A Testing Framework for Identifying Susceptibility Genes in the Presence of Epistasis
2005; Elsevier BV; Volume: 78; Issue: 1 Linguagem: Inglês
10.1086/498850
ISSN1537-6605
AutoresJoshua Millstein, David V. Conti, Frank D. Gilliland, W. James Gauderman,
Tópico(s)Gene expression and cancer classification
ResumoAn efficient testing strategy called the “focused interaction testing framework” (FITF) was developed to identify susceptibility genes involved in epistatic interactions for case-control studies of candidate genes. In the FITF approach, likelihood-ratio tests are performed in stages that increase in the order of interaction considered. Joint tests of main effects and interactions are performed conditional on significant lower-order effects. A reduction in the number of tests performed is achieved by prescreening gene combinations with a goodness-of-fit χ2 statistic that depends on association among candidate genes in the pooled case-control group. Multiple testing is accounted for by controlling false-discovery rates. Simulation analysis demonstrated that the FITF approach is more powerful than marginal tests of candidate genes. FITF also outperformed multifactor dimensionality reduction when interactions involved additive, dominant, or recessive genes. In an application to asthma case-control data from the Children’s Health Study, FITF identified a significant multilocus effect between the nicotinamide adenine dinucleotide (phosphate) reduced:quinone oxidoreductase gene (NQO1), myeloperoxidase gene (MPO), and catalase gene (CAT) (unadjusted P=.00026), three genes that are involved in the oxidative stress pathway. In an independent data set consisting primarily of African American and Asian American children, these three genes also showed a significant association with asthma status (P=.0008). An efficient testing strategy called the “focused interaction testing framework” (FITF) was developed to identify susceptibility genes involved in epistatic interactions for case-control studies of candidate genes. In the FITF approach, likelihood-ratio tests are performed in stages that increase in the order of interaction considered. Joint tests of main effects and interactions are performed conditional on significant lower-order effects. A reduction in the number of tests performed is achieved by prescreening gene combinations with a goodness-of-fit χ2 statistic that depends on association among candidate genes in the pooled case-control group. Multiple testing is accounted for by controlling false-discovery rates. Simulation analysis demonstrated that the FITF approach is more powerful than marginal tests of candidate genes. FITF also outperformed multifactor dimensionality reduction when interactions involved additive, dominant, or recessive genes. In an application to asthma case-control data from the Children’s Health Study, FITF identified a significant multilocus effect between the nicotinamide adenine dinucleotide (phosphate) reduced:quinone oxidoreductase gene (NQO1), myeloperoxidase gene (MPO), and catalase gene (CAT) (unadjusted P=.00026), three genes that are involved in the oxidative stress pathway. In an independent data set consisting primarily of African American and Asian American children, these three genes also showed a significant association with asthma status (P=.0008). The importance of accounting for gene-gene interactions in the search for susceptibility genes for complex diseases has been widely suggested to explain difficulties in replicating significant findings. Recent human and animal studies of complex diseases have identified susceptibility genes that marginally contribute to a common trait, to a minor extent only or not at all, but that interact significantly in combined analyses (Kuida and Beier Kuida and Beier, 2000Kuida S Beier DR Genetic localization of interacting modifiers affecting severity in a murine model of polycystic kidney disease.Genome Res. 2000; 10: 49-54PubMed Google Scholar; Naber et al. 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The data are divided into 10 equal parts, and the phenotypes of subjects in each 1/10 of the data are predicted by the MDR model derived from the remaining 9/10 of the data. For each 9/10 of the data, several steps are performed. For every set of k genes, MDR classifies each multilocus genotype as “high risk” or “low risk,” depending on the ratio of cases to controls. The subjects in the “high risk” groups are then pooled. The k-gene set that maximizes the cases:controls ratio in the pooled “high risk” group is selected as the “best” gene set. Disease status for subjects in the remaining 1/10 of the data is then predicted on the basis of genotype risk for the “best” gene set. The overall “best” gene set is determined by the data split with the lowest prediction error. Prediction error is averaged over the 10 data splits and is used as a measure of predictive power. Another useful measure, termed “consistency,” is the number of data splits with the same “best” set of factors. We developed a new search strategy designed to identify susceptibility genes among a group of candidate genes in the presence of gene-gene interactions. The candidate genes may be selected for their role in a specific biochemical pathway or from a prior genome scan for linkage. A powerful testing framework based on likelihood-ratio tests (LRTs) is presented here that simultaneously tests multilocus effects across various orders of interaction. Our search strategy also employs a screening statistic to reduce the total number of gene sets that are tested for multilocus effects. We present an assessment of power and type I error from simulation analysis and compare the method's performance with that of MDR. We then apply both our method and MDR to a case-control data set from the CHS that includes 12 candidate loci measured in asthmatic and nonasthmatic subjects. Consider a disease phenotype, D, and a sample of cases (D=1) and controls (D=0) selected from some population. We assume that genotypes are obtained for each subject for a set of diallelic, autosomal candidate loci. For each candidate locus, indexed by i, j, k,…, we define a covariate, G, with possible values 0, 1, or 2, corresponding to genotypes aa, Aa, and AA, respectively. This defines a log-additive coding scheme, a robust approach when the specific genetic model is unknown (Schaid Schaid, 1996Schaid DJ General score tests for associations of genetic markers with disease using cases and their parents.Genet Epidemiol. 1996; 13: 423-449Crossref PubMed Scopus (264) Google Scholar). We note, however, that the methods presented here are readily adaptable to alternative risk models (e.g., dominant, recessive, or codominant). We adopt a logistic model to relate genes to D. For example, the fully saturated model for a set of three candidate genes has the form logit[P(D=1)]=β0+βiGi+βjGj+βkGk+βijGiGj+βikGiGk+βjkGjGk+βijkGiGjGk .(1) The model contains three main effects, three two-way interactions, and one three-way interaction. An analogous saturated model for two genes would be logit[P(D=1)]=β0+βiGi+βjGj+βijGiGj ,(2) whereas a model for a single gene would be logit[P(D=1)]=β0+βiGi .(3) LRTs can be used to identify susceptibility genes by testing the parameters in the above models. An LRT statistic is computed as χ2=2(Lfull−Lreduced), where Lfull is the log-likelihood of the data computed under a fully specified model and Lreduced is the log-likelihood computed under the constraint that one or more parameters equal zero. Under the null hypothesis, this statistic has a χ2 distribution with df equal to the difference in the number of unconstrained parameters between the full and reduced models. Three LRT testing strategies for identification of genes will be considered. The simple model in equation (3) is used to test the null hypothesis βi=0 for each candidate gene. We refer to this test as the marginal test of Gi, since the estimated effect from this model, βi, represents an average of the main effect of Gi and any interactive effects with other loci. With a total of K candidate genes, there are K marginal tests. The threshold for significance is adjusted for multiple testing by controlling false-discovery rates (FDRs) (Benjamini and Hochberg Benjamini and Hochberg, 1995Benjamini Y Hochberg Y Controlling the false discovery rate: a practical and powerful approach to multiple testing.J R Stat Soc Ser B. 1995; 57: 289-300Google Scholar), although other approaches (e.g., Bonferroni adjustment) could be adopted. In brief, Benjamini and Hochberg (Benjamini and Hochberg, 1995Benjamini Y Hochberg Y Controlling the false discovery rate: a practical and powerful approach to multiple testing.J R Stat Soc Ser B. 1995; 57: 289-300Google Scholar) defined FDR as the ratio of the number of falsely rejected null hypotheses to the total number of rejected null hypotheses. They showed that the expected FDR can be controlled by a procedure that applies a cutoff to the unadjusted ordered P values, P(1), P(2),…,P(i),…,P(m). All null hypotheses with P values at or below cutoff t are rejected; specifically, t=max<FENLP=CUBSTYLE=SP(i):P(i)≤iαm} . In this strategy, tests are performed in a series of stages, with an incremental increase in the highest-order interaction parameter considered at each subsequent stage. The first stage tests the main effect of each gene, the second stage tests all possible two-way interactions, the third stage tests all three-way interactions, and so forth. To avoid retesting the same effects, a test in a higher stage (e.g., test of a specific two-way interaction in stage 2) is conditioned on any component factors (e.g., either of the two genes involved in that two-way interaction) that were already declared significant in a lower stage (e.g., stage 1). Gene sets are tested for multilocus effects, whether or not marginal effects were found. Type I error is controlled by dividing the overall α level by the number of stages and allocating this adjusted α level, α*, to each stage. Within each stage, the threshold for significance is adjusted by controlling FDR. The specific stages are as follows. 1.First stage. Perform marginal LRTs of βi for each of the K candidate genes. Declare a test significant if Pi<α*1, where Pi is the P value that corresponds to the ith LRT and α*1 denotes the significance threshold for first-stage tests corrected to control FDR. A total of K tests are conducted in this stage.2.Second stage. For all possible two-gene sets (K(K−1)/2), the full model (eq. [2]) is tested against the reduced model, logit[P(D=1)]=β0+βiGiI()+βjGjI() ,where I() is an indicator function that assumes the value 1 if the corresponding term was statistically significant in a first-stage test and 0 otherwise. Thus, if both βi and βj were statistically significant in the first stage, the reduced model would be β0+βiGi+βjGj, and the interaction between Gi and Gj would be tested in a 1-df test in this second stage. On the other hand, if neither βi nor βj was statistically significant in the first stage, then a 3-df test of βi, βj, and βij would be conducted in the second stage. This selective conditioning is done to avoid retesting effects that have already been declared significant. Significance is declared if Pij<α*2, where Pij is the P value that corresponds to the ijth LRT and α*2 denotes the significance threshold for second-stage tests corrected to control FDR.3.Third stage. All three-gene sets are tested (the number of tests is K(K−1)(K−2)/6) in a fashion similar to the method in stage 2. The saturated model (eq. [1]) is tested against the reduced model, logit[P(D=1)]=β0+βiGiI()+βjGjI()+βkGkI()+βijGiGjI()+βikGiGkI()+βjkGjGkI() ,where, again, the indicator function I() assumes the value 1 if the term was in a model that achieved statistical significance in a previous stage and 0 otherwise. It should be stated explicitly that a model that includes higher-order terms would always include the component lower-order terms. The ITF approach described thus far can be directly generalized to multilocus effects involving four or more genes. It is clear that the number of tests conducted in the ITF method can be quite large when K is large. Adjusting the type I error for so many tests may cause an unacceptable loss in power. We developed a method for prescreening all possible gene sets, to focus attention on those that are most likely to be informative in the ITF. Let Gijk denote a multilocus genotype over a set of three candidate genes i, j, and k. Then, by the Bayes theorem, the probability that a case possesses the particular genotype Gijk is P(GijkD=1)=P(D=1Gijk)P(Gijk)P(D=1) .The factor P(Gijk) describes the population distribution of Gijk, which, under our assumption of locus independence, is simply a product of the corresponding genotype frequencies. If the three loci combine to affect disease risk, P(Gijk|D=1) will differ from P(Gijk) by an amount that depends on the magnitude of risk that Gijk confers. One might compute a measure of difference between the observed distribution of Gijk in cases and that expected on the basis of the product of genotype frequencies and then focus the third stage of the ITF on only those sets with a difference that exceeds some threshold. However, the use of only cases in this screening step will induce a bias into the ITF because of the explicit use of disease status. Rather, we propose to compute this difference measured with the pooled sample of cases and controls, to avoid this bias. A deviation from the expected prevalence of Gijk in the entire case-control sample could be the result of a deviation from the expected prevalence of Gijk in cases and could thus indicate association with disease. The measure of difference we propose to use is a χ2 goodness-of-fit statistic that compares the observed with the expected distribution of Gijk in the combined case-control sample. The χ2 statistic is then used as the criterion by which to choose gene combinations for inclusion in ITF—that is, only gene sets with a calculated χ2 statistic above a selected cutoff value are analyzed. The form of the χ2 statistic should match the underlying assumptions of risk—in other words, for the risk model in equation (1), the genotype groups would be chosen to match risk levels associated with each interaction term. For instance, there would be four genotype groups for two-gene sets, corresponding to Gi×Gj=0, 1, 2, or 4, and five genotype groups for three-gene sets, corresponding to Gi×Gj×Gk=0, 1, 2, 4, or 8. The χ2 statistic, henceforth referred to as the “CSS” (chi-squared subset) statistic, would then take the form CSS=∑i=1r[ni−E(ni)]E(ni) .Here, ni is the observed number of subjects, irrespective of case status, in the ith genotype group, and r is the total number of genotype groups. The expected ni, E(ni), is estimated on the basis of the sample marginal genotype frequencies of each gene. For example, let n4 equal the observed number of subjects with Gi×Gj=4—in other words, genotype AA at locus i and BB at locus j—then, for two-gene sets, E(n4)=(nAAnBB)/N2, where N denotes the total sample size. We emphasize the point that use of the CSS statistic to limit the number of gene sets considered does not bias subsequent tests. Under the global null hypothesis of independence between genotype G and phenotype D, any variable that is strictly a function of G will also be independent of D. Specifically, the reduced set of gene combinations (G*) that results from screening with the CSS statistic is strictly a function of G, since case-control status is not used in computing CSS. Therefore, the reduced set is also statistically independent of D under the global null. As an initial proof of concept, we first provide evidence to show that accounting for interactions leads to increased efficiency in tests of candidate genes. We assume a model with no main effects and a two-gene interaction with an odds ratio (OR) of 2.0—that is, under equation (2), βij is set to log(2), and βi and βj are set to zero. Phenotype prevalence was set to 10%, allele frequencies were set to 0.3, power was set to 80%, and the significance level was assumed to be 0.05 with a two-sided alternative hypothesis. Conditional on all of these parameter settings, the method of Longmate (Longmate, 2001Longmate JA Complexity and power in case-control association studies.Am J Hum Genet. 2001; 68: 1229-1237Abstract Full Text Full Text PDF PubMed Scopus (81) Google Scholar) was used to estimate required sample sizes for a variety of LRTs derived from equation (2). Test 1 (see table 1) shows the sample size required (N=130) to detect G1 (or G2) by use of a standard marginal test. A 2-df test of β1 and β2 (test 2) requires only N=90, a 44% increase in efficiency. A 3-df test of the saturated model
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