The Cochran-Armitage trend test is commonly used as a genotype-based test for candidate gene association. Corresponding to each underlying genetic model there is a particular set of scores assigned to the genotypes that maximizes its power. When the variance of the test statistic is known, the formulas for approximate power and associated sample size are readily obtained. In practice, however, the variance of the test statistic needs to be estimated. We present formulas for the required sample size to achieve a prespecified power that account for the need to estimate the variance of the test statistic. When the underlying genetic model is unknown one can incur a substantial loss of power when a test suitable for one mode of inheritance is used where another mode is the true one. Thus, tests having good power properties relative to the optimal tests for each model are useful. These tests are called efficiency robust and we study two of them: the maximin efficiency robust test is a linear combination of the standardized optimal tests that has high efficiency and the MAX test, the maximum of the standardized optimal tests. Simulation results of the robustness of these two tests indicate that the more computationally involved MAX test is preferable.
In many observational studies, a higher intake of individual antioxidants is inversely associated with lung cancer risk. Data from in vitro and animal experiments suggest that there are biochemical interactions among antioxidant nutrients; therefore, consideration of multiple antioxidants simultaneously may be important in terms of risk estimation. The authors constructed a dietary antioxidant index and evaluated its ability to predict lung cancer risk within the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study cohort. At baseline (1985-1988), 27,111 Finnish male smokers aged 50-69 years completed a dietary questionnaire that assessed usual frequency of consumption and portion sizes for the previous 12 months. A total of 1,787 incident cases of lung cancer were identified during a follow-up period of up to 14.4 years (1985-1999). Principal components analyses were individually applied to the carotenoid, flavonoid, and vitamin E nutrient groups, and summation of retained principal component scores, plus selenium and vitamin C, yielded the composite antioxidant index. In multivariate proportional hazards models, the relative risks for lung cancer according to increasing quintiles of the antioxidant index were 1.00 (referent), 1.00 (95% confidence interval (CI): 0.87, 1.14), 0.91 (95% CI: 0.79, 1.05), 0.79 (95% CI: 0.68, 0.92), and 0.84 (95% CI: 0.72, 0.98) (p for trend = 0.002). These findings support the hypothesis that a combination of dietary antioxidants reduces lung cancer risk in male smokers.
SummaryGenome-wide association study (GWAS), typically involving 100,000 to 500,000 single-nucleotide polymorphisms (SNPs), is a powerful approach to identify disease susceptibility loci. In a GWAS, single-marker analysis, which tests one SNP at a time, is usually used as the first stage to screen SNPs across the genome in order to identify a small fraction of promising SNPs with relatively low p-values for further and more focused studies. For single-marker analysis, the trend test derived for an additive genetic model is often used. This may not be robust when the additive assumption is not appropriate for the true underlying disease model. A robust test, MAX, based on the maximum of three trend test statistics derived for recessive, additive, and dominant models, has been proposed recently for GWAS. But its p-value has to be evaluated through a resampling-based procedure, which is computationally challenging for the analysis of GWAS. Obtaining the p-value for MAX with adjustment for the covariates can be even more time-consuming. In this article, we provide a simple approximation for the p-value of the MAX test with or without adjusting for the covariates. The new method avoids resampling steps and thus makes the MAX test readily applicable to GWAS. We use simulation studies as well as real datasets on 17 confirmed disease-associated SNPs to assess the accuracy of the proposed method. We also apply the method to the GWAS of coronary artery disease.
When applying the Cochran-Armitage (CA) trend test for an association between a candidate allele and a disease in a case-control study, a set of scores must be assigned to the genotypes. Sasieni (1997, Biometrics 53, 1253-1261) suggested scores for the recessive, additive, and dominant models but did not examine their statistical properties. Using the criteria of minimizing the required sample size of the CA trend test to achieve prespecified type I and type II errors, we show that the scores given by Sasieni (1997) are optimal for the recessive and dominant models and locally optimal for the additive one. Moreover, the additive scores are shown to be locally optimal for the multiplicative model. The tests are applied to a real dataset.
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