In utero interactions between incompatible maternal and fetal genotypes are a potential mechanism for the onset or progression of pregnancy related diseases such as pre-eclampsia (PE). However, the optimal analytical approach and study design for evaluating incompatible maternal/offspring genotype combinations is unclear.Using simulation, we estimated the type I error and power of incompatible maternal/offspring genotype models for two analytical approaches: logistic regression used with case-control mother/offspring pairs and the log-linear regression used with case-parent triads. We evaluated a real dataset consisting of maternal/offspring pairs with and without PE for incompatibility effects using the optimal analysis based on the results of the simulation study.LTA), von Willebrand factor (VWF), and alpha 2 chain of type IV collagen (COL4A2) with possible incompatibility effects.We identified a single coding scheme for the incompatibility effect that was equally or more powerful than all of the alternative analysis models evaluated, regardless of the true underlying model for the incompatibility effect. In addition, the log-linear regression was more powerful than the logistic regression when the heritability was low, and more robust to adjustment for maternal or fetal effects. For the PE data, this analysis revealed three genes, lymphotoxin alpha (The incompatibility model should be evaluated for complications of pregnancy, such as PE, where the genotypes of two individuals may contribute to the presence of disease. Typically, many diseases or complications arising during pregnancy, such as pre-eclampsia (PE), have been considered primarily maternal disorders. For example, in the context of genetic studies, it is frequently the maternal genotype that is considered in evaluating increased risk for disease (summarized in ). HoweveIn this paper we will focus on the genetic 'incompatibility' between maternal and fetal alleles, i.e., where the maternal and fetal genotypes do not exactly match. One possible explanation for the underlying biological mechanism of disease in this scenario is that the genetic differences between the mother and fetus may induce an immunological response by the mother. One of the best known examples of fetal contributions to risk of pregnancy related complications is a genetic incompatibility between mother and fetus at the RhD locus. RhD hemolytic disease of the newborn (HDN) occurs when the mother is Rh negative (dd) and does not possess the allele for the antigen present in the offspring (Dd), and has been immunized by transplacental passage of RhD-positive red cells during a previous pregnancy . This paPE, a leading cause of maternal and perinatal mortality and morbidity worldwide, affects 3–7% of all pregnancies in developed countries -12, althSome investigators have proposed that PE may be due to an abnormal maternal immune response to a semi-allogenic fetus ,20. HencIn evaluating the incompatibility model, different underlying mechanisms for the genetic incompatibility can be proposed. For example, the incompatibility effect is not necessarily asymmetric, as in the case of the RhD locus, and disease could occur anytime the fetus possesses an allele that is not present in the mother, regardless of which allele it is. Thus, it remains to be investigated what is the best approach for evaluating the incompatibility model when the true underlying genetic model is unknown.A second consideration is the study design and analytical approach used to evaluate association between incompatible maternal/offspring genotypes and disease risk. We consider two alternatives. The first approach was selected to reflect the study design for the PE study that we evaluate here, where case and control mother/offspring pairs were recruited. For this study design, the case and control pairs can be compared using logistic regression. Alternatively, we consider a second approach using log-linear regression , which compares the distribution of genotypes of case parent-offspring trios to their expected distribution. This approach potentially has several advantages in that the paternal contribution to disease can be more fully understood since the paternal genotype is known, and the trio design offers the opportunity to control for population stratification using family-based approaches . We propThe log-linear regression model for studying incompatibility effects was first proposed by Sinsheimer and coworkers , called To clarify the relative advantages of these two analytical approaches, we conducted a simulation study to evaluate the power and type I error of several defined incompatibility models and their performance using the logistic regression and log-linear regression model unadjusted and adjusted for maternal and fetal effects. The following three a priori hypotheses were tested: i) A single most powerful incompatibility model with good statistical properties  exists regardless of the true underlying model; ii) The logistic regression has comparable power to the log-linear regression when maternal and fetal effects are absent and unadjusted for in the model; and iii) The log-linear regression performs better than the logistic regression when maternal and fetal effects are present and adjusted for. The best analysis model was used to identify maternal/fetal genotype incompatibilities in the PE dataset using the logistic regression. In this study, we show that a single analytical model exists with the best performance under conditions similar to PE when the true underlying generating model is unknown. In addition, the performance of the logistic regression compared to the log-linear regression is dependent on heritability and on the adjustment of the presence of maternal and fetal effects. Although we were limited to performing the logistic regression in the PE dataset, overall power of the log-linear regression was only 10% greater than the logistic regression.A genotype incompatibility arises when the maternal and fetal genotypes are different Table . SeveralDatasets were generated for each incompatibility model Table . One hunf, of 0.1 to 0.4 in increments of 0.1. Mendelian inheritance was used to generate the offspring genotype given the parental genotypes. Overall, 100,000 triads were generated for each allele frequency. Next, we simulated the phenotypic value given the genotypes of the trio. In order to adhere to the notion that PE is a disease of pregnancy, the phenotype is not assigned to a particular individual but rather to the mother/offspring pair.The first step in the simulation was to generate genotypes for the parent-offspring trio. Assuming Hardy-Weinberg equilibrium, genotypes of mothers and fathers were generated under allele frequencies for the high-risk allele, i denote the underlying quantitative liability phenotype of the ith family unit in a sample of N families, and gm, goff, the genotypes of the mother and offspring at the candidate locus, respectively. μ denotes the overall mean of the liability while the polygenic and environmental component Eo, is a random value from a normal distribution with a specified mean μe and variance σ2e. Xi is an indicator variable that represents the genotype combination of the mother/offspring pair, and is 0 if the incompatibility does not exist and is 1 if it does exist. β is the incompatibility parameter that represents the degree of deviation from the overall mean due to the incompatibility effect. The following equation was used to compute the phenotypic value for each mother/offspring pair given known model parameters:Let P2e) and incompatibility effect (β) were selected based on these values in addition to the proportion of families with an incompatibility. A random value for the environmental variance (σ2e) was generated, and the incompatibility effect was computed using the following equations for the locus-specific heritability (h2) and total phenotypic variance (σ2T):Without loss of generality, the overall mean and environmental mean were restricted to 0. To ensure that the heritability and the prevalence remained at the pre-specified levels, the environmental variance  = 1], was set to approximately 50%. This constraint was added to generate a more complex genetic model in which other causes of disease may exist  aside from the incompatibility. In certain models and under certain allele frequencies, it was not possible to satisfy this constraint given the prevalence of 5%. In such cases the proportion of mother/offspring pairs that exceeded T given an incompatibility was relaxed to fit a prevalence of 5%.To generate cases, a threshold (T) was determined from the model parameters such that 5% of the phenotypic values exceeded the threshold. An additional constraint was that the proportion of mother/offspring pairs that exceeded the threshold (T) given an incompatibility  vs. control [0]) for each SNP genotype individually (mother and offspring). An additive genetic model  was used to code each SNP where the homozygote corresponding to the allele with the minor allele frequency (MAF) was coded as 2.Given that a large number of tests were conducted, correcting for multiple testing was necessary. The false discovery rate (FDR) was used to correct for multiple testing since this procedure is less conservative than the Bonferroni correction, and can account for the inter-marker correlation that may be present among markers genotyped within the same candidate gene or region .All of the analysis models were slightly conservative, since the type I error rates were less than the expected value of 0.05 in most cases. In addition, all of the models had comparable type I error rates in both the logistic and log-linear regression models with the exception of model 6, where the type I error rate was 50% less compared to model 5 Figure . Thus, tAnalysis model 5 Table  was equaAs expected, the power to detect a statistically significant incompatibility was the highest when the true underlying generating model was identical to the analysis model Figure . This reThe trend in the type I error rate as a function of allele frequency differed between the logistic and log-linear regression Figure . The typThe relative power of the logistic regression and the log-linear regression depended on the heritability. For a heritability of 0.15 and 0.25, the power of the log-linear regression was greater than the power of the logistic regression when averaged over all of the analysis models by 25% and 15%, respectively. In contrast, for a heritability of 0.35, the power of the log-linear regression was less than the power of the logistic regression by 9% Figure . OverallAdjusting for maternal and fetal effects in addition to the incompatibility effect, by adding these effects into the analysis model, generally decreased power compared to adjusting for the incompatibility effect alone Figure . The decTo evaluate the PE data, we were limited to the logistic regression approach, since fathers were not recruited in this study. However, based on the results of the simulation study, we selected analysis model 5 to test the incompatibility effect, and we did not adjust for maternal and fetal effects. None of the SNPs in this study had a statistically significant incompatibility effect after correcting for multiple testing using the FDR approach and hence only nominal p-values are presented. However, this analysis revealed several interesting candidate SNPs with nominal p-values < 0.01 for the incompatibility effect Table .LTA) gene showed the strongest evidence for association with PE in the incompatibility model (p = 0.0007). The marginal maternal and fetal effects were not statistically significant , where cases have a lower frequency of incompatibility compared to controls  gene showed evidence for association with PE in the incompatibility model (Table Two SNPs in the von Willebrand Factor (el Table . None ofel Table . In partCOL4A2) also had two SNPs with suggestive evidence of association with PE for the incompatibility model including rs2296849 (p = 0.0046) and rs421177 (p = 0.0054). None of the remaining 7 SNPs evaluated in this gene showed evidence of association with PE for the incompatibility model, except COL4A2_633876793 (p = 0.0474). These two SNPs are both intronic polymorphisms in introns 37 and 38, respectively, of this gene. The two SNPs have moderate levels of LD between them, with r2 of 0.62, and are located within 6 kb of each other. Both SNPs were more likely to have different (incompatible) genotypes for the mother/offspring pairs with PE compared to mother/offspring pairs without PE  the type of sample that must be recruited, and 2) the ability to test for maternal and fetal effects in addition to the incompatibility effects. In theory, estimating incompatibility effects can be biased when maternal and fetal effects are present, but are not accounted for. Likewise, when an incompatibility is present and not modeled explicitly, offspring and maternal effects, or both, can be biased . Our obsCOL4A2 is an extracellular matrix gene which encodes one of the six subunits of type IV collagen, the major structural component of basement membranes [COL4A2 is a plausible candidate, since defects in the extracellular matrix due to polymorphisms in one of the subunits of type IV collagen, may be involved in the failure of transformation of uterine arteries that occurs in PE as well as other obstetrical complications, which some investigators attribute to abnormal trophoblast migration. In addition, there is some evidence to suggest that collagen is increased in PE, including a two-fold increase in expression level of collagen in the PE placenta [Our analysis for incompatibility effects in the PE data set revealed several interesting candidate genes. embranes , and mayembranes . COL4A2 placenta , and decplacenta . Thus, pVWF, a large glycoprotein encoded by a gene on chromosome 12, is synthesized by vascular endothelial cells and circulates in human plasma. A possible mechanism of action for VWF is that abnormalities in VWF in fetal endothelial cells may interact with circulating maternal VWF during fetal trophoblast invasion of maternal spiral arteries and hence lead to the progression of PE. Although it is unclear how this interaction would lead to disease, this proposed mechanism is supported by the fact that altered patterns of VWF multimers are found to occur frequently in patients with thrombotic thrombocytopenic purpura in the acute and chronic stages, which shares some clinical and laboratory findings with PE including thrombocytopenia. In addition, although the sample sizes were small, Pottecher and coworkers  showed sLTA was the most significant gene found to be associated with PE in the incompatibility model. LTA, also known as tumor necrosis factor-β (TNFβ), is a pro-inflammatory cytokine with a broad spectrum of immunological activities [LTA gene lies in close proximity to TNF, the gene for tumor necrosis factor α [α is significantly increased in PE patients. Although LTA has not been found to be associated with PE, it is possible that polymorphisms in the maternal and fetal LTA gene may decrease the circulating levels of LTA leading to a reduction in the inflammatory response, and a reduced risk for PE. This association offers a unique scenario where incompatible genotypes benefit the mother and fetus rather than causing harm.tivities . Circulativities -38. In afactor α -41. StudThe findings of this study highlight one important concept regarding the incompatibility model, which is that a genetic incompatibility between maternal and fetal genotypes can be beneficial. It is therefore somewhat unfortunate that the term "incompatibility" is used in this context since the negative connotation of the word implies that disease occurs only when the maternal and fetal genotypes are different. However, it may, in fact, be beneficial for the maternal and fetal genotypes to be different, resulting in positive selection, i.e., an excess of heterozygosity. Preference for different genotypes may be a mechanism to promote outcrossing due to the effects of dominance, since mating with close relatives will increase the chance of homozygous recessive genotype combinations. Alternatively, a preference for different genotypes may be an artifact of overdominance, where it is beneficial for the offspring to be heterozygous. Heterozygosity may be advantageous for several reasons such as increased variation in gene products resulting in improved chances to bind foreign proteins, or an increased chance of possessing rare alleles that infectious organisms have not yet developed resistance to.One example of a locus where it is thought to be beneficial to be heterozygous is the Major Histocompatibility (MHC) locus. The increased heterozygosity at this locus may be a result of disassortative mating, where mates are preferentially selected to have different MHC alleles. This selection process is hypothesized to occur through the olfactory system, where individuals prefer the odor of people with different MHC alleles -44. HoweGeneralization of the study findings outside the scope of this work should be done with caution. We simulated genetic models based upon estimated model parameters for PE. Previous studies evaluating the heritability of the variance in liability of PE found that 35% of the variance is attributable to maternal effects, 20% to fetal effects, and 13% to the couple effect . TherefoThere are several limitations of the study. We were unable to simulate incompatibility effects independent of maternal or fetal effects and hence the power to detect an incompatibility effect was significantly reduced in the adjusted models compared to the unadjusted models. However the log-linear models were more robust to this adjustment. In addition, we only looked at minor allele frequencies ranging from 0.1 to 0.4. Model 5 may have performed equally well to the true analysis models due to similar frequencies of the incompatible genotype combinations to the true analysis model. This is a characteristic of model 5 as it incorporates all possible incompatible genotype combinations by the other models, and hence under similar allele frequencies, the proportions may be similar. Specifically model 5 may have had the best performance compared to model 6 since the number of incompatible genotype combinations was greater in model 5 compared to model 6 and the genotype combinations were dominated by AA, Aa genotype combinations. This may also explain the relative performance of models 1 and 4 compared to model 5; however, it seems unrealistic to simulate conditions where the MAF is > 0.4 which is very rare in populations . NeverthCOL4A2, VWF, and LTA which may have a significant functional role in the progression of PE under the incompatibility model, although none of these findings were statistically significant after correcting for multiple testing using the FDR. Little is known about the biological mechanism though which maternal and fetal incompatibility of these genes may have an adverse or protective effect on the mother. Future studies both epidemiological and molecular are needed to confirm the biological mechanism of the incompatibility effect among these genes. However, these findings will be helpful in the design and interpretation of future studies of incompatibility effects, particularly studies of PE.In summary, we have identified a single incompatibility model that has optimal properties in terms of power and type I error compared to the alternative models under the specific conditions simulated. Our results also indicate that the relative performance of the logistic regression and log-linear regression approaches are similar, and that issues of study design including the ability to recruit fathers and the presence of marginal maternal and fetal effects are the most important considerations. We also identified three genes, The authors declare that they have no competing interests.KABG and NP contributed to the conception and design of the methodological study, carried out the statistical analysis, participated in the interpretation of data, and drafted the manuscript. GT and HK designed and coordinated the molecular genetic studies for the PE dataset, contributed to the interpretation of data, and critically reviewed the manuscript. RR conceived of and directed the PE study, contributed to the data interpretation, and critically reviewed the manuscript. JKN and RG participated in patient recruitment and validated the clinical information for the PE study. All authors read and approved the final manuscript.EquationsFor the following equations, the variables are defined in Table The pre-publication history for this paper can be accessed here:


Dysfunction in the endolysosome, a late endosomal to lysosomal degradative intracellular compartment, is an early hallmark of some neurodegenerative diseases, in particular Alzheimer's disease. However, the subtle morphological changes in compartments of affected neurons are difficult to quantify quickly and reliably, making this phenotype inaccessible as either an early diagnostic marker, or as a read-out for drug screening.blue cheese (bchs) mutant was taken as a genetic neurodegenerative model for direct in situ visualization and quantification of endolysosomal compartments in affected neurons. Endolysosomal compartments were first detected automatically from 2-D image sections using a combination of point-wise multi-scale correlation and normalized correlation operations. This detection algorithm performed well at recognizing fluorescent endolysosomes, unlike conventional convolution methods, which are confounded by variable intensity levels and background noise. Morphological feature differences between endolysosomes from wild type vs. degenerative neurons were then quantified by multivariate profiling and support vector machine (SVM) classification based on compartment density, size and contrast distribution. Finally, we ranked these distributions according to their profiling accuracy, based on the backward elimination method.We present a method for automatic detection of fluorescently labeled endolysosomes in degenerative neurons in situ. The Drosophila bchs1 or bchs58. In contrast, the density measurement differentiates all three bchs phenotypes (loss of function as well as overexpression) from the wild type.This analysis revealed a statistically significant difference between the neurodegenerative phenotype and the wild type up to a 99.9% confidence interval. Differences between the wild type and phenotypes resulting from overexpression of the Bchs protein are detectable by contrast variations, whereas both size and contrast variations distinguish the wild type from either of the loss of function alleles Our model demonstrates that neurodegeneration-associated endolysosomal defects can be detected, analyzed, and classified rapidly and accurately as a diagnostic imaging-based screening tool. Major efforts are underway to identify drug candidates for the treatment of Alzheimer's disease. Most of these are aimed at interference with the production or activity of the amyloid peptide Aβ, since this is the most likely causative agent of the disease . HoweverThe endolysosome refers to a vesicular degradative organelle spanning the late endosomal and lysosomal compartments . Endolysblue cheese (bchs), a putative lysosomal transport protein in Drosophila [blue cheese mutant larvae. This system was chosen for examining neurodegenerative endolysosomal changes because of several advantages over other neurodegeneration models. First, the neurodegenerative phenotype in blue cheese comes about due to a defect in a presumptive lysosomal processing pathway [Neuronal loss- and gain-of-function in osophila ,11 lead osophila  and disi pathway ,12,13. Sin situ profiling of neuronal endolysosomes as a potential platform for morphogenetic screening. In our method, the endolysosomes are visualized by transgenic expression in isolated motorneurons of a green fluorescent protein (GFP)-fusion of an endolysosomal protein, Spinster[Previously, changes in endolysosomal morphology and/or number have been noted under various neurodegenerative conditions ,9. Howev Spinster. This ma Spinster and that Spinster.The analysis presented here first uses a novel image filtering method to detect fluorescently labeled endolysosomal compartments, which appear as spots, in the NMJs of larval motorneurons. The detection method relies in its ability to segment images of neurons robustly and accurately in situ to yield endolysosomal compartments, or spots, as regions of interest (ROIs) that can be analyzed objectively. Standard segmentation methods based on edge detection  and inteThe second step of our method uses a support vector machine (SVM) classifier  with a rin situ profiling of morphological features of endolysosomal compartments is possible, and could therefore serve as a potential platform for morphogenetic screening of neurodegenerative diseases either in animal or cell culture models. The method consists of imaging a large number of motorneuronal endolysosomal compartments of diverse contrast levels, whose features are not visually obvious, and are not accessible by conventional measurement methods. The SVM classifier evaluates changes in contrast, size and density features of these compartments in a rapid, unbiased manner, and on a far larger quantity of image data than would be possible manually, e.g. by analysis of electron micrographs, or fluorescence images.The novelty of this study lies in the application of standard machine learning and statistical analytical methods to an in-vivo neurodegenerative model. It has previously been noted that the endolysosomal compartments of degenerating neurons are affected not only functionally, but also in terms of appearance, e.g. size, shape, and density ,28. Our To our knowledge, this is the first reported image-based multivariate analysis of a neurodegeneration-related feature at the cell biological level. The strength of the approach is that it can identify and quantitatively describe a diagnostic aspect of the neurodegenerative phenotype, namely alterations in key endolysosomal features. Because of its speed, robustness, and accuracy, the proposed method has potential applications in screening the palliative effects of anti-neurodegenerative drugs on an in vivo model.blue cheese gene [blue cheese EP2299 (Enhancer-Promoter line 2299) [even skipped driver line  , were anne 2299) ) of eachne 2299) , with anribed in ). Genotyi. ii. iii. iv. bchs1 iii. bchs58 and iv. EP+ respectively. Df(2L)c17 and bchs1 are genetic deletions and strong loss of function alleles of blue cheese [bchs58 carries a stop mutation in the blue cheese coding region, but does not produce detectable protein (own observations and [The aforementioned genotypes will henceforth be referred to as i. Wild type ii. e cheese  while bcions and ). Larvalions and . Neuromux- and y- axes which provided sufficient resolution for imaging the endolysosomal compartments.The images were acquired with a 60×/1.42NA lens at 490 nm excitation/528 nm emission wavelengths using the Deltavision Fluorescence deconvolution imaging system  equipped with a motorized Olympus IX70 inverted wide-field fluorescence microscope, a 12 bit Coolsnap HQ CCD camera and a 100 W mercury lamp. A stack of 512 × 1024 pixel optical sections spaced at 0.3 μm was acquired for every NMJ in the larvae samples with no binning. The sampling pixel size was 0.1 μm × 0.1 μm along the blue cheese allele) since we determined that certain measurements were sensitive to variations in exposure conditions (not shown). However, it was not possible to use a common acquisition setting for all three studies due to the widely varying fluorescence of the spots between the different groups. The acquisition setting was selected such that the dynamic range of the CCD chip was not exceeded, and an optimal contrast of the endolysosomal compartments with respect to the background was achieved. Images were deconvolved using the constrained iterative algorithm [Three morphological parameters were used to characterize the differences between endolysosomal compartments in wild type and in each of the different mutant genotypes as shown in Table lgorithm  providedEndolysosomal compartments within NMJs were imaged in 2-D optical sections and their contrast, size and density were quantified via the following three sequential steps: (i) enhancement of NMJ spots, (ii) detection and labelling of NMJ spots, and (iii) extraction of spot size, density and contrast.The normalized cross-correlation (NCC) as a measure of the similarity between the local spot intensity profile and a predefined Laplacian of Gaussian (LoG) filter was calculated as follows:bx,y and g7 × 7 are column-wise vector representations of the local image neighbourhood centred at pixel coordinates  and the 7 × 7 LoG spot filter respectively whereas bx, y and g7 × 7 respectively.where x, y) to a total of J "spot-like" LoG filtersThe point-wise multi-scale correlation (MSC) is given by eqn. (2). The MSC measure is based on the degree of correlation of a localized region at  = ⟨bx,y, gi+1 × 2i+ 12⟩, 2i+1 denotes the filter dimension where i = 1, 2, ..., J and J = 5 in this case.where T1 i.e. |NCC| > T1.Combined NCC and MSC detection was done by first detecting regions whose normalized cross correlation magnitude exceeded a predefined threshold T2 i.e. |MSC| > T2. A sufficiently low threshold value was determined for T2, via a trial and error approach on the available set of image sections, such that the spot regions were effectively distinguished from noise. Appropriate T1 and T2 levels (T1 = 0.4 and T2 = 23) were chosen from a range of threshold T1 and T2 values that were empirically tested for their classification accuracy  ranging from 0.01 μm2 to 0.1 μm2 (1–10 pixels). Contrast information was also encoded as a histogram distribution with 14 categories  uniformly divided within the 0–255 gray-scale where the contrast measurement of a spot is defined as the difference between the peak intensity of the spot and the background intensity surrounding it. The background intensity follows the minimum pixel value within a 15 × 15 window centered around the peak intensity location. A 15 × 15 window size was chosen since it is sufficiently large to contain any given spot.For feature measurements, size information was encoded as a histogram distribution with 10 size categories  typically resembled the average distance between adjacent spots for the wild type case. We formally define spot density D asThe feature "spot density" was obtained by determining the centroid of each spot, corresponding to the location of its peak intensity. Subsequently a circular area with a fixed radius N is the number of spots, r is the fixed radius and A is the total area occupied by the spots. D is normalized such that it lies between 0 and 1. Smaller areas of overlap give a lower spot density. The accuracy of the density measure is adversely affected if there are too few spots or if the spot distribution in an NMJ section is nonuniform. To ensure its robustness, we compute the density measure for cases where the spot population is sufficiently large (N ≥ 50). We observe that the spot distribution in the NMJs is generally uniform. However, in any given NMJ section, there may be two or more clusters of spots that are disjoint due to the intervening regions being out of focus at that focal section. In such cases, the density measure is based on the largest cluster of spots in that section.where φ) and kernel width of the radial function (σ) as input arguments, we selected φ' and σ' which gave the highest classification accuracy from the following range of input values φ = {0.1, 1, 10, 100, 1000} and 0.2 ≤ σ ≤ 40 where the step size Δσ = 0.2. Once implemented, R-SVM outputs a decision value di for every input feature vector xi where the sign of di is used to predict the class to which xi belongs and the magnitude is a measure of the distance of xi from the decision boundary.Acquired feature data was analyzed using a radial basis function Support Vector Machine (R-SVM) classifier . A leavet2 value which is expressed as followsThe discriminating power of individual features was quantified based on the Student's t-test  value whm1 and m2 are the mean values of a given feature in the wild type and mutant class respectively, σ1 and σ2 are the corresponding standard deviation values and n1 and n2 are the sample sizes of the two classes.where The Hotelling t-test  in eqn. m1 and m2 denote the mean distribution of feature vectors in the two classes whereas S = S1/n1 + S2/n2 given that S1 and S2 are the corresponding covariance matrices.The notations The differences between the wild type and mutant mean distribution profiles for contrast and size were plotted in histograms. The scalar value for spot density was plotted as a probability density function with a Gaussian distribution characterized by the mean and standard deviation in spot density values from a given genotype.ω12, ω13 and ω14 which are projection vectors that optimally separate wild type vs. bchs1, wild type vs. bchs58 and wild type vs. EP+ respectively. They are formally defined as follows:Fisher's linear discriminant  is applibchs was chosen as a model system in which to analyze changes in the morphology of endolysosomal compartments in degenerating neurons in situ. Neuronal degeneration in bchs mutant animals has been well-described and is believed to affect endolysosomal function and trafficking [bchs or overexpressing Bchs in motorneurons and that also expressed the endolysosomal marker spinster-GFP in motorneurons known to be affected by the neurodegenerative phenotype . Third instar larvae of the relevant genetic backgrounds were filleted and neuromuscular termini at the body wall were imaged with high-resolution wide-field microscopy   Differences in endolysosomal compartment features, including spot contrast, size, and density of spots, were quantified and compared between the wild type and the three mutant classes using a radial basis support vector machine (R-SVM).B) 25 contrast, size and spot density features were ranked in terms of their discriminating abilities using the backward elimination scheme [C) The differences in features between the wild type and the mutants were visualized from both univariate feature analysis and Fisher's linear discriminant ,27.bchs mutants , and potential artefacts or noise were eliminated by ensuring that the detected regions also had corresponding point-wise MSC measures whose magnitudes exceeded another predefined threshold T2 .In order to overcome the problem of differing intensities and contrast in fluorescently labelled endolysosomal compartments, which make detection by standard convolution algorithms difficult , we deviT1 and T2 ranging from 0.3–0.7 and 15–30 respectively. A relatively small standard deviation of ~2% is observed for the classification accuracy.Fig. After detection of spots by NCC and MSC, size, contrast and spot density feature measurements were extracted from the detected spots of a given NMJ image section . A stack of images was captured for every NMJ in every class, but the number of images in each stack varied depending on sample thickness. Each 2-D image section of an NMJ constitutes a data point that is represented by a feature vector with a total of 25 entries from which contrast, size and spot density measurements have 14, 10 and 1 entry respectively. Table bchs1, wild type vs. bchs58 and wild type vs. EP+.A radial basis function Support Vector Machine (R-SVM) classifier  was devibchs1 vs. WT or bchs58 vs. WT), and then challenged to classify images of unknown origin. Optimal classification accuracies of 78.1%, 72.2% and 82.0% were obtained for wild type vs. bchs1, bchs58 and EP+, respectively. Their corresponding SVM parameters representing the standard deviation of the Gaussian kernel σ and the penalty factor φ were as follows: ,  and  respectively for the three genotypes. Table bchs1, bchs58 and EP+ mutant class respectively.The R-SVM was trained with data sets for each parameter from pairs of genotypes  were calculated. The mean decision values for all the individual decision values obtained by the SVM for each NMJ section of a particular category of mutant vs. wild type were averaged and plotted with standard errors Fig. . The difUsing univariate and multivariate analyses, we assessed the value of various features to the SVM in determining its ability to predict genotypic origin . The purpose of feature ranking is to determine which features have the greatest discriminating power, and can thus be used most efficiently to assign a class (neurodegenerative vs. WT) to a given sample. This analysis also enables us to visualize the differences within each wild type vs. mutant pair.Extraction of size, density, and contrast). The Hotelling t-test [T2 statistic was applied in a sequential backward elimination scheme [C1,...,14), size  and density (D) features based on their discriminating power. We start with a complete set of features and sequentially remove those features that reduce the T2 value the least. Thus the feature of least importance is removed first and the most important is removed last. In the event that two or more features have the same T2 value, we remove the feature that corresponds to the lowest univariate T2. The use of T2 statistics is desirable due to its strictly monotonic function where its value for a subset of features is always less than or equal to that of the full set. Fig. T2 value where, at every stage, the least important feature is sequentially removed for each wild type vs. mutant pair.The different feature categories, including 10 different size bins, 14 contrast bins, and the single density measurement were taken as individual features  with a Gaussian distribution characterized by their respective mean and standard deviation in spot density. The spot density of the wild type endolysosomes is, in general, higher than those of any of the mutant classes Fig. . This isω12, ω13 and ω14 which optimally separate wild type vs. bchs1, wild type vs. bchs58 and wild type vs. EP+ respectively. These eigenvectors are then used to visualize the differences in distribution between the wild type and the mutant phenotypes. The discrimination between the wild type and mutant classes are visualized  do not contribute to this discrimination. Interestingly, the same two axes (ω12 and ω13) are both the best at discriminating wild type from mutants bchs1 and bchs58  endolysosomes from neurodegenerative motorneurons can be accurately recognized and differentiated from the wild type. These differences are not obvious by inspection, and manual collection of such quantitative data from a large number of image samples is prohibitively labour-intensive. As a solution to this problem, the automated algorithm detects differences between the neurodegenerative mutant compartments and normal compartments with a highly statistically significant confidence interval of 99.9%.bchs1 and bchs58. Density measurements were different in all three bchs genotypes (loss of function as well as overexpression) from the wild type. Ranking of feature importance makes it in principle possible to select the features most relevant to an assessment of the neurodegenerative phenotype, and increase the speed and accuracy of a diagnostic readout.The ranking of the different feature measurements against each other showed that the relative importance of a particular feature in distinguishing the origin of a sample varied between genotypes. For example, the differences between the wild type and phenotypes resulting from overexpression of the Bchs protein (EP+) are largely attributable to contrast variations. On the other hand, both size and contrast variations differentiated the wild type from either of the loss of function alleles While the contrast, size, and density feature differences between genotypes are quite subtle, as is evident from Fig. bchs loss of function alleles gave endolysosomal spot size profiles that were bigger than wild type, and this feature was prominent in determining genotypic origin. This may be related to the observation of enlarged lysosomal compartments in the neurodegenerative lysosomal storage diseases [bchs [Interestingly, both the neurodegenerative diseases ,39 and ies [bchs . Anotherbchs mutant) can be defined, since particular eigenvectors and distributions along these vectors appear to be typical for certain genotypic classes, as is seen in Fig. An important finding of this study was that Fisher's linear Discriminant categorized both loss of function alleles according to the same eigenvectors, even given the subtlety of the differences in features. This demonstrates the power of the method to identify essential feature information and classify phenotype  based on relatively small data sets. Moreover, subclasses of phenotype (e.g. Bchs overexpressor vs. In conclusion, as one of the key early pathological features of neurodegenerative disease, it is significant that the endolysosomal phenotype is now open to analysis by an automated, potentially high throughput process. The technique described here may be useful in rapid screening of drug candidates, since it can easily be applied to images in cell culture models of neurodegeneration. This type of analysis should also allow rapid, unbiased evaluation of degenerative changes in different in vivo models, which are undetectable by traditional manual methods, and may ultimately be useful as a means of reliably diagnosing a systemic cellular condition that affects the endolysosomal compartment and predisposes neurons to degeneration.The authors declare that they have no competing interests.SK developed and implemented the algorithms for image processing, feature extraction and feature classification. SK also carried out the statistical analysis and drafted the manuscript. YW was responsible for the genetics, preparation of larvae and the acquisition of images. VV assisted in the implementation of the algorithms and the acquisition of images. RK conceived of the study, participated in its design and coordination, and helped to draft the manuscript.


The success achieved by genome-wide association (GWA) studies in the identification of candidate loci for complex diseases has been accompanied by an inability to explain the bulk of heritability. Here, we describe the algorithm V-Bay, a variational Bayes algorithm for multiple locus GWA analysis, which is designed to identify weaker associations that may contribute to this missing heritability.V-Bay provides a novel solution to the computational scaling constraints of most multiple locus methods and can complete a simultaneous analysis of a million genetic markers in a few hours, when using a desktop. Using a range of simulated genetic and GWA experimental scenarios, we demonstrate that V-Bay is highly accurate, and reliably identifies associations that are too weak to be discovered by single-marker testing approaches. V-Bay can also outperform a multiple locus analysis method based on the lasso, which has similar scaling properties for large numbers of genetic markers. For demonstration purposes, we also use V-Bay to confirm associations with gene expression in cell lines derived from the Phase II individuals of HapMap.V-Bay is a versatile, fast, and accurate multiple locus GWA analysis tool for the practitioner interested in identifying weaker associations without high false positive rates. Genome-wide association (GWA) studies have identified genetic loci associated with complex diseases and other aspects of human physiology ,2. All rMethods for multiple locus GWA analysis must address a number of problems, including 'over-fitting' where too many associations are included in the genetic model, as well as difficulties associated with model inference when the number of genetic markers is far larger than the sample size . Two genDespite the appealing theoretical properties of multiple locus methods that make use of hierarchical models or partitioning, these methods have not seen wide acceptance for GWA analysis. There are at least two reasons for this. First, an ideal multiple locus analysis involves simultaneous assessment of all markers in a study and, given the scale of typical GWA experiments, most techniques are not computationally practical options ,10,16-18Here we introduce the algorithm V-Bay, a (V)ariational method for (Bay)esian hierarchical regression, that can address some of the computational limitations shared by many multiple locus methods ,10,16-18The specific model implemented in V-Bay is a hierarchical linear model, which includes marker class partitioning control of model over-fitting. This is particularly well suited for maintaining a low false-positive rate when identifying weaker associations . V-Bay iResults we focus on the simulation results for single population simulations, but we also implement a version of the algorithm to accommodate known population structure and missing genotype data. We demonstrate that in practice, V-Bay consistently and reliably identifies both strong marker associations, as well as those too weak to be identified by single-marker analysis. We also demonstrate that V-Bay can outperform a recently proposed multiple locus methods that uses the least absolute shrinkage and selection operator (lasso) penalty [We take advantage of the computational speed of V-Bay to perform a simulation study of performance, for GWA data ranging from a hundred thousand to more than a million markers. In the  penalty , a theorThe V-Bay algorithm consists of two components: a hierarchical regression model with marker class partitioning and a variational algorithm for approximate Bayesian inference. The underlying hierarchical model of V-Bay is a Bayesian mixture prior regression  that hasApproximate Bayesian inference with V-Bay is accomplished by an algorithm adapted from variational Bayes methods . As withThe computational efficiency of V-Bay derives from two properties: it is a deterministic algorithm and the objective function has a factorized form. Since V-Bay is deterministic it does not need the long runs of Markov chains required by exact Bayesian MCMC algorithms . For GWAMethods). V-Bay therefore has better computational scaling properties than most currently proposed multiple locus algorithms for full likelihood or exact MCMC Bayesian analysis, when simultaneously considering all markers in a GWA study [More precisely, V-Bay has linear time complexity scaling with respect to both marker number and sample size per iteration  probability that the marker has an association with the phenotype. While different significance thresholds based on -log10 p-vbay can be assigned to control false positive rate, as illustrated in Figure We assessed significance of marker associations using -logWe empirically analyzed V-Bay performance on 150 simulated GWA data sets. Marker numbers for these data were one-hundred thousand, six-hundred thousand, or one million markers and were simulated using the approximate coalescent simulator MaCS . We simuAs illustrated in Table -7). Further simulations indicated that even for a uniform distribution of individual heritabilities , V-Bay performs better for similar sample sizes and individual heritabilities. For example, for 32 loci with a sample size of 1000, and false-discovery rate of 5.0% the average power of V-Bay was 93%. This is greater than the corresponding power of 72% for single-marker analysis with the same false-discovery rate. In general, regardless of sample size, if there are enough loci with associations that are not too weak, then V-Bay outperforms single-marker analysis.Whether small associations are identified by V-Bay depends on the interplay between the sample size of the GWA study and the percentage of variation explained by the individual marker associations. For example, Figure Methods). Therefore loci with large effects may still have low individual heritabilities if the minor allele frequencies of the true loci are low (or vice versa). For example, for our simulations where the total heritability was controlled to be 0.5, and the individual heritabilities were shifted to be smaller overall, V-Bay performance was far closer to single-marker analysis. When we increased the individual heritabilities associated with associations in these simulations, while holding the total heritability at 0.5, V-Bay can outperform single-marker analysis. For all simulations, when an individual heritability falls below a certain threshold, neither approach could detect the association. There exists a limit to how weak an association can be and still be detected by V-Bay, given the sample size of the GWA study. Even in the worst case scenarios simulated, with many loci with small individual heritabilities and a small sample size, the performance of V-Bay was not significantly different from single-marker analysis across simulations. This result suggests that even if the number of loci were increased , the performance of V-Bay would at worst be the same as single-marker analysis.V-Bay performance is a direct function of the individual heritabilities, and not the total heritability of the phenotype. The individual heritability is defined by both the minor allele frequency and the effect size . A typical result from these analyses is presented in Figure cis-association. For this probe, V-Bay, the lasso, and our multiple population single-marker analysis indicated a strong cis-association. Since this association was also found with single-marker analysis, identification was not due to V-Bay but to the analysis of the pooled data from different populations . In 90% of cases, where our single-marker analysis reproduced the most significant ciations  were ider et al. ). Still,V-Bay addresses computational efficiency and performance concerns associated with many multiple locus GWA algorithms. While V-Bay currently utilizes a hierarchical partitioning model, the same approach could be used to implement scalable algorithms for a wide range of models. For example, different shrinkage or penalization models such as the lasso ,14, ridgn individuals with m markers is a standard multiple regression model:The V-Bay algorithm consists of two components, a hierarchical regression model with marker class partitioning and a variational Bayes computational algorithm. The hierarchical regression is adapted directly from Zhang et al.  with minyi is the phenotype of the ith individual, μ is the sample mean, xij is the genotype of the jth marker of the ith individual, βj is the effect of the jth marker, and ei ~ N μ.where The second level of the hierarchical model consists of a partitioning of markers into positive, negative, and zero effect classes and the prior control over the distributions of these classes. The partitioning is accomplished by modeling each of the regression coefficients using mixture prior distributions:βj with a value of zero, and N+ and N- are positive and negative truncated distributions [where ibutions . The priθβ, ϕβ, ψβ all to one. The hyperparameters m, is greater than the sample size, n, we truncate the Dirichlet distribution such that In our analyses we chose an uninformative Dirichlet prior by setting the parameters hrinkage . We founThe variational Bayes component of V-Bay is constructed by approximating the joint posterior density of the hierarchical model:in terms of a factorized form:Methods). The algorithm is therefore equivalent to updating these expected sufficient statistics.and then minimizing the KL-divergence between the factorized and full form. Equation (5) is a natural factorization for the V-Bay hierarchical model since most of the priors are conjugate. The posterior factorized distributions all have closed form expressions and each parameter is completely characterized by an expected sufficient statistic  Additio, Methodsq(βj)) and the full joint distribution is performed by considering the expectation of the full log joint distribution with respect to each parameter. For a generic parameter θ, the expectation step is equivalent to setting:Minimizing the KL-divergence between each marginal distribution (e.g. θ -indicating expectation of the log of equation (4) with respect to every other parameter's factorized distribution, except q (θ). This defines a system of equations which can be iterated through until convergence [nm) per iteration .with C some normalizing constant, and Evergence ,27. Withθ) which lower bounds the log posterior probability of the data . The lower bound ℒ(θ) is defined as the expectation of the log of equation (4) with respect to every factorized distribution plus the entropy of each factorized distribution. In the full form, the convergence of V-Bay to a local maximum of the lower bound ℒ(θ) is guaranteed because of the convexity of ℒ(θ) with respect to each parameter's approximate posterior distribution [Methods).The factorization of equation (4) is used to define a function ℒ models, while with initializations of only a few non-zero expectations of βj's, V-Bay tends to update these values close to zero before converging. We therefore use the approach of setting all expectations of βj parameters equal to zero as a starting point for all runs of V-Bay, an approach that has precedent in simultaneous marker analysis [Given that global convergence to a single stationary point is not guaranteed , the staanalysis . This alWe have found that the order in which the parameters are updated can affect local convergence, particularly when there is missing genetic data. In general, the different association models we found using different orderings were not widely different from one another, often differing in whether they included one or two specific associations. For cases where we found ordering did make a difference, we ran V-Bay with multiple random orderings and used the conservative criteria of considering only associations found to be significant in at least 80% of the cases to be true positives for all simulations and data analyses compared to single-marker analysis. The cutoff of 80% corresponds directly to a false discovery rate of 0%. We also considered a less stringent cutoff and an observed false discovery rate of 5% in the comparison to the lasso.http://mezeylab.cb.bscb.cornell.edu/Software.aspx. The software has basic control parameters available to the user and only requires tab delimited genotype and phenotype files as input. The algorithm itself consists of the following steps: 1) randomize marker ordering, 2) initialize the expected sufficient statistics and expectations of parameters, 3) update the expected sufficient statistics for a particular parameter, given the expectations of all the other parameters, 4) update the expectations of a particular parameter given the expectations of all the other parameters, 5) repeat steps 3 and 4 for all the parameters in the model, 6) check convergence based on the current estimate of the lower bound, ℒ(θ). Further functional details are presented in Additional file 10 of p-vbay = pj+ + pj- statistic for each marker, which can be used to assess significance of a marker association.An implementation of V-Bay is available at a posteriori (MAP) estimates are obtained by maximizing the following penalized log-likelihood:Originally proposed by Tibshirani , recentlβ|Y) is the log-likelihood for the relevant generalized linear model. By penalizing the magnitude of each βj coefficient, MAP estimates shrink the coefficient values compared to the estimates under the unpenalized model. This shrinkage causes most coefficients to be exactly zero, so that only very few markers are selected to be nonzero for a single value of λ. This penalty produces a convex log-likelihood surface with a single maximum even for underdetermined systems (i.e. when there are more markers than samples). Therefore, the lasso can jointly consider all markers in a single model and simultaneously account for variance in the response caused by multiple markers. The lasso model is fit for multiple values of λ and a single subset of coefficients is selected to be nonzero by 10-fold cross-validation. Confidence scores are obtained for each selected marker by comparing an unpenalized model with all selected markers to a model that omits each marker in turn. An F-test is performed for each marker, but note that these confidence scores cannot be interpreted as typical p-values since they are obtained from a two step procedure. Algorithmic details for fitting the LASSO model for the linear-Gaussian case are provided by [where ℓ. The genotypes were represented in the linear model with a consistent dummy variable encoding of {0, 1, 2} across loci. The additive effects were drawn independently from a Γ distribution or from a model with fixed effects. The locations for loci were randomly sampled throughout the genome. For each genomic data set, 4, 8, or 32 loci with phenotype associations were simulated. The total heritability of the phenotype was fixed at either 0.5 or 0.9. The MAF is computed for each sampled locus in the genetic model since each locus is chosen from the SNPs generated by MaCS. By combining the MAF with the effects sampled for each locus in the genetic model, it is possible to determine the proportion of observed variation contributed by each locus. This individual heritability for each locus is defined as follows:fj is the MAF of locus j, βj is the additive effect of the locus j, and where τ = 1000), and were updated in a similar fashion as the other parameters in the V-Bay algorithm. The V-Bay algorithm was run until the tolerance for the likelihood portion of the lower bound ℒ(θ) was < 10-9. For the simulations with missing data, the minor allele frequency across loci (fj ∀j) was estimated given the observed genotype data, and then the missing data points were sampled from a Bin, i.e. assuming Hardy-Weinberg equilibrium, for both V-Bay and single-marker analysis. We did random re-sampling of missing data to test the robustness of the output of V-Bay and the single-marker analysis .GWA analysis of the simulated data were performed using both V-Bay and a linear regression single-marker analysis. When population structure was incorporated, the linear model 1) becomes a fixed effect ANOVA model, for both V-Bay and the single-marker analysis. The population means in V-Bay were treated as having normal priors centered on zero with a very large variance . The genetic architectures were simulated as with the larger scale simulations, but with only 4 or 32 loci being sampled randomly from the one-hundred thousand markers, and effects sampled from a Γ distributions for 10 replicated data sets. Eight random reorderings of the markers were used with the V-Bay analysis, and the false discovery rate for V-Bay was controlled based on the consensus of associations found across reorderings with p-vbay> 0.99 . The false discovery rate for the lasso (using F-statistics) and single-marker analysis were controlled based on the p-values computed for each method respectively.6 SNPs on chromosomes 1 to 22. The X and Y chromosomes were not analyzed by Stranger et al. and we ignored these chromosomes in our analyses as well. Stranger et al. [cis-eQTL associations, found by testing within populations, where every SNP in a 2 Mb window around each gene was analyzed. We performed a GWA analysis, with both V-Bay and a single-marker regression, for their top 100 most significant expression probes. We combined genotypic data across populations, where we accounted for the effect of population structure in each case by including appropriate covariates. We also tested the top 20 probes, not in their association list that had the largest residual variance after correcting for population structure. Only 120 expression probes were analyzed to conserve CPU cycles; all 879 could easily be analyzed in a future study. The total missing data for this SNP set was 1.78%. We accounted for missing data using the same approach as with our simulated data analysis.We performed a GWA analysis for gene expression levels measured in the eternal lymphoblastoid cell lines that were generated for the 210 unrelated individuals of Phase II of the International HapMap project . This sar et al.  reportedhttp://mezeylab.cb.bscb.cornell.edu/Software.aspx. The source code is released under the GNU General Public License http://www.gnu.org/licenses/. The binary was compiled for 32-bit architecture on Ubuntu 8.04 http://www.ubuntu.com/ using the compiler gcc http://gcc.gnu.org/ and the GNU scientific library http://www.gnu.org/software/gsl/. To recompile from source both gcc and GSL are required. Documentation describing how to use V-Bay as well as example data sets are also available at http://mezeylab.cb.bscb.cornell.edu/Software.aspx.Both binaries and source code for the V-Bay software are available at the following URL: V-Bay: Variational Bayes algorithm for genome-wide association analysis; GWA(S): Genome-Wide Association (Study); MAF: Minor Allele Frequency; eQTL: expression-Quantitative Trait Loci; ANOVA: Analysis of Variance; EM: Expectation-Maximization algorithm; SNP: Single Nucleotide Polymorphism; ROC curve: Receiver Operating Characteristic curve; Lasso: Least Absolute Shrinkage and Selection Operator.BAL developed and implemented the V-Bay algorithm, performed the simulation and data analyses, and wrote the software. BAL and JGM designed the simulation and data analyses. GH implemented the lasso algorithm, and ran the lasso algorithm for the simulation and data analyses. BAL and JGM wrote the manuscript. All authors read and approved the final version of this manuscript.Portable Document File (PDF) containing additional results and methods that are referred to in the text.Click here for file


While recently performed genome-wide association studies have advanced the identification of genetic variants predisposing to type 2 diabetes (T2D), the potential application of these novel findings for disease prediction and prevention has not been well studied. Diabetes prediction and prevention have become urgent issues owing to the rapidly increasing prevalence of diabetes and its associated mortality, morbidity, and health care cost. New prediction approaches using genetic markers could facilitate early identification of high risk sub-groups of the population so that appropriate prevention methods could be effectively applied to delay, or even prevent, disease onset.This paper assessed 18 recently identified T2D loci for their potential role in diabetes prediction. We built a new predictive genetic test for T2D using the Framingham Heart Study dataset. Using logistic regression and 15 additional loci, the new test was slightly improved over the existing test using just three loci. A formal comparison between the two tests suggests no significant improvement. We further formed a predictive genetic test for identifying early onset T2D and found higher classification accuracy for this test, not only indicating that these 18 loci have great potential for predicting early onset T2D, but also suggesting that they may play important roles in causing early-onset T2D.To further improve the test's accuracy, we applied a newly developed nonparametric method capable of capturing high order interactions to the data, but it did not outperform a logistic regression that only considers single-locus effects. This could be explained by the absence of gene-gene interactions among the 18 loci. Diabetes mellitus has become one of the major global health issues in the twenty-first century. In the past few decades, the incidence of diabetes has risen rapidly. Owing to its dramatically increased prevalence and associated high morbidity, mortality, and health care cost, early detection and prevention of diabetes have become critical. The most common form of diabetes is type 2 diabetes (T2D), which accounts for over 90% of all cases of diabetes. Although no established cure has been found for T2D, there is evidence that the progress of T2D can be largely prevented through exercise and diet control. In a large-scale study conducted in the United States, lifestyle intervention  has been shown to reduce the risk of T2D by 58% among high-risk individuals over 3 years .KCNJ11, rs1801282 (Pro12Ala) of PPARG, and rs7903146 of TCF7L2, Weedon et al. [Detecting T2D at its earliest stage is the key to more effectively applying lifestyle intervention to reduce morbidity and mortality. Recent research has focused on the genetic prediction of T2D . A predictive genetic test, which uses genetic markers  to predict an individual's future risk of disease, can be conducted early in life  and thus form one of the most appealing early disease prediction methods. Based on three widely replicated genetic variants, rs5219 Glu23Lys) of Lys of KCWe selected 18 T2D SNPs from the Framingham Heart Study (FHS), among which 11 are the same and 7 have alleles in high linkage disequilibrium with the 7 other SNPs used in Lango et al.'s study. We combined these 18 SNPs to form a new predictive genetic test, and compared it with the previous three-marker test , which hWe used both logistic regression  and a newly developed nonparametric method  to buildβi is the regression coefficient for the ith genetic variable and μ is the probability of an individual developing T2D. Since, as indicated by Lango et al. [glm function in the statistical package R.where o et al. , all theThe above logistic regression does not take into account any interaction effect, and may result in a low performance if there is a strong interaction effect. Alternatively, we can fit a logistic regression with interaction effects. However, for 18 loci a logistic regression model with all two-way interactions requires 171 parameters and fitting a model with such a large number of parameters will lead to biased estimates and an inflated type 1 error rate . The newHypothesis testingA) with that of the previous three-marker test (A0), we set up a hypothesis of interest (H0 : A = A0) and constructed an appropriate test statistic to test the hypothesis:In Lango et al.'s study , the tesUnder the null hypothesis, this test statistic follows a standard normal distribution in a large sample. The variance of the estimated AUC, nD and D and where OC curve .We included 252 unrelated diabetes cases from the 252 diabetes families , and 979 unrelated controls, one from each of the remaining families. Diabetes cases with age of diabetes onset less than 40 years were excluded from the study to eliminate patients with possible type 1 diabetes. We took the 18 loci used in Lango et al's study; we extracted 11 SNPs from the 500 k GWAS dataset and the 50 k candidate-gene dataset, and replaced the remaining seven SNPs that were absent from either dataset with existing SNPs that were in strong linkage disequilibrium with the SNPs used in Lango et al.'s study . We also compared the discriminative ability of our test with that from Lango et al. [A0 equal to 0.6 ; in the FHS no strong evidence was found to suggest a difference of classification accuracy between the two tests .Based on these 18 loci, we constructed predictive genetic tests using both the additive logistic regression model and the robust optimal ROC curve approach. The performance of the predictive genetic test from logistic regression (AUC = 0.606) was slightly better than that from the robust optimal ROC curve method (AUC = 0.596) (Figure o et al.  by usingThere is evidence that genetic variants might play important roles in causing early-onset T2D . SimilarOngoing GWAS provide a powerful approach to uncovering common unknown genetic variants causing complex diseases. The discovered genetic variants, together with previous findings, not only improve our understanding of the genetic etiology of common complex diseases, but also may create new opportunities to improve health care by making early disease prediction possible.In this study, we combined 18 loci to form a predictive genetic test for T2D from FHS data. Our findings were consistent with previous studies that suggested a limited improvement of the test by incorporating an additional 15 loci into the previous test based on three loci. That this success was limited can be attributed to at least two causes. First, the currently discovered genetic variants only explain a small proportion of the genetic contribution to T2D . Second,We found the 18 loci predisposing to T2D had substantially better ability to detect patients with early-onset T2D than to detect patients with late-onset T2D. This result, although still preliminary, suggests a promising predictive genetic test for early-onset T2D. Our result also confirms a previous hypothesis suggesting there is a major genetic influence on early-onset T2D, but that joint effects of environmental and genetic risk factors influence on late-onset T2D.In additional to logistic regression, we also applied our newly developed optimal robust ROC curve method in this study. Although, in this specific case, there seemed to be no additional accuracy in using the optimal robust ROC curve method, the new method may potentially increase a test's performance in other scenarios in which there is gene-gene interaction. Thus, depending on the nature of the disease etiology, an appropriate method could be chosen. For a simple scenario involving a relatively small number of loci with no gene-gene interaction expected, logistic regression would be preferred. When there is a large number of loci with high order interactions, the optimal robust ROC curve method should be applied instead.Using the FHS dataset, we found little increase in discriminative ability as a result of combining 15 additional T2D loci discovered from the recent GWAS, together with three already known loci, to form a predictive genetic test. Although the currently identified T2D loci do not have sufficient power for predicting T2D, they may have a larger impact on early-onset T2D, and hence could be used to predict early-onset T2D.AUC: Area under the ROC curve; FHS: Framingham Heart Study; GWAS: Genome-wide association studies; ROC curve: Receiver operating characteristic curve; SNP: Single-nucleotide polymorphism; T2D: Type 2 diabetesThe authors declare that they have no competing interests.QL and RCE conceived the idea and participated in its design and coordination. QL, YS, and XW carried out programming and analyses. SW and YC contributed to the initial conception and design and provided critical revisions of the manuscript. All authors read and approved the final manuscript.


Repeated blocks of genome sequence have been shown to be associated with genetic diversity and disease risk in humans, and with phenotypic diversity in model organisms and domestic animals. Reliable tests are desirable to determine whether individuals are carriers of copy number variants associated with disease risk in humans and livestock, or associated with economically important traits in livestock. In some cases, copy number variants affect the phenotype through a dosage effect but in other cases, allele combinations have non-additive effects. In the latter cases, it has been difficult to develop tests because assays typically return an estimate of the sum of the copy number counts on the maternally and paternally inherited chromosome segments, and this sum does not uniquely determine the allele configuration. In this study, we show that there is an old solution to this new problem: segregation analysis, which has been used for many years to infer alleles in pedigreed populations.Segregation analysis was used to estimate copy number alleles from assay data on simulated half-sib sheep populations. Copy number variation at the Agouti locus, known to be responsible for the recessive self-colour black phenotype, was used as a model for the simulation and an appropriate penetrance function was derived. The precision with which carriers and non-carriers of the undesirable single copy allele could be identified, was used to evaluate the method for various family sizes, assay strategies and assay accuracies.Using relationship data and segregation analysis, the probabilities of carrying the copy number alleles responsible for black or white fleece were estimated with much greater precision than by analyzing assay results for animals individually. The proportion of lambs correctly identified as non-carriers of the undesirable allele increased from 7% when the lambs were analysed alone to 80% when the lambs were analysed in half-sib families.When a quantitative assay is used to estimate copy number alleles, segregation analysis of related individuals can greatly improve the precision of the estimates. Existing software for segregation analysis would require little if any change to accommodate the penetrance function for copy number assay data. Copy The Mendelian constraints underlying analyses such as those noted above have been well studied in the area of segregation analysis. Originally the term "segregation analysis" referred to the determination of the mode of inheritance of a phenotype but in recent decades it has come to include the inference of genotypic probabilities in pedigreed populations. The peeling algorithm of Elston and Stewart  is appliThe data required for single locus segregation analysis are four-fold: 1) a pedigree relating individuals to each other; 2) phenotypes on some individuals in the population; 3) a penetrance function expressing the probabilities of phenotype based on genotype; and 4) estimates of the frequencies of the genotype alleles in the population. Probabilities of mutation can also be incorporated. Assays that return estimates of the number of copies in diploid DNA can be thought of as a phenotypic measurement, and if assumptions are made about the distribution of the variation around the expected value of the assay then it is relatively straightforward to derive the appropriate penetrance function. Software to perform computations for segregation analysis is available and may include options to estimate penetrance functions as well as to estimate allelic probabilities (e.g. ).Awt, responsible for white fleece, known to be dominant to allele Aa [Awt is a number of different alleles, having two or more copies of a 190 kb DNA segment including the agouti signalling protein (ASIP) coding region, while allele Aa has a single copy of the region with a non-functional ASIP promoter. Furthermore, Norris and Whan [Ac1, Ac2 ... to refer to alleles with one copy, two copies and so on, with allele Aa being equivalent to our allele Ac1 and allele Awt being replaced by our alleles .In this paper, we demonstrate that segregation analysis is an old solution to a new problem, by applying a segregation analysis method to simulated data to explore the inference of copy number alleles at the Agouti locus in sheep. The recessive self-colour black condition in domestic sheep has been studied for many years, with allele llele Aa ,31, respllele Aa  and recellele Aa  have shoand Whan  have desIn this study, we demonstrate that segregation analysis methods are well suited to the inference of copy number alleles, and that if knowledge on the actual allele configurations is sufficiently important then the utility of a quantitative assay can be greatly improved through the incorporation of relationship data. On small datasets, our methods can be implemented in readily available software such as Mendel , accountn, the expected value of the assay is the ratio n - 2 junctions and two copies of the 5' breakpoint. As diploid DNA has at least two copies (at least one on each chromosome) this ratio takes values from the series  which asymptotically approaches unity. It is important to note that since the assay is quantitative, variation occurs around the expected ratios. The magnitude of the variation can differ among laboratories, and even among batches of samples in one laboratory, so we have treated it as unknown and conducted analyses for a range of values. As a lower limit, we chose a CV of 3% (which equates to a standard deviation of 0.01 for the class with an expected ratio of 1/3). This figure is a little smaller than that derived empirically from ranking 111 assay samples and estimating the mean and standard deviation for the 35 samples that were extremely unlikely to be from a class other than that with an expected ratio of 1/3, the most easily distinguished class. The CV of 3% was used as the lower limit since it is achievable with real data, but we also conducted analyses assuming CV values of 6% and 9%. The expected ratios and standard deviations considered are summarized in Table The characteristics of the assay are reported in Norris and Whan . In an a2 statistic obtained by comparing the vector of copy number count frequencies with the frequencies expected given a vector of frequencies for alleles segregating in Hardy-Weinberg equilibrium. Black Merino sheep in wool flocks are commonly culled soon after birth and thus are never presented in a commercial sale yard, so to avoid ascertainment bias we excluded the Ac1/Ac1 class when calculating the X2 statistic. Table From the expected ratios and standard deviations, and assuming a distribution for the variation around the expected value, the probability of each copy number count can be estimated for each observed assay value. We assumed a normal distribution and estimated copy number count probabilities for a population of 87 phenotypically white Merino ewes coming from commercial sale yards. These are summarized in Table Ac1/Ac1 with certainty and conversely, for sheep with genotype Ac1/Ac1 the phenotype is known to be black wool with certainty. The assay is not relevant for these animals. For white sheep, the penetrance function relates to the assay rather than to the phenotype. That is, the penetrance function is the probability of returning a particular assay value given the genotype. Again under the assumption of normality, this is proportional to the height of the normal distribution relevant to the underlying genotype. Table For black sheep, the genotype is known to be Ac1/Ac1 animal was selected. In the absence of evidence to the contrary, we assumed that the genotype at the Agouti locus had no effect on fitness other than through artificial selection. The simulation was run for 20 years. In the founder populations, allele frequencies at the Agouti locus were as in Table As the stud Merino sheep industry is likely to use a test for the genotype at the Agouti locus, small, highly selected and relatively closed flocks were simulated. In each replicate, 10 studs were simulated, each mating five rams to 200 ewes each year. Selection was on a trait uncorrelated to Agouti, except for the last generation when no homozygous In our simulation study, we performed the assay on half-sib groups of animals and their parents, ignoring relationships between parents. This is equivalent to "cutting" inbreeding loops in a relatively naive but systematic way, rather than the more sophisticated approaches such as in . We chosGenotype probabilities were estimated using a restricted implementation of the Elston-Stewart algorithm , restricAc1/Ac2 and in all cases when a lamb had the genotype Ac1/Ac2 it was declared to be a carrier with over 99.9% certainty.Table The effect of jointly analyzing half-sib families of varying size is displayed in Table False positives (declaring non-carriers to be carriers) are absent and false negatives (declaring carriers to be non-carriers) are less frequent as family size increases. This is an important result since in industrial applications, this second form of error has a much greater adverse impact. The fact that we do not find proportions of type II errors in accordance with appropriate p-value threshold  is not unexpected, just as we do not expect to identify 95% of carriers with a 95% probability.Table In Table Ac1 allele. More importantly in a selective breeding environment, including family data resulted in a large increase in the power to declare individuals as non-carriers of the Ac1 allele.At the Agouti locus in sheep, colour phenotype is affected by a recessive, single copy allele, which cannot always be uniquely identified using the available assay. Furthermore, the assay has almost no power to determine that an animal is free of the undesirable single copy allele. Exploiting the family structures common in sheep flocks, across the scenarios examined, the joint analysis of half-sib families resulted in a modest increase in the power to declare individuals as carriers of the undesirable th last row, Table The improvement is dramatic: from 7% of non-carrier lambs being identified as clear at the 99.9% level when a lamb is assayed and analyzed alone  in formulating the penetrance function, the joint analysis of half-sib families does not increase the proportion of false negatives. On the contrary, it reduces the proportion, from 7% at a 5% threshold for lambs analyzed alone, to as few as 1% if 16 half-sibs are analyzed together. As noted earlier, the assignment of a non-carrier status to carriers is most undesirable in industrial applications of the assay. A ram, sold as a non-carrier, that subsequently produces progeny exhibiting the self colour black condition, can adversely affect the reputation of the stud selling the ram, and the reputation of the assay. Furthermore, if the ram is used only in flocks that are clear of the In this paper, we have focused on an example from livestock, the self colour black condition in sheep which means we have assumed large half-sib families and restricted ourselves to analyzing these in isolation. These analyses are very quick and the analysis of high-throughput quantitative CNV assay data for half-sib families would be feasible using this method. However, a half-sib family structure is not a requirement for a segregation analysis, and even for family sizes of one or two half-sibs with the sire being also assayed, power was increased to a higher value than when analyzing an individual alone. Readily available segregation analysis software makes optimal use of all pedigree links in estimating allele probabilities, and is suitable for copy number allele calling in human pedigrees and other pedigrees with smaller family sizes.de novo CNV affecting quantitative traits would be similar to using hidden Markov model based approaches [In our simulation study, we assumed that parameters relating to penetrance function were known. Specifically, we assumed allele frequencies and parameters for a normal distribution for the error associated with the quantitative assay. These were estimated from a sample of unrelated sheep, but could be estimated from the population of interest. This aspect of segregation analysis was not applied in this study, but software such as Mendel  can be uproaches ,21, but The precision of copy number allele estimates from quantitative assay data in pedigreed populations is greatly increased if the pedigree information is used in the estimation, and segregation analysis methods based on the peeling algorithm are well suited to this application. In the case of the Agouti locus and the recessive self-colour black condition, where the purpose of the test is to identify animals to use as parents, the proportion of lambs correctly identified (at the 99.9% level) as non-carriers increased from 7% when the lambs were analysed alone to 80% when the lambs were analysed in families. Any segregation analysis software can be used provided that the appropriate penetrance function is specified.The authors declare that they have no competing interests.JMH wrote the software for simulating and analysing the datasets, carried out the analyses and drafted the manuscript. VAW conducted the molecular genetic studies and contributed to the manuscript. BJN contributed to the design of the study and to the manuscript. All authors have read and approved the final manuscript.