Copy number variations (CNV) are important causal genetic variations for human disease; however, the lack of a statistical model has impeded the systematic testing of CNVs associated with disease in large-scale cohort.Here, we developed a novel integrated strategy to test CNV-association in genome-wide case-control studies. We converted the single-nucleotide polymorphism (SNP) signal to copy number states using a well-trained hidden Markov model. We mapped the susceptible CNV-loci through SNP site-specific testing to cope with the physiological complexity of CNVs. We also ensured the credibility of the associated CNVs through further window-based CNV-pattern clustering. Genome-wide data with seven diseases were used to test our strategy and, in total, we identified 36 new susceptible loci that are associated with CNVs for the seven diseases: 5 with bipolar disorder, 4 with coronary artery disease, 1 with Crohn's disease, 7 with hypertension, 9 with rheumatoid arthritis, 7 with type 1 diabetes and 3 with type 2 diabetes. Fifteen of these identified loci were validated through genotype-association and physiological function from previous studies, which provide further confidence for our results. Notably, the genes associated with bipolar disorder converged in the phosphoinositide/calcium signaling, a well-known affected pathway in bipolar disorder, which further supports that CNVs have impact on bipolar disorder.Our results demonstrated the effectiveness and robustness of our CNV-association analysis and provided an alternative avenue for discovering new associated loci of human diseases. CCL3L1-related segmental duplication influences susceptibility to HIV-1/AIDS de novo CNVs have been associated with autism Copy number variations (CNV) are DNA segments with gains or losses in copy number longer than 1 kb compared to a reference genome. At least 12% of the human genome has been identified as copy number variable The increasing functions found for CNVs in human diseases make a genome-wide systematic survey of CNVs become intriguing. However, there are no such effective tools for testing the association of CNVs with disease in genome-wide scale. Although many challenges have been reviewed previously SNP site-based testing) to conform to pathophysiologically functioning way of CNV. We also conducted a geographical pattern-comparison of CNV (named as window-based testing) to ensure confidence. We applied this strategy to genome-wide data with seven common diseases from the Wellcome Trust Case-Control Consortium (WTCCC) Here, we developed an integrated strategy to test CNV-association with disease in large-scale case-control studies in which single-nucleotide polymorphisms were used to calculate the copy numbers. Our strategy processed the data in a hierarchical mode to address the challenges individually . The second feature is comparison of the CNV's geographical pattern between cases and controls. Our method applied a window-based chromosome-along clustering algorithm to the candidate CNV-loci, and then tested these clustering results statistically. The accidental signal noise could be easily excluded through the clustering procedure, and the credible CNVs from common ancestry or with identical physiological significance tend to congregate around nearby nodes in the clustering heat map. The statistical testing on these congregated CNVs is more accurate than SNP site-based testing, and provides further confidence to our results.Two features of our CNV-association strategy were proved effective in the following results. The first is the multiple hypotheses for the functioning mode of CNVs in disease. CNVs may affect phenotype through regulating gene's expression, such as the common CNV-loci for the gene P values are different from common P values in multiple tests, in that these P values tend to be related with the neighboring sites, which is a phenomenon caused by the geographical stretch of CNVs. Thus, the classical Bonferroni correction is not suitable. A permutation method based on the actual data was required to generate the theoretical distribution of multiple P values. Here, we hypothesized that the case-control effect size for every loci is null, and the difference of measurements originate from individual selection. We permuted the labels of cases and controls, recalculated the association P values, and then computed the false discovery rate (FDR) to educe the appropriate significance level for the association results : 43 are associated with bipolar disorder , 17 with coronary artery disease , 5 with Crohn's disease , 41 with hypertension , 61 with rheumatoid arthritis , 37 with type 1 diabetes  and 15 with type 2 diabetes . Thirty-six CNV-loci were identified from these SNP sites through combining neighboring SNP sites . These results indicate that these SNP sites belong to the same copy number variable region and that these convergent associations are unlikely to be random events. The high quality of the final clustering heat map provides confidence for these susceptible CNV-loci, and the relatively clean CNV-pattern boundaries in the clustering heat map also indicates the high credibility of these CNVs . Some of the susceptible CNV-loci in our study are associated with multiple diseases . For example, CEACAMs  are matrix molecules localized at the apical glycocalyx of normal colonic epithelium. They are bacteria receptors CASP9 , which participates the immune attack in a murine model of type 1 diabetes To further confirm the effectiveness of our strategy, we performed data mining within a 0.2-Mb region , POU3F1 , MTF1 , CCDC91 (coiled-coil domain containing 91), KCNQ5 (MIM 607357) and Olfactory receptors . INPP5B hydrolyzes the calcium-mobilizing second messenger inositol 1,4,5-trisphosphate (IP3), which is a signal-terminating reaction in the calcium/IP3 pathway and may directly affect neurophysiologic regulation Figure S4A), which make sense that deletion might down-regulate the INPP5B expression, leading to inability of terminating the excited calcium flux. POU3F1, also known as Oct6, plays a crucial role in neurodevelopment and has been shown to be potentially relevant in schizophrenia POU3F1 was also proved to affect calcium flux through binding to the promoter region of PIK3C3 (MIM 602609), a member of the phosphatidylinositide 3-kinase family, and mutations in PIK3C3 have been shown to be involved in a subset bipolar disorder and schizophrenia patients MTF1 binds to the metal responsive element, which is regulated by lithium salts in the treatment of bipolar disorder Figure S4C). The gene CCDC91 in this locus may affect protein sorting and membrane trafficking through interacting with GGAs  CCDC91 are associated with bipolar disorder, and its binding partner AP1G1 was up-regulated in the post-mortem cerebellum of schizophrenia patients KCNQ5 (potassium voltage-gated channel subfamily KQT member 5) may contribute to episodic disturbances of mood and behavior as well-characterized roles in other ion-channelopathies KCNC2 and KCNQ2, were found to be associated with bipolar disorder KCNQ5 is connected to phosphoinositide signaling through regulation by PIP5K2A(MIM 603140), a schizophrenia-associated gene P value = 4.91×10−4, genotypic P value = 2.02×10−3) in the WTCCC paper Obvious physiological relevance of these results was observed in the susceptible genes identified for bipolar disorder, including Figure S5), which strongly suggests the role of this pathway in bipolar disorder. Moreover, detailed analysis of these associated genes  implicated that CNVs with similar boundary and pattern might play roles in the inheritance of bipolar disorder.Therefore, all those associated genes listed above are related to phosphoinositide/calcium pathway , which reflects that CNV-association are unique from genotype-association and could be new way in discovering associated loci with human disease. In comparison of the associated genes, we found that potassium voltage-gated channel subfamily (KCNQ5 in CNV-association and KCNC2 in genotype-association), olfactory receptors could be found in the both results.CNVs are different genetic variations from SNPs, in that they are deletion or amplification of DNA fragments but not single-nucleotide polymorphisms. Here, we compared our CNV-association results with SNP genotype-association in WTCCC. There was little tendency-accordance between the both results on SNP site level . This phenomenon results from two limitations of genotype association: the genotyping model in the association test is limited to three genotypes  and the genotyping quality is dependent on the sample-wide intensity mapping of the A and B alleles. Both of these limitations are not suitable for SNPs in copy number variable regions with chaotic intensity mapping and with genotypes not limited to three . Similar phenomenon of CNVs' effect on genotype-association has been found in the locus of CYP2D6 in breast cancer One interesting finding is that a large proportion (25.1%) of our results were absent in genotype-association analysis  can support this hypothesis: amplification of two genes (PDPR and AARS) in 16q22.1 might impose a counteractive effect on CAD, while loss of copy number may cause weaker recovery from heart attack as they function in post-ischemic heart INPP5B may induce leakage-cleanup of IP3 in the nerve conduction, and then induce patients to lose control of excited emotion, while gain of copy number shows no obviously effect in bipolar disorder. In 14q11.2, a common copy number variable region, copy number differentiation may produce irregular isoforms of olfactory receptors, and then causes mis-perception in the olfactory and neuronal cells. Pattern discordance could be found in many CNV-loci of RA and T1D, which might be from aberration of DNA recombination and repair in somatic and germ cells. The CNVs with pattern discordance may make an impact on these diseases by interfering the genes' functions explicitly or through cell-recognition in complicated immune pathway. In a word, copy number variations may work in very complex way in the development of disease, and the function of risk CNV-loci need a locus-by-locus analysis.The functions of CNVs are interesting topics in disease-risk study, the complexity of which has been mentioned previously Two Affymetrix Mapping 500K chip datasets were used in the present work, which include the Wellcome Trust Case-Control Study Consortium (WTCCC) data for seven diseases  We processed the data using SNPs annotated in the NCBI build 35 and build 36 reference databases, and the results in the different builds were almost the same. In the main text and supporting information, results were only shown for build 35. Since the sex chromosomes are different from autosomes in copy number detection and comparison, only the autosomes were tested in our work.CNVs are mostly detected from SNP genotyping data, thus a precise transformation from SNP allele intensity into copy number is essential in testing the association between CNVs and diseases. In our work, a powerful hidden Markov model that makes the best of the SNP allele information was applied. To make sure that the parameters of hidden Markov model were suitable for all the high-throughput dataset of WTCCC, we developed a training program to calculate these parameters. This hidden markov model is depicted in the SNP site-based testing to measure the disease-association on a specific SNP site and (ii) Window-based testing to measure the CNV-pattern differentiation in and around the selected SNP site. Additionally, multiple trend testing was also applied for exploring CNV-association with disease (see details in Text S1). The SNP site-based testing was used to selected candidate for window-based testing, and the window-based testing ensured the credibility of the identified CNV-loci. This statistical flow chart is shown in The significance of the CNVs was evaluated in two levels of statistical tests: (i) 5 in the original paper; but here we use 3 to denote the CNV genotype.The SNP data from the genotyping chips was first converted to copy number (hidden copy number state) using a well-trained hidden Markov model. The hidden Markov model treated the series of SNP sites, which were arranged along the chromosome sequence, as a hidden Markov chain. The copy number calculation on the site of the hidden Markov chain is dependent on the signal of each SNP site and the copy number of neighboring SNP site. Two measurements for each SNP site were used to calculate its copy number: (i) the Log R Ratio (LRR), which is the log2-transformed value for the normalized intensity-sum of the SNP alleles, and (ii) the B allele frequency (BAF), which actually is a normalized anti-tangent value for intensity-ratio of the SNP alleles. The expected value for each SNP genotype cluster and intensity-sum, which were used in the normalization for LRR and BAF, were the 90% trimmed mean of all of the corresponding values from the WTCCC samples. All of the measurements and transformations above were calculated according to the instructions from the original technical paper The hidden Markov model needs a series of parameters to calculate the hidden Markov state, including the LRR's expectation (and standard deviation) for each state, the BAF's expectation (and standard deviation) for each state, the transition probability matrix for inferring relationship among SNP-series, and other parameters. These parameters were trained from the CEU data of HapMap and the program was performed automatically to eliminate bias from manual selection in the original technical paper The influence of changes in copy number (amplification and/or deletion) on physiological function is far from fully understood, so testings for amplification, deletion or the both were used to measure the significance on single SNP site. We postulated triple NULL hypotheses that (i) amplification  possess similar statistical power in all the diseases and all the window-based P values were pooled to calculate the FDR. P value in the observed data, P values in the observed data and permuted data respectively, P value, in the observed data) by the corresponding FDR could provide the estimation of false positives from random coincidence of individual selection. In the SNP site-based testing, FDR<0.05 was used to determine the proper number of candidates for the window-based testing. In the window-based testing, the boundary of the FDR was adjusted to ensure that false positives in the final results were less than 1 copy number window (centered SNP site).A permutation-based method was used to obtain the significance level for the SNP site-based testing. In the permutation procedure, the labels of the cases and controls were randomly permuted 1000 times, and then the http://www.ihs.ac.cn/xykong/CNV_Association_Test.rar.Supporting information include supporting data with five figures and two tables, and supporting methods in Figure S1The genome-wide distribution of the CNV-association results in the seven diseases. The −log10 of the SNP site-based P values in our testing with the three hypotheses, in which deletion (labeled as Loss), amplification (labeled as Gain) and both (labeled as Abnm) were evaluated as abnormal separately, are plotted against the position on each chromosome. For clarity, P values that passed the SNP site-based testing are highlighted in green and the SNP sites that passed the window-based testing are highlighted in yellow.(1.10 MB DOC)Click here for additional data file.Figure S2Comparison with the previous genotype-association analysis demonstrates the priority of the CNV-association test in copy number variable regions. “Gen” and “Add” indicate the genotypic test and trend test, respectively, in the WTCCC paper. The −log10 of the SNP site-based P values in our test with the triple NULL hypothesis  were plotted against the −log10 of the P values from the genotype association test from the WTCCC (A–G). For clarity, the genotype association P values<10−5 are highlighted in green, the CNV-association P values that passed the single SNP site-based testing are in blue and the CNV-association P values that passed the window-based testing are in red. SNPs absent from the genotype association analysis are plotted by default as zero and highlighted in brown, in which many SNPs that passed the SNP site-based testing are labeled with black.(0.78 MB DOC)Click here for additional data file.Figure S3Evidence that CNVs can lead to chaotic genotyping clusters in copy number variable regions. The selected sample-wide intensity maps show the typical influence of CNVs in the seven diseases labeled with abbreviations (A–F). All of the 17000 individuals are labeled with grey, individuals with CNVs in the disease group are in red and individuals with CNVs in controls are in green.(0.49 MB DOC)Click here for additional data file.Figure S4Selected CNV-loci that show strong evidence of association with diseases. The −log10 of the SNP site-based P values are plotted against the genomic location, in which the SNPs that passed the window-based testing are indicated in dark blue for the deletion hypothesis, dark green for the amplification hypothesis and orange for the deletion and amplification hypothesis. SNPs that lacked significance are shown in light colors . Functionally affected regions were characterized within a 0.2 Mb region centered on the identified SNP sites, and the region boundary  coincided with the length limitations or the location of neighboring genes. The clustering heat map for 41 SNP windows (each corresponding to the upper CNV-region) demonstrated good CNV boundaries in and around the “first class node.” In the heat map, black indicates a copy number of 0, red a copy number of 1, light grey a copy number of 2 and green a copy number of 3.(6.21 MB DOC)Click here for additional data file.Figure S5The cartoon depicts the function of the calcium-related pathway in bipolar disorder. The Ca2+/IP3 pathway has been reported to be closely related to bipolar disorder, and the molecules revealed in previous studies are labeled with blue circles and in red font. IP3 precursors in the membrane and metabolites in the cytosol are denoted by different shaped boxes. INPP5B, POU3F, Olfactory receptors  and KCNQ5, which were found to be associated to CNVs in our work, are labeled with black font and orange circles (or boxes).(0.09 MB DOC)Click here for additional data file.Table S1List of SNP sites showing significance in the window-based testing.(0.63 MB DOC)Click here for additional data file.Table S222 risk genes that were validated from previous studies.(0.20 MB DOC)Click here for additional data file.Text S1Supporting methods of multiple testing for trend.(0.08 MB DOC)Click here for additional data file.


Few genetic factors predisposing to the sporadic form of amyotrophic lateral sclerosis (ALS) have been identified, but the pathology itself seems to be a true multifactorial disease in which complex interactions between environmental and genetic susceptibility factors take place. The purpose of this study was to approach genetic data with an innovative statistical method such as artificial neural networks to identify a possible genetic background predisposing to the disease. A DNA multiarray panel was applied to genotype more than 60 polymorphisms within 35 genes selected from pathways of lipid and homocysteine metabolism, regulation of blood pressure, coagulation, inflammation, cellular adhesion and matrix integrity, in 54 sporadic ALS patients and 208 controls. Advanced intelligent systems based on novel coupling of artificial neural networks and evolutionary algorithms have been applied. The results obtained have been compared with those derived from the use of standard neural networks and classical statistical analysisAdvanced intelligent systems based on novel coupling of artificial neural networks and evolutionary algorithms have been applied. The results obtained have been compared with those derived from the use of standard neural networks and classical statistical analysis. An unexpected discovery of a strong genetic background in sporadic ALS using a DNA multiarray panel and analytical processing of the data with advanced artificial neural networks was found. The predictive accuracy obtained with Linear Discriminant Analysis and Standard Artificial Neural Networks ranged from 70% to 79% (average 75.31%) and from 69.1 to 86.2% (average 76.6%) respectively. The corresponding value obtained with Advanced Intelligent Systems reached an average of 96.0% (range 94.4 to 97.6%). This latter approach allowed the identification of seven genetic variants essential to differentiate cases from controls: apolipoprotein E arg158cys; hepatic lipase -480 C/T; endothelial nitric oxide synthase 690 C/T and glu298asp; vitamin K-dependent coagulation factor seven arg353glu, glycoprotein Ia/IIa 873 G/A and E-selectin ser128arg.This study provides an alternative and reliable method to approach complex diseases. Indeed, the application of a novel artificial intelligence-based method offers a new insight into genetic markers of sporadic ALS pointing out the existence of a strong genetic background. Amyotrophic lateral sclerosis (ALS), the most common form of motoneuron disease, is a relatively rare (incidence: 1–3/100.000 per year), progressive and fatal disease characterised by neurodegeneration involving primarily motor neurons of the cerebral cortex, brain stem and spinal cord. To date, most studies have focused upon the familial form of the disease, which accounts for less then 10% of cases, and which is usually inherited as autosomal dominant inheritance. The gene coding for copper/zinc superoxide dismutase 1 (SOD1) appears to be mutated in 10–20% in the familial form [Genetic risk factors for ALS have been extensively studied and some "major genes", in addition to SOD1, have been recognised as being responsible for the monogenic inheritance pattern. There are now at least six dominant inherited adult onset ALS genes of which only three have been identified so far . HoweverCurrent hypotheses suggest a complex interplay between multiple mechanisms including genetic risk factors, oxidative stress, neuroexcitatory toxicity, mitochondrial dysfunction, intermediate neurofilament disorganization, failure of intracellular mineral homeostasis involving zinc, copper, or calcium, disrupted axonal transport, abnormal protein aggregation or folding, and neuroinflammation ,4. RecenAmong the genetic factors that may predispose to sporadic ALS, neurofilaments, apolipoprotein epsilon 4 genotype, excitotoxicity genes, ciliary neurotrophic factor (CTNF), cytochrome P450 debrisoquine hydroxylase CYP2D6, apurinic apyrimidinic endonuclease (APEX), mitochondrial manganese superoxide dismutase SOD2, monoamine oxidase allele B and paraoxonases, have been reported in different studies, partly with contradictory results -9. Not aSome years ago our group had the opportunity of working on another multifactorial complex disease such as venous thrombosis and analysing the results by an innovative statistical approach, Artificial Neural Networks (ANNs) . Indeed,The literature data together with the impressive results we obtained with ANNs, by which we were able to identify a subset of polymorphisms related to the disease, prompted us to employ the same approach also in ALS hoping to discover specific genetic patterns underlying the sporadic form of this disease. We applied a multiarray approach including allelic variations in genes that could be involved in the pathogenesis of ALS disease since it has been demonstrated that inflammation, cellular adhesion, and lipid pathways are linked to such a disease ,11. On tGenotyping of ALS cases and controls was performed. We applied advanced intelligent systems based on novel coupling of artificial neural networks and evolutionary algorithms and compared the results with those obtained by linear discriminant analysis and a simple back propagation approach.Surprisingly, we discovered a novel strong genetic background allowing a correct classification of cases and controls with a higher than 90% accuracy.The study population included subjects of Caucasian origin belonging to Italian ancestry and consisted of 54 sporadic ALS (SALS) patients and 208 control subjects.Diagnostic Criteria for ALS disease were based on the World Federation of Neurology El Escorial Revisited document . All patControl subjects were selected from a healthy control population, randomly collected from healthy blood donors admitted to the "Healthy Blood Donor Service" of Niguarda Ca' Granda Hospital. We checked the absence of personal and familial history of ALS in this group through direct interview.This study was approved by the local ethics committee.DNA was extracted using a salting out procedures . We applThe marker TNF beta thr26asn is twice present in the arrays as a control for the multiplex PCR and the hybridization procedures.All ALS subjects were screened for SOD1 mutation through PCR amplification and direct sequencing according to standard procedures .Each record related to a known clinical condition or to a sample population, and comprised 62 variables corresponding to the 60 SNPs plus case and control. We eliminated from the database those markers for which only one genotype was present  A and 14(+3) T ins) both in cases and controls. All the analysed polymorphisms may have three genotype classes: wild type, heterozygous and homozygous status. The association of these variables with ALS status was tested by ANNs and the results were compared with those obtained by a linear discriminant analysis. The models we used aimed at correct classification of the subjects in two classes:1) SALS patients (cases),2) healthy subjects (controls).a priori definition. The mathematical approach of ANNs consists in measuring the general dependence of random variables related to a group of subject without making any assumption about the nature of their underlying relationships.No other specific genetic model potentially linked to the analysed SNP was evaluated; ANNs are able to build a model with a strong genetic basis just collecting all the information included within the SNP without any In this study we applied supervised ANNs, in order to develop a model able to predict with high degree of accuracy the diagnostic class starting from genotype data alone.Supervised ANNs are networks which learn by examples, calculating an error function during the training phase and adjusting the connection strengths in order to minimize the error function. The learning constraint of the supervised ANNs make their own output coincide with the predefined target. The general form of these ANNs is: y = f, where w* constitutes the set of parameters which best approximate the function.Back Propagation (BP) ANNs [We employed the BP) ANNs . This tyLearning, i.e. the modelling of the input-output relation represented by data, occurs through minimization of the error in output and retropropagation of this to the internal nodes, one hidden units, using the algorithm of the descending gradient in the majority of cases. In particular each weight is corrected by the formula:where for the retropropagated error for the last layer and:for all the other layers.y = f(x) function.In theory, a Back Propagation having a sufficient number of hidden units is able to reconstruct any The BP used in this work was intentionally improved through the use of the SoftMax equation, specific for classification problems :and through the use of the Selfmomentum equation  which apn.where the learning cycle is indicated by From a practical point of view, the Selfmomentum equation allows the solution of all of the problems solved by the Momentum, in a much faster way, maintaining the unitary learning coefficient (Rate = 1).The architecture of ANN BP-FF is an input layer according to the number of selected variables, one hidden layer according to the different input layer . The output layer consisting in one of two prediction targets .We employed as benchmark linear discriminant analysis (LDA) applied on the same training and testing data sets used for ANNs. For the analysis of LDA, the SAS version 6.04  using forward stepwise procedure was employed.Data preprocessing was performed using two different re-sampling criteria of the global dataset.We employed the so-called 5 × 2 cross-validation protocol . In thisThe TWIST system is an ensemble of two algorithms: "Training and Testing" (T&T) and "Imput Selection" (I.S.) algorithm .The T&T system is a robust data resampling technique that is able to arrange the source sample into sub-samples that all possess a similar probability density function. In this way, the data is split into two or more sub-samples in order to train, test and validate the ANN models more effectively. The T&T is based on a population of n ANNs managed by an evolutionary system. In its simplest form, this algorithm reproduces several distribution models of the complete dataset DΓ (one for every ANN of the population) in two subsets . The genome of each "network-individual" thus codifies a data distribution model with an associated validation strategy. The n data distribution models are combined according to their fitness criteria using an evolutionary algorithm. The selection of "network-individuals" based on fitness determines the evolution of the population; that is, the progressive improvement of performance of each network until the optimal performance is reached, which is equivalent to the better division of the global dataset into subsets. The evolutionary algorithm mastering this process, named "Genetic Doping Algorithm" (GenD) (33) has similar characteristics to a genetic algorithm but it's able to maintain an inner instability during the evolution, carrying out a natural increase of biodiversity and a continuous "evolution of the evolution" in the population. The elaboration of T&T is articulated in two phases:DΓ; in this way the configuration that most "suits" the available dataset is determined: the number of layers and hidden units and some possible generalizations of the standard learning law. The parameters thus determined define the configuration and the initialization of all the individual-networks of the population and will then stay fixed in the following computational phase. Basically, during this preliminary phase there is a fine-tuning of the inductor that defines the fitness values of the population's individuals during evolution.- preliminary phase: in this phase an evaluation of the parameters of the fitness function that will be used on the global dataset is performed. During this phase an inductor The accuracy of the ANN performance with the testing set will be the fitness of that individual .- Computational phase: the system extracts from the global dataset the best training and testing sets. During this phase the individual-network of the population is running, according to the established configuration and the initialization parameters. From the evolution of the population, managed by the GenD algorithm, the best distribution of the global dataset D Γ into two subsets is generated, starting from the initial population of possible solutions Parallel to T&T runs I.S. The IS system is an adaptive system, which is also based on the evolutionary algorithm GenD, and which is able to evaluate the relevance of the different variables of the dataset in an intelligent way. Therefore it can be considered on the same level as a feature selection technique. From a formal point of view, I.S. is an artificial organism based on the GenD algorithm and consists of a population of ANN, in which each one carries out a selection of the independent variables on the available database. The elaboration of I.S., as for T&T, is developed in two phases:E0 necessary to train the inductor is determined through preliminary experimental tests.- Preliminary phase: during this phase an inductor - Computational phase: the inductor is active, according to the stabilized configuration and the fixed initialization parameters, to extract the most relevant variables of the training and testing subsets. Each individual-network of the population is trained on the training set The evolution of the individual-network of the population is based on the algorithm GenD. In the I.S. approach the GenD genome is built by n binary values, where n is the cardinality of the original input space. Every gene indicates if an input variable is to be used or not during the evaluation of the population fitness. Through the evolutionary algorithm, the different "hypotheses" of variable selection, generated by each ANNs of the population, change over time, at each generation: this leads to the selection of the best combination of input variables. As in the T&T systems the genetic operators crossover and mutation are applied on the ANNs population; the rates of occurrence for both operators are self-determinated by the system in adaptive way at each generation.When the evolutionary algorithm no longer improves its performance, the process stops, and the best selection of the input variables is employed on the testing subset.In order to improve the speed and the quality of the solutions that have to be optimized, the GenD algorithm makes the evolutionary process of the artificial populations more natural and less centered on the individual liberalism culture.The combined action of T&T and I.S. systems allow us to solve two frequent problems in managing ANNs. Both systems are based on a Genetic Algorithm, the Genetic Doping Algorithm (GenD) developed at Semeion Research Centre .GenD was provided with 100 individuals, generated randomly. Each individual represents a possible distribution of the whole dataset into two subsets. Two independent Multilayers Perceptrons (MLPs) with 4 hidden units, are trained for 100 epochs and tested in blinded manner on the two subsets. A function of the testing results of the two independent MLPs defines the fitness of each individual.A crossover function is applied on the populations of 100 individuals and new individuals are generated. A mutation operator is applied to the new individuals and to the individuals whose fitness is weakest. In the GenD algorithm the rate of crossover and the rate of mutation are self-determined by the system in adaptive way at each generation. This loop is applied for at least 300 generations, or stopped when the system does not show any significant improvement at least from 50 generations. The individual whose distribution of the whole dataset into two subsets is the best one from the blind testing results is saved and then used as optimal distribution to train and test more sophisticated ANNs.We implemented both algorithms in C language and we used a Pentium III CPU to run the system on real data. Around 48 hours were spent for each run. We remind that T&T and I.S. algorithms have to be used only once to train the system. Once trained, the system can answer on line to any new pattern.After this processing, the features that were most significant for the classification were selected and at the same time the training set and the testing set were created with a function of probability distribution similar to the one that provided the best results in the classification.A supervised Multi Layer Perceptron, with four hidden units, was then used for the classification task.We collected 54 patients : 28 males  and 26 females  with a male/female ratio 1.1:1. The site of clinical onset was spinal in 61.1% (33/54) and bulbar in 38.9% (21/54) of cases. The mean disease duration at the time of observation was 3.2 years (range 1–10 years). The frequency of bulbar onset in females (16/29) resulted greater than in males (5/28).All patients were previously screened for SOD1 gene mutation by sequence analysis and no genetic variations were found.Control subjects were 144 males and 67 females; age range 21 to 75 years, (average 38.94).Table Results obtained with Linear Discriminant Analysis were compared with those obtained with a simple Back Propagation approach Table  and 3.In these experiments we applied the random criterion to divide the dataset five times in training and testing sub-sets applying the 5 × 2 Cross Validation protocol.The predictive accuracy obtained with Linear Discriminant Analysis and standard artificial neural networks ranged from 70% to 79% (average 75.31%) and from 69.1 to 86.2% (average 76.6%) respectively.With the TWIST approach, every experiment was conducted in a blind and independent manner in two directions: training with sub-sample A and blind testing with sub-sample B vs training with sub-sample B and blind testing with sub-sample A. The results from the best five applications of TWIST procedures are reported in Table Seven genetic variants were always independently selected by the five TWIST procedures: apolipoprotein E (APOE) (chromosome 19q13.2) arg158cys; hepatic lipase (LIPC) (chromosome 15q21-23) -480 C/T; endothelial nitric oxide synthase (NOS3) (chromosome 7q36) 690 C/T and glu298asp; vitamin K-dependent coagulation factor seven (F7) (chromosome 13q34) arg353glu, glycoprotein Ia/IIa (ITGA2) (chromosome 5q23-q31) 873 G/A; E-selectin (SELE) (chromosome 1q22-q25) ser128arg.Table The number of genetic variants selected four times over five experiments consisted of: peroxisome proliferator activated receptor gamma (PPARG) pro12ala (chromosome 3p25), lipoprotein lipase (LPL) asp9asn (chromosome 8p22), paraoxonase 1 (PON1) met55leu and paraoxonase 2 (PON2) ser311cys (chromosome 7q21.3), tumor necrosis factor beta (TNF beta) thr26 asn (chrom 6p21.3), methylenetetrahydrofolate reductase (MTHFR) 677 C/T (chrom 1p36.3), angiotensin II receptor type1 (AGTR1) 1166 A/C (chromosome 3q21-25), atrial natriuretic peptide (NPPA) 664 G/A (chrom 1p36-21), epithelial Na channel subunit (SCNN1A) trp493arg, (chromosome 12p13), FVII -232 ins/del, SELE leu554phe, Tumor Necrosis Factor alpha  -376 G/A and -308 G/A (chromosome 6p21.3).The TNF beta thr26asn was used as further control. First it was selected by four TWIST systems and later, since the information linked to such a variation was already recruited, none of the TWIST systems selected this SNP.The following gene/genetic variants were never selected by the five TWIST procedures: apolipoprotein A4 (APOA4) (chromosome 11q23) thr347ser; apolipoprotein C3 (APOC3) (chromosome 11q23.1-q23.2) -641 C/A and 482 C/T; beta 3 adrenergic receptor (ADRB3) trp64arg (8p12-p11.2); LPL ser447term; PON1 gln192arg; low density lipoprotein receptor (LDLR) (chromosome 19p13.3) exon 18 NcoI +/-; cholesteryl ester transfer protein (CETP) -631 C/A and -629 C/A (chromosome 16q21); NOS3 922 A/G; G-protein beta 3 subunit (GNB3) 825 C/T (chromosome 12p13); beta 2 adrenergic receptor (ADBR2) arg16gly (chromosome 5q31-q32); beta fibrinogen (FGB) -455 G/A (chromosome 4q28); TNF alfa -238 G/A and TNF beta thr26asn.The mechanism of neurodegeneration in ALS remains an enigma. The major problem is that little is known about the disease mechanism, making candidate gene selection difficult and haphazard. It follows that an unconventional approach of making no a priori assumptions about the location of the variants of interest might be appropriate, provided that a similarly unconventional statistical approach is available to manage the data complexity.Comparison of results obtained using three different analytical approaches , points out the need to employ systems that are really able of handling the disease complexity instead of treating the data with reductionist approaches unable to detect multiple genes of smaller effect in predisposing to the disease. The possibility of obtaining high diagnostic accuracy from limited and selected genetic information using these new analytical tools, shows that even in so-called sporadic ALS the genetic background plays a fundamental role.Another important obstacle in approaching the molecular basis of a rare disease like ALS in a conventional manner, is related to the difficulty of finding a homogeneous sample population large enough to be analysed for a wide number of genetic variants. Artificial neural networks, at variance with the classical statistical tests, can manage complexity even with relatively small samples and the subsequent unbalanced ratio between variables and records. In this connection, it is important to note that adaptive learning algorithms of inference, based on the principle of a functional estimation like artificial neural networks, overcome the problem of dimensionality.Internal validation of the prediction accuracy is one of the most important problems in neural networks analysis. In fact, the restriction of training procedures to only a part of the dataset, generally half of it, causes a potential loss of power to recognize hidden patterns. In this study optimization of the training and testing procedures were addressed using the evolutionary training and testing algorithm, which ensured that the two halves of the dataset contained the same amount of relevant information. Thus, the best division of the whole dataset into a training and a testing set was reached after a finite number of generations. Finally ANNs were able to identify gene combinations  that are likely to produce accurate predictions of ALS for a single individual, regardless of some possible limitations such as Male/Female ratio and age differences among the case and control groups. This study enrolled more than 50 medical cases with an accurate diagnosis of ALS and we were able to test them for 69 SNPs in 35 genes. Although the SALS patients analyzed represent a small cohort, it is nevertheless really representative from an epidemiological point of view .Besides, all ALS patients were previously screened for SOD1 gene mutations with negative results, thus confirming the sporadic nature of the disease. However, the sample size of 54 cases analysed for more than 60 SNPs, prompted us to look for valid, powerful and efficient statistical tools to approach and evaluate our data.On the basis of the observed results some information related to the methodological approaches used can be assumed. The multiarray approach was previously validated by ourselves  and otheIndeed, ApoE arg158cys was selected by all the five TWISTs while the ApoE cys112arg was selected only once. For NOS variants, the position -922 in the promoter region was never selected while the -690 variant in the promoter region too and the non synonymous variant in position 698 were both selected by all the five TWISTs. The two Factor VII and Selectin (SELE) genetic variants both containing the information necessary for the correct attribution to the disease vs healthy status, were selected five times (FVII arg353glu and SELE ser128arg) and four times (FVII del/ins and SELE leu554phe), respectively. The role of the paroxonase in predisposing to ALS disease appears to be confirmed: PON1 met 55leu and PON2 ser311cys were chosen four times, whereas PON1 gln192arg was never. PPARγ pro12ala was chosen four times: we can assume a generic role of this receptor on ALS disease since PPARγ is at the crossroads between lipid metabolism and innate immune response . In addiFew genetic variants were never selected by any of the TWIST procedures. One possible reason is that some information had already been picked up by the systems, e.g. for PON1, NOS and TNF. Moreover, regarding APOA4 and APO C3 variants we observed that they lie on chromosome 11 which may not be at all involved in the disease. Indeed, a very recent paper on genome wide genotyping in ALS , found nFrom a biological point of view, the identified gene variations confirm some of the already known results (ApoE and PON for example) and identify new gene/genetic variations not known to be involved in the disease. Our results strengthen the involvement of oxidative stress as well as angiogenesis (NOS) and immune response (TNF) pathways. Besides, our results shed light on the involvement of lipid pathways . Indeed, a role for polyunsaturated fatty acids has been postulated for the misfolding protein aggregations in several neurodegenerative diseases including familial ALS . FurtherOur study has a major focus on disentangling the effect of interacting multiple low penetrance alleles on complex diseases. We analysed genetic variables within genes possibly involved in the ALS disease and thanks to artificial intelligence agents such as those employed in this study, on the basis of a subset of genetic data only, we were are able to conveniently differentiate ALS cases from control subjects. We still do not know which specific variation within the subset of SNP is linked to the disease, however ANNs are able to discriminate among cases and controls with only seven genetic SNPs.We are aware that this is an exploratory study and that it should be replicated in another and much larger sample size, nevertheless this study offers new insight into genetic markers of sporadic ALS pointing out the existence of a strong genetic background. The data provide useful information to direct future research on the complexity of the genetic profile of ALS subjects.SP carried out the molecular genetic study, participated in the design of the study, coordinated and drafted the manuscript. EG participated in the design of the study, in the statistical analysis, coordinated and drafted the manuscript. MCP participated in genotyping. AM participated in conceiving the study. MB performed the statistical analysis and developed the intelligent systems. All authors read and approved the final manuscript


The phrase "mendelian randomization" has become associated with the use of genetic polymorphisms to uncover causal relationships between phenotypic variables. The statistical methods useful in mendelian randomization are known as instrumental variable techniques. We present an approach to instrumental variable estimation that is useful in family data and is robust to the use of weak instruments. We illustrate our method to measure the causal influence of low-density lipoprotein on high-density lipoprotein, body mass index, triglycerides, and systolic blood pressure. We use the Framingham Heart Study data as distributed to participants in the Genetics Analysis Workshop 16. In epidemiological studies, establishing and measuring causal relationships is of primary importance. Unfortunately, randomization, the most important tool for unraveling causal relationships, is not generally available. Despite advances in study design and statistical adjustment, the possibility of confounding and reverse causation continues to be problematic. In recent years it has been suggested that nature itself has already performed a set of randomized experiments by assigning genes according to Mendel's laws . These gX and Y. Because U is unmeasured, there is no way of estimating the strength of this relationship using ordinary epidemiological methodology such as linear regression. In simplistic terms, the logic behind MR is that G can only affect Y by affecting X. Therefore, an association between G and Y is best explained by a causal relationship between X and Y. In IV methods, we look only at how that part of X which is influenced by G affects Y. In order to do this we need to make at least the following three assumptions [Figure umptions :1. G is not independent of X.2. G is independent of U.3. G is independent of Y given U and X.X and Y.Only Assumption 1 is testable. Assumptions 2 and 3 must be accepted or rejected using subject-specific knowledge. It is well known that there are many potential violations of these conditions when using MR. Such problems include: linkage disequilibrium, pleiotropy, population stratification, and canalization [IV techniques are well known tools in econometrics, and there is an extensive body of literature discussing the properties of various estimators. Popular methods of estimation include two-stage least-squares regression and limited information maximum-likelihood estimation . These mWith few exceptions to date, discussions of MR have focused on population data. However, there is a large amount of existing family data, and there are well known advantages to family-based studies. For example, MR may provide the ability to check for mendelian errors, and it may provide protection against population stratification . In thisLDLR (OMIM 606945) and APOB genes (OMIM 107730), because they have direct influences on LDL. We make some additional comments in justification of our approach in the discussion.We apply this approach to measure the causal relationship between low-density lipoprotein levels (LDL) and the variables high-density lipoprotein (HDL), triglycerides (TG), body mass index (BMI), and systolic blood pressure (SBP) in the Framingham Heart Study data as distributed to participants in the Genetic Analysis Workshop 16 (GAW16) as Problem 2. For our IV we use single-nucleotide polymorphisms (SNPs) from the 50 k data set, which are in or near the LDLR gene in this data set. To select SNPs from APOB we compared the available SNPs to those analyzed in an independent sample by Benn et al. [p-value less than 0.001, appeared to be acting in an additive manner, and were shared in common with the Framingham Heart Study 50 k SNP data. These SNPs were rs1042031 and rs679899.We utilized the 50 k genotype data for all three cohorts of the Framingham Heart Study data. Data were obtained and used in compliance with the data use agreement and the Case Western Reserve University Institutional Review Board. We found only one SNP rs2738457) in the 38457 in LDL was calculated using the Friedewald equation. In order to deal with possible heterogeneity of effect and make use of the multiple visits, each of the phenotypic observations was stratified by age at examination. The following strata were used: 0-29, 30-44, 45-60, and over 60 years of age. An approximate year of birth for each individual was calculated as the mean difference between the approximate exam date and the age at exam. All phenotype variables besides age and approximate year of birth were log-transformed for analysis in ASSOC (S.A.G.E. v5.4.1). In all analysis, the mean centered year of birth, age, and sex were used as covariates. SBP was adjusted by adding 10 to those on treatment .K pedigrees and nk individuals in each pedigree. Suppose also that xk and yk are nk × 1 vectors representing the variables X and Y in Figure k is a nk × t matrix representing coded genotypes, and Ak and Bk represent matrices of covariates for xk and yk respectively. Let y and G be defined analogously. We assume the following two linear structural equations:Suppose there are exk and eyk are (possibly) correlated error terms. A variance-component model is assumed to describe the covariance structure Here, βxy is the parameter that represents the causal effect size. Suppose that we wish to test the hypothesis H0 : βxy = βH. The basic approach we suggest here is to form a new traitNote that Combining Eq. (3) with Eqs. (2) and (1), we obtainerk. Under the model assumptions, r(βH) is independent of G given the covariates if and only if βxy = βH. Hence, we may test the hypothesis H0 : βxy = βH using some form of a family-based genetic association test. The test may be recomputed along an entire grid of values. Those values that are rejected at some alpha level lie outside the confidence interval. If the association between G and x is not statistically significant, then in most cases the confidence interval will cover the entire real line. For finite samples it is also possible that the confidence interval is the null set.for suitably defined βxy. We then ran ASSOC iteratively over a grid of values for βH between the end points. Values for which the maximization algorithm clearly did not properly converge were not used. We used cubic spline interpolation as implemented in the R function "splinefun" to find the boundaries on the confidence interval and the point estimate. As a point estimate we used the maximum p-value.We have chosen to use the method implemented in the program ASSOC of S.A.G.E. (v5.4.1) to test for genetic association. This family-based test of association between markers and a continuous phenotype developed by George and Elston  allows fR2 values reported below are calculated as N1 and N2 are the total number of non-missing observations on x and G, respectively.We also used ASSOC to assess the causal relationships directly. We have labelled this method as "regression" below, although it is not strictly a linear regression because the familial correlation is accounted for using the same variance-component model described above. The As mentioned in the Introduction, we chose to look at the effect of LDL on a number of other variables : Single-nucleotide polymorphism; TG: Triglycerides.The authors declare that they have no competing interests.NJM conceived of the statistical method, analyzed the data, and drafted the manuscript. CG-M helped select the traits and advised on the epidemiological aspects of the study. CMS contributed to the statistical development and writing of the paper.


We have developed a graphical display tool called SIMLAPLOT for visualizing different ways in which continuous covariates may influence the genotype-specific risk for complex human diseases. The purpose of our study was to examine continuous covariates in the Genetic Analysis Workshop 15 simulated data set using our novel graphical display tool, with knowledge of the answers. The generated plots provide information about genetic models for the simulated continuous covariates and may help identify the single-nucleotide polymorphisms associated with the underlying quantitative trait loci. One of the most challenging aspects of complex genetic traits is developing intuition regarding genotype × phenotype relationships across the distribution of a continuous covariate. Standard family-based and case-control association tests do not directly examine the role of continuous disease-related covariates in genetic models. Such covariates may themselves have a genetic basis in the form of a quantitative trait locus (QTL), or they may interact statistically with one or more susceptibility genes (gene × environment (G × E) interaction). A third possibility is that they may define more homogeneous subgroups of patients or families, in which the main effect of a particular susceptibility gene is more easily detected. While family-based designs offer protection against spurious associations as a result of population stratification, they are known to be less efficient than case-control designs for some disease models. Case-control designs may also have advantages over family-based designs in terms of distinguishing QTL models from G × E interaction models. To improve our understanding of a variety of complex genetic models used in simulation studies, we developed a novel graphical display tool, SIMLAPLOT, which produces plots of the relationship between affection status, continuous covariate values, and marker genotypes. SIMLAPLOT provides a way to examine genetic model parameters for continuous traits and to evaluate models by comparing plots from observed data to theoretical model plots. By applying SIMLAPLOT to the simulated Genetic Analysis Workshop 15 (GAW15) data, our goal was to identify the SNPs in highest linkage disequilibrium (LD) with simulated QTLs underlying measured continuous covariates and to characterize the corresponding genetic models qualitatively.SIMLAPLOT is a supplement to the simulation program SIMLA . SIMLA uAFF = 1 if affected and AFF = 0 otherwise. G codes for the three possible genotypes  at a bi-allelic susceptibility locus or nearby marker based on the user-specified mode of inheritance . β1 is the log-transformed odds ratio for the susceptibility locus. E is a continuous, normally distributed covariate; it can be an environmental risk factor, an endophenotype, or a quantitative trait, which depends on an underlying QTL. β2 is the log-transformed odds ratio for a user-specified one-unit increase of the continuous covariate. G × E is defined as the product of G and E, and β3 is the log-transformed odds ratio for this interaction term. β0 adjusts for the user-specified disease prevalence in the population of simulated individuals.where SIMLAPLOT evaluates QTL models, G × E interaction models, and genetic main effect models with covariate-defined heterogeneity. It produces four types of plots to explore different aspects of the relationship between affection status, continuous covariate values and marker genotypes in each model.E, if E is a risk factor for the simulated disease phenotype, either alone or in combination with genetic susceptibility.Three penetrance curves, one for each genotype, are produced. These curves display changes in penetrance as a function of E if the genotypes correspond to a QTL, if there is interaction with an environmental covariate, or if E is an indicator of genetic heterogeneity.Three frequency curves, one for each genotype, are produced. At each point on the x-axis, the sum of the three frequencies is 1.0. The respective frequencies change as a function of E, or the strength of G × E interaction.The covariate distributions are plotted for each genotype, separately for affected and unaffected individuals. The comparison of the two plots reflects the main effect of E, which may or may not be genotype-dependent, allele frequency for the susceptibility locus, QTL or nearby marker, all relevant odds ratios, the mode of inheritance, and the type of model . Some parameters, such as genotype-specific means and variances, can be estimated from an existing data set, and some parameters are approximated based on the assumed model, e.g., QTL. SIMPLAPLOT also produces the same types of plots based on the observed data (data-based). Comparison of the observed to the theoretical distributions may suggest an appropriate model for the observed data set. To produce these plots SIMLAPLOT uses a kernel density estimate of the form b [SIMLAPLOT will plot the theoretical conditional distributions for the different models given the following input parameters: mean and standard deviation for  width b . Kernel  width b .p-Values and their ranks were obtained for all 100 simulated replicates.We applied SIMLAPLOT to the GAW15 simulated data sets using the quantitative covariates IgM, anti-CCP (anti-cyclic citrinullated protein), and severity of RA (rheumatoid arthritis). We analyzed all SNP markers on chromosomes 9, 11, and 18. Because covariate values exist only for affected individuals, we specified a relative risk of 1.0 and focused on two types of plots: the conditional genotype probability (plot type 2) and the covariate distribution for each genotype in affecteds (plot type 3). The input parameters for an assumed QTL model (plots labeled "model-based"), such as genotype-specific mean and variance, were estimated from the observed data for the specified SNP. We demonstrate SIMLAPLOT with data from Replicate 1. To evaluate our qualitative conclusions, we performed quantitative trait association analysis using the Monks-Kaplan method . p-ValueWhen SIMLAPLOT was applied to the continuous covariate IgM with markers on chromosome 11, three markers  were identified as potential QTL loci Figs. . Figure p-value ranged from 10-29 to 10-42. The next most significant SNPs were 387 and 388, with p-values lower than 10-5.Figure p-value of all SNPs on chromosome 18 for all replicates of the simulated data. SNP 270 was excluded as a QTL by QTDT, since the Monks-Kaplan test was not significant in 92% of the simulated replicates  plots of conditional genotype distributions across covariate values are compared. SIMLAPLOT may also help differentiate QTL models from interaction and heterogeneity models involving continuous covariates by comparing plots for affected and unaffected individuals.The author(s) declare that they have no competing interests.


Because multiple loci control complex diseases, there is great interest in testing markers simultaneously instead of one by one. In this paper, we applied two model selection algorithms: the stochastic search variable selection (SSVS) and the least absolute shrinkage and selection operator (LASSO) to two quantitative phenotypes related to rheumatoid arthritis (RA).LRRC8D, LRP1B, and COLEC12. These genes have not been reported to be associated with RA. LASSO also identified a common locus on gene KTCD21 for the two phenotypes .The Genetic Analysis Workshop 16 data includes 2,062 unrelated individuals and 545,080 single-nucleotide polymorphism markers from the Illumina 550 k chip. We performed our analyses on the cases as the quantitative phenotype data was not provided for the controls. The performance of the two algorithms was compared. Using sure independence screening as the prescreening procedure, both SSVS and LASSO give small models. No markers are identified in the human leukocyte antigen region of chromosome 6 that was shown to be associated with RA. SSVS and LASSO identify seven common loci, and some of them are on genes SSVS outperforms LASSO in simulation studies. Both SSVS and LASSO give small models on the RA data, however this depends on model parameters. We also demonstrate the ability of both LASSO and SSVS to handle more markers than the number of samples. It is now feasible to perform large-scale, high-density genome-wide association studies (GWAS) to search for common genetic variants underlying common diseases . Due γ is introduced to perform variable selection for regression models. If γj = 1 the jth variable is included in the model; if γj = 0, the jth variable is excluded from the model. A homogenous ergodic Markov chain can be generated by the Gibbs sampler. The empirical distribution of γ based on the Markov chain will converge to the actual posterior distribution of γ  is n × p, β = , and θ2 is scalar.where γi is defined as the indicator whether marker i is selected in the model or not. SSVS uses the idea that the true posterior distribution of γi values can be estimated by generating a Markov chain that converges to its stationary distribution. βi values are distributed according to a mixture distribution of two normal distributions with different variances, which enables the detection of associated variables:A latent variable γ is selected as a Bernoulli prior with the same parameter over all the γi values:The prior for p) to other values such as 0.1,0.2,...,0.9 does not significantly change the power of SSVS (data not shown). The distribution of θ2 conditional on γ is given byUsing simulation studies, we confirmed that changing . These causal markers were always included in the analysis. The phenotype was simulated from a linear model with the five causal markers:εi values are independent and identically distributed N. Different marker densities, coefficients (β), and SSVS parameters were considered. For each scenario, 1,000 simulations were performed. The average area under the curve (AUC) was calculated for each scenario. The AUC is the area under the receiver operator characteristic (ROC) curve, which is a plot of the sensitivity versus (1-specificity). An AUC of 0.5 represents a completely random guess. For SSVS, the AUC is calculated using the following formula modified from the method of Ma and Huang [where the nd Huang :C is the set of indices of the causal markers and Cc is the set of indices of the non-causal markers. nc and where λi is the iteration at which the ith marker enters the model.where X denotes the genotype data that are standardized columnwise, and y denotes the phenotype data, then w is defined asThe genotype was coded as 0 for homozygous rare alleles, 1 for heterozygous alleles, and 2 for homozygous common alleles. Missing alleles were imputed according to the genotype frequency calculated from the available data for 0.7% of missing genotype data. As a prescreening step, markers with a minor allele frequency less than 0.01 were discarded. The phenotype data was log-transformed. To decrease the dimensionality of the marker data, sure independence screening (SIS) was performed . SIS useSIS selects the largest component-wise magnitudes of the vector. Here, we selected the 1,000 markers with the largest correlations with the quantitative traits for SSVS and LASSO. Because the number of samples are 746 and 867 for the IgM and the anti-CCP phenotypes, respectively, we demonstrate the use of SSVS and LASSO to select a model in which the number of markers is greater than the number of samples. SIS reduces computational time required by the model-selection methods. SIS has been shown to retain important variables in the screened model with a large probability when a set of conditions are satisfied .σ = 0.05 for SSVS and the values of τ were chosen according to the suggested ratios of β is small , LASSO performs worse than the single-marker F-test. In other scenarios, LASSO performs better than the single-marker F-test.In the simulation studies, we considered different marker densities, causal marker effects, and SSVS parameters. We also compared the two methods with a standard single-marker F-test. The results are summarized in Table cCulloch . When thMarkers with a minor allele frequency less than 0.01 were screened out. After this step, 425,555 markers for the IgM phenotype and 425,586 markers for the anti-CCP phenotype remained. After removing the samples with missing phenotypes, 746 samples for the IgM phenotype and 867 samples for the anti-CCP phenotype were left. The correlation between the phenotype and the genotype was calculated. The top 1,000 markers were chosen for each of the two phenotypes. Then, SSVS and LASSO were run on both phenotypes.σ = 0.05 and τ = 1,2,3, were used such that σ = 0.05 and τ = 1 are shown in Figure For SSVS, we used a cutoff of 0.9 for the posterior probabilities of markers being included in the model. The parameter values in the simulation studies, KTCD21 at chromosome location 11q14.1. These markers have been enclosed in a diamond in Figure The LASSO algorithm was run for 500 iterations unless it terminated earlier automatically because there were no more significant markers. The optimal cut-off for the number of iterations was selected using a 10-fold cross-validation. The minimum cross-validation error was achieved at 31 iterations for the IgM phenotype and at 33 iterations for the anti-CCP phenotype. It identified 31 significant markers for the IgM phenotype and 33 for the anti-CCP phenotype. The marker positions are also shown in Figure LRRC8D on chromosome 1 . On chromosome 4, SSVS selected rs192068 and LASSO selected rs1540052, while on chromosome 10, SSVS selected rs807013 and LASSO selected rs17113682 (enclosed by triangles). Both marker pairs are within 100 kb of each other, but neither of them are located on annotated genes. SSVS and LASSO selected two common markers, rs2186830 and rs334438, on chromosome 18 (enclosed by triangles). Among them, marker rs2186830 is located on the gene COLEC12. None of these genes have been reported to be associated with RA in the literature.SSVS and LASSO identified a few common loci for the IgM phenotype and the anti-CCP phenotype. For the IgM phenotype, SSVS selected rs1938032 and LASSO selected rs12032393; both markers are located on the gene γ values, we did not see a significant difference in the power of SSVS (data not shown). However, changing σ and τ will change the results. Further study is required on how to select these parameters. On the other hand, LASSO is very fast and hence the model is selected very quickly. It can handle large number of markers because the computational time in each step is proportional to the size of the model at that iteration. However, a big problem with LASSO is the selection of the cut-off. The Cp type score mentioned in Efron et al. [β values. The problem of overshrinking can be minimized by using different penalties for different coefficients, which is performed in the adaptive LASSO [SSVS and LASSO have advantages and disadvantages in their application to the model selection problem. SSVS is computationally intensive and cannot handle a very large set of markers. Hence, a more aggressive marker screening step needs to be done. The Gibbs sampler also requires the selection of prior parameters. In our simulation studies, by changing the prior of the n et al.  does notve LASSO . In addiβ), the best results were achieved by different values of τ. SSVS with τ = 1 had the maximum power compared with other values of τ. While for β = 2, SSVS with τ = 2 has the maximum power compared to τ = 1,3. It indicates that different values of hyper-parameters are required to detect markers with different effects.For SSVS, we found that for different marker coeffcients  region on chromosome 6 has been reported to be associated with the disease by various association and linkage studies ,12. HoweIn this paper, we compared SSVS and LASSO on simulated and real data. SSVS outperforms LASSO as well as the single-marker F-test in the simulation studies. The two methods were compared on the RA data provided by the Genetic Analysis Workshop 16 workshop after a dimension reduction using the SIS. Association studies were carried out for the two quantitative phenotypes using the two algorithms. The two methods identified two common markers for the anti-CCP antibody phenotype and two and three marker pairs that are located close to each other for the rheumatoid factor IgM phenotype and the anti-CCP antibody phenotype, respectively.LRRC8D, LRP1B, and COLEC12. However these genes have not been reported to be associated with RA. In summary, SSVS and LASSO are very useful tools in GWAS studies for quantitative data.Some of these markers were found to be in annotated genes such as anti-CCP: Anti-cyclic citrullinated peptide; AUC: Area under the curve; GWAS: Genome-wide association study; HLA: Human leukocyte antigen; IgM: Immunoglobulin M; LARS: Least angle regression; LASSO: Least absolute shrinkage and selection operator; RA: Rheumatoid arthritis; ROC: Receiver operator characteristic; SIS: Sure independence screening; SSVS: Stochastic search variable selection.The authors declare that they have no competing interests.SS participated in the design of the study, performed the statistical analysis and helped to draft the manuscript. LC conceived of the study, and participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.


Genome-wide association studies are often limited in their ability to attain their full potential due to the sheer volume of information created. We sought to use the random forest algorithm to identify single-nucleotide polymorphisms (SNPs) that may be involved in gene-by-smoking interactions related to the early-onset of coronary heart disease.Using data from the Framingham Heart Study, our analysis used a case-only design in which the outcome of interest was age of onset of early coronary heart disease.Smoking status was dichotomized as ever versus never. The single SNP with the highest importance score assigned by random forests was rs2011345. This SNP was not associated with age alone in the control subjects. Using generalized estimating equations to adjust for sex and account for familial correlation, there was evidence of an interaction between rs2011345 and smoking status.The results of this analysis suggest that random forests may be a useful tool for identifying SNPs taking part in gene-by-environment interactions in genome-wide association studies. The prospects and promises of the completed Human Genome Project include improvement in the development of novel therapeutics, intervention strategies for personalized treatment of common diseases, and new diagnostic methods for both rare and common diseases. While completion of the project took years, recent technological advances have reduced costs such that genome-wide association studies (GWAS) are a popular design for genetic epidemiological studies. However, the computational matrix remains daunting, often with genotypes from several hundred thousand SNPs collected on thousands of individuals.Coronary heart disease (CHD) is a common disorder with multiple risk factors and a recognized likelihood of significant gene-by-environment interactions. As an example, a candidate gene approach has shown that the hazard ratio of composite cardiovascular disease is elevated preferentially in smokers having the APOE ε4 allele, with a significant interaction between genotype and smoking status ,2.Though GWAS may include hundreds of thousands of single-nucleotide polymorphisms (SNPs), current computational and practical limitations often prevent researchers from fully exploiting the genetic information available. The rate at which genetic data are generated greatly outpaces our ability to fully analyze them. Many studies are faced with difficult choices to make the analyses feasible. Even though there is evidence that many diseases do not follow the single-gene mendelian inheritance model, genetic analyses frequently cannot account for all possible interactions due to limited computational resources.p-values. As a part of Genetic Analysis Workshop 16 (GAW16), this paper explores the ability of RF algorithms to identify SNPs that may be involved in gene-by-smoking interactions related to our outcome of interest, age of early onset CHD.For these reasons, machine learning has become increasingly popular with large genetic datasets. Machine learning involves iterative building of predictive models from complex datasets, and has the potential to resolve these genome-wide computational challenges. The random forest (RF) algorithm, a type of machine learning, can be used to reduce the data and identify potential gene-by-environment interactions. This approach is an appealing alternative to other analytical methods for GWAS that typically base selection of "significance" entirely on The Framingham Heart Study (FHS) GWAS data (GAW16 Problem 2) was used in this analysis. The data includes genotype, phenotype, environmental exposure status, and family structure information on 7,130 participants from three enrolment periods with cohort follow-up of over 100,000 person-years (estimated). Local institutional review board approval was obtained.We used age at incident of CHD or censoring as the outcome variable. Hard CHD was classified as recognized myocardial infarction diagnosed through an electrocardiogram or enzymes, coronary insufficiency, or death attributed to CHD. The Third Generation of FHS was excluded from analyses because there was no follow-up information available beyond enrollment, there were only 26 cases of CHD, and most of these were considered previously existing due to minimal information at the enrollment visit regarding the CHD incident date.p < 0.001; 12,622 SNPs). A total of 355,649 SNPs met all quality-control criteria. Additionally, 29 individuals missing data for >5% of the SNPs were removed.Dense genotyping of approximately 550,000 SNPs across 22 autosomal chromosomes for each FHS subject was performed by Affymetrix using the 250 k Sty, 250 k Nsp, and the supplemental 50 k platforms (GeneChip Human Mapping 500 k Array Set and the 50 k Human Gene Focused Panel). Quality control of the genotype data was performed with PLINK v1.0.3 . SNPs wePhenotype and exposure information were tabulated with SAS v9.1.3  and a categorical ever/never smoking status variable was created using the most recent data from a visit before incident CHD. To account for potential period effects, we estimated the decade of birth for each participant and created a categorical variable for each decade. While the RF algorithm cannot account for pedigree explicitly, we created binary indicators for each family ID to include as covariates. We used perl scripts for data management, creating a singe flat file that merged genotype, pedigree, phenotype, and exposure data.L and R, so as to maximize the heuristic best-split criterion:The RF algorithm is a machine-learning classifier made up of many decision trees and has qualities well suited for genome-wide, gene-by-environment and gene-by-gene interaction studies . Each trL and R are partitioned by left and right child nodes, respectively, and terminates when the partitions are sufficiently small. The resulting terminal nodes are assigned values equal to the mean of the outcome  in the corresponding partitions. This process is repeated to produce many decision trees (a forest) whose predicted outcomes are combined into a single value by taking a majority vote  or finding the mean value . The data that were excluded from the training set form the testing set, which is used to gauge the accuracy of a tree. To measure the importance of a particular variable on a given tree, the values of that variable are randomly permuted among the data in the testing set and the predictions are recomputed. The difference between the two predictions provides a measure of variable importance, with important variables showing a larger discrepancy between the predictions.The procedure continues recursively, so that the subsets with replacement from the total pool of 224 cases via bootstrap aggregating, a process that allows for simulation of larger data sets and minimizes overfitting that can occur in traditional training/validation set design. Following Breiman's recommendations, one-third of the input variables  were randomly chosen for consideration at each node in a decision tree, and the variable from this subset that produced the best (heuristic) split was found. The tree nodes were recursively split until at most five cases remained in each terminal node.The RF was run using a derivative of the publicly available RF regression code , rewrittThe inclusion in the data set of multiple members from a single family could result in a SNP mistakenly being reported as important. To guard against this possibility, the importance of the family ID variable was also measured. If a SNP appeared to be important solely due to similarity between family members, then the family ID variable would also be reported as important.SNPs identified as important by RF for determining the outcome (age of CHD onset) were run in the controls to determine whether the association was age-related. Smoking status was treated as a simple covariate in the RF model. The interaction between the SNP, smoking status, and CHD was then determined using generalized estimating equations (GEE) via PROC GENMOD in SAS to account for family structure and adjust for sex. The number of alleles was treated as a class variable, therefore assuming no genetic model.p-value = 0.002). In the 0-allele group, non-smokers had a mean age of incident CHD of 75.1 yr compared to 70.7 yr among smokers . There was a statistically significant difference between smokers and non-smokers in the 1-allele group, where non-smokers had a higher mean age of incident CHD compared to smokers (67.7 vs. 61.3 yr), with a Wald p-value of 0.003. The 2-allele group did not differ statistically , but the direction of the relationship differed such that smokers had a slightly higher mean age of incident CHD (62.8 vs. 66.2 yr). Similar results were obtained using t-tests when ignoring family membership and when different correlation matrices were specified in the GEE procedure.From the combined Original Cohort and Offspring Cohort of FHS, there were 224 incident CHD cases and 2,909 controls with complete data meeting the quality control criteria discussed above; 166 of the cases were classified as ever-smoked at the visit before the incident event, and of the 224 cases, there were 167 unique family IDs  and only 38 cases were a first-degree relative of one of the other cases. Among controls, 1,530 were classified as "ever smoked" at the last visit with available data. The RF algorithm generates a variable importance score for each variable included in the analysis. After ranking the covariate importance score in each of four runs of RF using 500 trees each, there was one SNP (rs2011345) that ranked as the most important SNP and within the top 10 of all ranked covariates in three of the four runs  in a sex-adjusted model, and only the 29,776th smallest p-value (p = 0.079) for the sex-adjusted SNP-by-smoking status interaction model in PLINK . Other important covariates identified by the RF runs included sex, smoking status, and decade of birth--the latter picking up a potential survival bias where older individuals included in the study are more likely to have a later age of onset.The optimized RF algorithm identified smoking status and the rs2011345 SNP as important classifiers in RF. Subsequent regression models confirmed that the SNP and smoking status had significant main effects with the outcome, and also a significant interaction. While RF deemed this SNP important, it may have been overlooked had the analysis been based exclusively on regression and FMO4, Map Viewer build 36.3). This region appears to be in linkage disequilibrium with the last two exons of FMO4 in the CEU cohort from the HapMap project (build 36). This gene is part of a family of enzymes involved in the metabolism of nicotine and other tobacco-related products. Additionally, this region (1q24) has been linked to essential hypertension [Whereas the relative magnitude of this interaction compared with all other potential interactions is presently untested, the following correlative information is of interest. SNP rs2011345 is approximately 11 kb from the 3' end of the flavin-containing monooxygenase 4 gene (rtension . Thus, tOur study has a few limitations. First, sample size limitations should be considered; while the interaction between rs2011345 and smoking was statistically significant, the study contained only 224 incident cases of CHD. Second, the interpretation of results is also limited by a relatively crude measure of smoking exposure. The available information on smoking behavior only provided a cross-sectional glimpse of the subject's smoking habits and, in some cases, incident CHD occurred a decade or more after the last known smoking status. Furthermore, the RF algorithm cannot account for familial correlation using traditional approaches. However, we were able to confirm the RF findings using a GEE model that accounts for familial correlation. While the 224 cases in this analysis did not have a large degree of relatedness, it could be an issue in the larger FHS population.p-value based methods. Nonetheless, it appears as though RF can provide an alternative to traditional regression techniques to reduce the high-dimensional data space of GWAS searching for gene-by-environment interactions.Future work addressing practical issues of RF may enhance its attractiveness as an analysis tool for GWAS. We used runs of 500 trees in this analysis and found the top covariates in the output to be more stable than in runs of 200 trees. Runs of 1,000 and 1,500 trees did not produce markedly different results. Another important problem is reconciling the different SNPs identified by RF with traditional CHD: Coronary heart disease; FHS: Framingham Heart Study; GAW: Genetic Analysis Workshop; GEE: Generalized estimating equations; GWAS: Genome-wide association studies; RF: Random forests; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.MJM contributed to the study design, data manipulation, reduction, non-RF statistical analyses, and drafted sections of the manuscript. LCD contributed to the conception and development of the study design, review of the literature, and drafted sections of the manuscript. AL programmed and ran the RF analysis and drafted sections of the manuscript. KJM provided statistical and methodological consultation. CDE and HGS supervised the work on this paper as part of the Genetic Analysis Workshop and provided assistance with the data manipulation. All authors participated in the review, discussion, and critiquing of the drafts of this paper.


More specifically, we adapt the multivariate logistic model, which is often used in segregation analysis and can allow for the family correlation structure, for association analysis. To correct the effect of hidden population structure, the first ten principal-components calculated from the matrix of marker genotype data are incorporated as covariates in the model. To test for the association, the marker of interest is also incorporated as a covariate in the model. We applied the proposed method to the second generation , in the Genetic Analysis Workshop 16 Framingham Heart Study 50 k data set to evaluate the performance of the method. Although there may have been difficulty in the convergence while maximizing the likelihood function as indicated by a flat likelihood, the distribution of the empirical  To overcome a potential problem ("spurious" association) caused by population stratification in population-based association studies, several methods have been proposed recently. These approaches are favored because unrelated case-control studies are considered more powerful and easier for collecting DNA samples than family-based studies.X2 to X2/λ, where λ can be estimated by using genomic marker data, and the adjusted statistic follows a chi-square distribution [X2(δ) with noncentrality parameter δ. The GC method is dependent on the estimate of λ, which is dependent on the markers selected for controlling the effect of population stratification and may result in either a conservative or liberal test statistic [The "Genomic Control" (GC) method adjusts the standard chi-square statistic ribution -4. When tatistic ,6.Another approach, named "Structured Association" (SA), is a Markov-chain Monte Carlo (MCMC)-based method that uses independent genomic markers to infer the number of subpopulations and the ancestry probabilities of individuals from putative unstructured subpopulations, and this inferred information is further used in the test for association ,7. The mRecently, principal-component analysis (PCA)-based methods, which calculate the principal components of marker genotype data to represent the genetic background, have been widely used in association studies ,9-13. SpIn this report, we propose a method to test the association between a binary trait and a marker by using a segregation model that allows for the family correlation structure. We apply an idea similar to Zhu et al.'s  to correWe use a regression model to specify a phenotype as a function of the genotype of a single nucleotide polymorphism (SNP) of interest. Because our focus is on binary traits, we apply the usual approach of logistic regression. We summarize the genotype data by a principal-component analysis to extrapolate axes of genetic variation that are defined as the top eigenvectors of a covariance matrix between samples. In data sets with population structure, axes of variation often have a geographic interpretation . Thus, iNf nuclear families, Nd unrelated cases, and Nc unrelated controls. For nuclear families, assume there are ki members in the ith family with the first two (j = 1 or 2) being the father and mother. Then we have in total N families with ki = 1 if i > Nf. In this way we define each unrelated case or unrelated control as a separate family of size one. That is, we have N = Nf + Nd+ Nc families. Let yij be the binary trait value, taking on the value 0 if unaffected and 1 if affected, for the jth individual in the ith family. Let gij be the marker genotypic value of the jth individual in the ith family, coded according to an additive mode of inheritance. M diallelic markers are genotyped. Let Xij =  be a column vector of the marker genotypic values for the jth individual in the ith family with xijl = 0,1, or 2, corresponding to a homozygote, the heterozygote, and the other homozygote, l = 1,2, ..., M We perform a PCA to summarize the marker data, but for this we only use unrelated individuals, i.e., the parents in each family and the unrelated cases and controls, because a naive PCA with all the available data will result in biased directions of maximum variability for the data. LetConsider samples that include both family and unrelated individuals. For simplicity, we only consider nuclear families. Suppose our data contain X. Let el be the lth eigenvector corresponding to the lth largest eigenvalue of Σ, l = 1, 2, ..., M. The lth principal component for individual j of family i, tijl, can be calculated by tijl =  of the ith family is [where amily is :Bij = β0 + βggij + β1tij1+ βLtijL + βIIij, and δi1, δi2, δi3 and δi4 are parameters that, respectively, measure the association between parent 1 and offspring, parent 2 and offspring, sib-pairs, and spouse pairs. These δi values take values in the range: Bij, Bil and where L is the product of the likelihoods for all families, δi4 = 0, i.e., husband and wife were assumed to be independent, and we further assumed all the remaining δ values are the same. Because our null hypothesis is no association, H0: βg = 0, rather than testing for a major gene, we maximized the likelihood function under the no major gene model, i.e., we assumed a single multivariate logistic distribution rather than a mixture of such distributions, which would be necessary for segregation. We used the Wald statistic to test the null hypothesis.The overall likelihood S.A.G.E. , which iWe applied our method to the GAW16 Framingham Heart Study 50 k data set. We only used the second generation, i.e., the Offspring Cohort. The founders of each family were included to calculate the principal components. If no founder of a family was available, we randomly chose one individual. The spouses of the Offspring were treated as unrelated individuals. Hypertension was defined based on the data at Examination One. We defined an individual as affected if his/her systolic blood pressure was greater than or equal to 140 mm Hg, or diastolic blood pressure was greater than or equal to 90 mm Hg, or he/she was on medication, and unaffected otherwise.The GAW16 50 k Offspring Cohort Data Set includes 3,850 individuals. Among them, 1,170 individuals were not genotyped and were not used for further analysis. Of the remaining 2,680 individuals, 89 were under the age of 18 and they were also removed because our analyzed phenotype is hypertension. There are 48,028 markers available, of which 6,051 have a missing genotyping rate of over 10% and 8,163 have minor allele frequencies less than 5%. Those 14,214 markers were dropped from any further analysis. Our analysis results were thus based on 2,591 individuals and 33,811 markers.p-values of the association test for all the SNPs were obtained using the software SEGREG in S.A.G.E. [p-values are not reported. The quantile-quantile (Q-Q) plot of the p-values for the rest of markers can be found in Figure p-values does not depart from that under the null hypothesis, suggesting the proposed method has a reasonable type I error rate. Notice that there is one SNP, rs4084639, standing out alone from the rest of the p-values. We next incorporated age, sex, and BMI as covariates in the model. However, this created a flat likelihood, so it is possible that non-convergence of the maximization in SEGREG occurred for 22,027 markers. The Q-Q plot of the p-values for the markers with definite converged maximization is presented in Figure We calculated the principal components for each individual using the remaining 33,811 markers using the software FamCC . The p-vS.A.G.E. . We firsWe proposed a novel association method that adopts the idea of dealing with residual family correlations as has been used for a segregation model for binary traits, but without using the usual mixture distribution that is an essential part of segregation analysis. Meanwhile, the proposed method also incorporates the marker principal components for controlling the effect of population stratification in family data, as proposed by Zhu et al. . One advWe only applied the proposed model to the GAW16 Framingham Heart Study 50 k data set. Because the underlying disease model is unknown we are unable to evaluate the power of the proposed method. Future studies will also include power comparison with the method proposed by Zhu et al.  as well We propose an association method using a segregation analysis based model to deal with family structure while controlling for population structure. By analyzing a real data set from the GAW16 Framingham Heart Study, we showed that the method performs well in the sense of controlling type I error rate, whenever we can be sure that the maximization of the likelihood function is successful.BMI: Body mass index; GAW16: Genetic Analysis Workshop 16; GC: Genomic control; MCMC: Markov-chain Monte Carlo; MLE: Maximum likelihood estimate; PCA: Principal-component analysis; Q-Q: Quartile-quartile; SA: Structured association.The authors declare that they have no competing interests.XZ and JA designed the methods. QF, TF, and YS performed the data quality control. QF analyzed the data. QF, XZ, and RCE interpreted the results and wrote the paper. All authors read and approved the final manuscript.