Mark A. Levenstien

Power and sample size calculations in the presence of phenotype errors for case/control genetic association studies

BackgroundPhenotype error causes reduction in power to detect genetic association. We present a quantification of phenotype error, also known as diagnostic error, on power and sample size calculations for case-control genetic association studies between a marker locus and a disease phenotype. We consider the classic Pearson chi-square test for independence as our test of genetic association. To determine asymptotic power analytically, we compute the distributions non-centrality parameter, which is a function of the case and control sample sizes, genotype frequencies, disease prevalence, and phenotype misclassification probabilities. We derive the non-centrality parameter in the presence of phenotype errors and equivalent formulas for misclassification cost (the percentage increase in minimum sample size needed to maintain constant asymptotic power at a fixed significance level for each percentage increase in a given misclassification parameter). We use a linear Taylor Series approximation for the cost of phenotype misclassification to determine lower bounds for the relative costs of misclassifying a true affected (respectively, unaffected) as a control (respectively, case). Power is verified by computer simulation.ResultsOur major findings are that: (i) the median absolute difference between analytic power with our method and simulation power was 0.001 and the absolute difference was no larger than 0.011; (ii) as the disease prevalence approaches 0, the cost of misclassifying a unaffected as a case becomes infinitely large while the cost of misclassifying an affected as a control approaches 0.ConclusionOur work enables researchers to specifically quantify power loss and minimum sample size requirements in the presence of phenotype errors, thereby allowing for more realistic study design. For most diseases of current interest, verifying that cases are correctly classified is of paramount importance.

Are Molecular Haplotypes Worth the Time and Expense? A Cost-Effective Method for Applying Molecular Haplotypes

Because current molecular haplotyping methods are expensive and not amenable to automation, many researchers rely on statistical methods to infer haplotype pairs from multilocus genotypes, and subsequently treat these inferred haplotype pairs as observations. These procedures are prone to haplotype misclassification. We examine the effect of these misclassification errors on the false-positive rate and power for two association tests. These tests include the standard likelihood ratio test (LRTstd) and a likelihood ratio test that employs a double-sampling approach to allow for the misclassification inherent in the haplotype inference procedure (LRTae). We aim to determine the cost–benefit relationship of increasing the proportion of individuals with molecular haplotype measurements in addition to genotypes to raise the power gain of the LRTae over the LRTstd. This analysis should provide a guideline for determining the minimum number of molecular haplotypes required for desired power. Our simulations under the null hypothesis of equal haplotype frequencies in cases and controls indicate that (1) for each statistic, permutation methods maintain the correct type I error; (2) specific multilocus genotypes that are misclassified as the incorrect haplotype pair are consistently misclassified throughout each entire dataset; and (3) our simulations under the alternative hypothesis showed a significant power gain for the LRTae over the LRTstd for a subset of the parameter settings. Permutation methods should be used exclusively to determine significance for each statistic. For fixed cost, the power gain of the LRTae over the LRTstd varied depending on the relative costs of genotyping, molecular haplotyping, and phenotyping. The LRTae showed the greatest benefit over the LRTstd when the cost of phenotyping was very high relative to the cost of genotyping. This situation is likely to occur in a replication study as opposed to a whole-genome association study.

Association of Angiotensinogen Gene Polymorphisms with Essential Hypertension in African-Americans and Caucasians

Obective: Molecular variants of angiotensinogen (AGT) have been linked to essential hypertension, and promoter variants have been shown to alter the transcription rate of AGT in vitro. We employed a case-control study to determine whether single nucleotide polymorphisms (SNPs) in the promoter region of AGT were associated with hypertension in African-Americans and Caucasians. Methods: The frequencies of the variants at base positions –6, –20, –217, –793, and –776, both alone and in combination (haplotypes), were compared between cases and controls in samples stratified based on race and sex. A logistic regression model was applied to test whether AGT genotypes were significant predictors of the disease while adjusting for race, sex, and age. Results: Subjects with the AA or AG genotype at locus –793 were significantly more likely to have the disease (OR = 1.88, 95% CI = 1.12–3.15). Additionally, the differences in haplotype frequency distributions between cases and controls were significant at the 7% level for all four subgroups (stratified by race and sex) after adjusting for multiple testing. Based on the odds ratios for each individual haplotype, the haplotype AAAAT (nucleotide sequences at base positions –6, –20, –217, –793, –776) in African-American males, African-American females, and Caucasian females may confer susceptibility to the disease in these population subsets. Conclusion: Overall, the present report provides statistical evidence for the association of AGT with essential hypertension.

Precision and type I error rate in the presence of genotype errors and missing parental data: a comparison between the original transmission disequilibrium test (TDT) and TDTae statistics.

BackgroundTwo factors impacting robustness of the original transmission disequilibrium test (TDT) are: i) missing parental genotypes and ii) undetected genotype errors. While it is known that independently these factors can inflate false-positive rates for the original TDT, no study has considered either the joint impact of these factors on false-positive rates or the precision score of TDT statistics regarding these factors. By precision score, we mean the absolute difference between disease gene position and the position of markers whose TDT statistic exceeds some threshold.MethodsWe apply our transmission disequilibrium test allowing for errors (TDTae) and the original TDT to phenotype and modified single-nucleotide polymorphism genotype simulation data from Genetic Analysis Workshop. We modify genotype data by randomly introducing genotype errors and removing a percentage of parental genotype data. We compute empirical distributions of each statistics precision score for a chromosome harboring a simulated disease locus. We also consider inflation in type I error by studying markers on a chromosome harboring no disease locus.ResultsThe TDTae shows median precision scores of approximately 13 cM, 2 cM, 0 cM, and 0 cM at the 5%, 1%, 0.1%, and 0.01% significance levels, respectively. By contrast, the original TDT shows median precision scores of approximately 23 cM, 21 cM, 15 cM, and 7 cM at the corresponding significance levels, respectively. For null chromosomes, the original TDT falsely rejects the null hypothesis for 28.8%, 14.8%, 5.4%, and 1.7% at the 5%, 1%, 0.1% and 0.01%, significance levels, respectively, while TDTae maintains the correct false-positive rate.ConclusionBecause missing parental genotypes and undetected genotype errors are unknown to the investigator, but are expected to be increasingly prevalent in multilocus datasets, we strongly recommend TDTae methods as a standard procedure, particularly where stricter significance levels are required.

Two approaches for consolidating results from genome scans of complex traits: selection methods and scan statistics.

This work has two purposes: (i) empirically selecting levels of significance that maximize the fraction of markers close to a gene (hit rate) when performing linkage analyses of simulated data and (ii) evaluating the utility of a previously reported scan statistic on the same data. Genotype data were simulated from a trait model of seven susceptibility genes. For purpose (i), five statistics were evaluated on all marker loci in fifty replicates; two-point lod and heterogeneity lod scores maximized over dominance (mlod, mhlod), a multi-allelic TDT test, an affected sib-pair test (ASP), and a model-free test on all sib-pairs (ALL_SIBS). Within each replicate the fraction of markers (hit rate) significant at specified levels of significance and also (a) within fifty markers of, or (b) on the same chromosome as a major gene was calculated. For purpose (ii), scan statistics of length 15 were calculated for each chromosome and their empirical significance levels estimated on the basis of 500 replicates generated under no linkage. The scan statistic was applied to the mhlod scores from one replicate (Replicate 5). Empirical p-values for the scan statistic were determined by computing mhlod scores on 500 replicates of simulated null data. For purpose (i), significance levels between 0.001 and 0.01 had the greatest hit rate for all five methods and both criteria. For criterion (a) at the 0.001 level of significance, both mlod and mhlod displayed the highest hit rates, approximately 0.4 for each. For criterion (b), all methods but ALL_SIBS and ASP had hit rates ranging between 0.4 and 0.5. For purpose (ii), the scan statistic proved equally or more powerful than the single-locus statistic for two of the seven susceptibility genes while the remaining five genes were not detected.