the yield is maximized when temperature is between y and the p design variables, f is the true, unknown response function and ϵ is the error term  of a factor, and + stands for a high level (level 2) of a factor.Choice of initial subsets of factor combinations are based on recognition that in a 3 design . The facI, is always C results inI, so we getC for every treatment combination can be determined. To create a The identity column, steepest ascent (or steepest descent). Steepest ascent is a sequential approach for finding the maximum response, where we search for a region of the factor space where the response is improved. The method of steepest ascent has three main steps . The R code for performing the simulations, and the predictions, can be found in File S2. Since our objective is to demonstrate application of steepest ascent to determine the maximum response, we first simulated the entire response surface using a list of five factors (Doubled haploid (DH) populations were simulated using R ( factors  with ope factors . For theinations .n (n is the number of segregating progeny), q is the number of QTL, a is a q-long vector of additive effects, epi is a 2q-long vector of epistatic effects, and ϵ is an n-long vector of random errors. ϵ has a normal distribution with mean of 0 and variance determined by h (proportion of phenotypic variance due to genetic variance) and the genetic variance. a and epi are simulated in such a way that a and I is the identity vector of length specified by the model.The simulated genomes of the DHs had 10 chromosomes, each having the same length. The markers were distributed throughout the genome in such a way that each chromosome had the same number of markers equally spaced along the length of each chromosome. There were no missing genotypic values and no missing phenotypic values. The recombination rate was simulated as a function of the number of the marker loci within a linkage group. The phenotypic values are simulated based on the model described asThe genetic variance is defined as’s model , and epii.e., accuracy of prediction at all 405 factor and factor level combinations, phenotypes were predicted using ridge regression BLUP and SVM methods. BLUP is a parametric statistical procedure for prediction consisting of a random effect term for the marker genotypes (http://www.r-project.org). Predictive accuracies were estimated using cross-validation, where the data were divided into training and testing sets. Let i, and let i. Accuracy of prediction To determine the response, enotypes  and SVM File S1, and the code for simulations and predictions can be found in File S2.The simulation code that produces Table S1).Three response surfaces were generated: one based on prediction accuracies of BLUP, Table S1).Most factor combinations produce similar prediction accuracies , and the distance between the average and either of the initial values .To determine the next set of factor combinations, we define a basis and calculate the step sizes (increments) for each factor. For establishing which treatment combinations need to be evaluated next to find the maximum response, the step size of the input variables needs to be determined. First, an input variable needs to be chosen  which will also influence the step size of the other variables. It is beneficial to choose a variable for which the most information is available, but it is also a common practice to choose the basis with the largest absolute value of the estimated regression coefficient.Because in our example the fitted model has the largest absolute estimated coefficient for epistasis, epistasis is the basis. We choose the step size for epistasis to be 0.25 because previous research indicated that the maximum response  that need to be evaluated next, we need to convert the step sizes in coded units into natural units. The step size in natural units can be calculated as the product of To determine the coordinates of the response surface (ed units . For exated next .Response surfaces).After adjusting for the operability regions of the five factors, the second set of experimental conditions for The estimated regression coefficients for the averaged response Factor levels for the next set of analyses resulted in decreasing factor levels for epistasis and number of markers  for maxiIn 2014, we conjectured that differences between estimated prediction accuracies of linear-model and algorithmic methods could be used as a computational diagnostic for an epistatic genetic architecture. Before designing the experiments for the steepest ascent/descent procedure, it is important to evaluate some initial experiments where we determine which factors might be important and which can be excluded from the model. We also have to define the region in which the factors can affect the response, also known as the operability region.The initial choices of the factors we consider and their range of values can have a large impact on the speed of approaching the optimal response, and whether the optimum is reached. For example, for the factor temperature we can choose the range to be between w is defined asy is the untransformed response and λ is the power parameter. For example, λ can be estimated via maximum likelihood. This rank-preserving transformation is also useful when we need to stabilize the variance of the response, or when the residual variance does not satisfy the normal assumptions. It is possible that the response surface has multiple peaks, and then more than one combination of the design variables satisfies the condition for having the optimal response. It is also likely that the range of starting values do not include the global peaks, but in the procedure of steepest descent (or ascent) we would arrive in the required range.Another design aspect to consider is the choice of the metric for the response. Especially when the range of the response is large, it is useful to transform the response. One of the most commonly used transformations is the Box–Cox power transformation . The trae.g., ecosystem impacts on growth and development of individuals , population structure, relationships between training and validation data sets, number of genetic markers, heritability, and number of individuals  could affect the predictive ability of GP methods. We were primarily interested in the potential of the computational diagnostic  in the population structure, the operability region need only include sufficient numbers to assure some redundancy among genotypic information. Indeed, we found that if the LD between markers and QTL is complete, then prediction accuracies are not improved with any additional markers. This outcome will likely not change with more complex population structures for finite numbers of segregating QTL.F2 progeny from a single cross of inbred lines in a crop such as maize. While 2000 DH progeny are possible, producing such numbers is unlikely without significant resource allocations. Thus, from a practical perspective, it is highly unlikely that the diagnostic can be employed routinely because the maximum values for the diagnostic occurred with large numbers of progeny in which the genetic architecture is comprised entirely of epistatic variance and broad sense heritability is unity. Also, the large difference in accuracy between SVM and BLUP occurs at the extreme of pure epistatic variance, which is a genetic architecture that has not been described for any trait. Thus, the reader should be aware that the GP models can have a similar accuracy in cases when the genetic architecture consists of a high proportion of epistatic variance, and only comparing prediction accuracies might not be a useful method to infer genetic architecture.The operability region for number of individuals was based on a possible number of DH progeny with application of DH technologies to F2 and backcross populations where the linkage groups had different lengths. This report is based on DH lines with linkage groups that consist of the same numbers of marker loci per linkage group and the same recombination among adjacent marker loci within linkage groups. Consequently, the LD among the simulated QTL was not the same in the two studies. The inconsistencies between the two reports are small, but the results suggest that LD among QTL, population structures, and genomic architecture also will influence prediction accuracies. In particular, it is likely that because of LD among QTL in our first set of simulations we unintentionally produced a second source of nonlinear interactions, i.e., pseudooverdominance.Lastly, the reader will note that prediction accuracy results are not exactly the same as results previously reported by www.g3journal.org/lookup/suppl/doi:10.1534/g3.117.044453/-/DC1.Supplemental material is available online at Click here for additional data file.Click here for additional data file.Click here for additional data file.