## Statistical Consideration and Power Calculation

Statistical analyses in pharmacogenetic studies using the candidate gene approach are fairly simple and straightforward. Several generic methods, such as logistic regression, Cox proportional hazards model, Kaplan-Meier estimates and log-rank test, are commonly used to determine the association between individual genetic polymorphism and treatment response, toxicity, and survival.

The major concern for the candidate gene approach in pharmacogenetic study is whether it has sufficient power to detect the expected effect. Pharmacogenetic studies in the literature have generally been underpowered, that is, the sample size is not large enough, which is one of the main reasons for the lack of reproducibility. The sample size requirement for a pharmacogenetic study depends on the prevalence of risk factor (e.g., variant allele frequency), the event (toxicity, treatment response, survival, etc) rate, the magnitude of effect, the significance level, and the desired power (generally >80%). The power calculation for binary variables (toxicity or treatment response) is relatively simple. For example, we used the statistical program PS (40) to calculate the minimum power for a sample size of 300 patients to detect a range of given odds ratios (ORs) associated with toxicity or tumor response (Fig. 1) with a two-sided alpha level of 5% where event (toxicity or response) rate ranges from 10% to 50% and variant allele frequency ranges from 5% to 50%. With this given sample size (300 patients), which is at the high end of sample sizes in the literature, ORs lower than 2.0 can only be detected with more than 80% power for situations where both event rate and/or prevalence of risk factor (i.e., variant allele frequency) are adequate (top five lines in Fig. 1).

Power calculations for survival data are more complex due to the nature of the analyses as well as factors that are involved in the accrual of participants (i.e., follow-up time, prevalence of risk factor, etc.). The following example is based on the method discussed by Simon and Altman (41) using an 18-month overall survival rate of 40%, two-sided alpha level of 5%, and no attrition for varying levels of risk factor prevalence and hazard ratios.

Figure 2 presents the minimum power to detect the given hazard ratios (1.1-3.0), where the variant allele frequency ranges from 1% to 50% for a sample size of 300 participants. With this given sample size, hazard ratios below 2.0 can only be detected with sufficient power (>80%) for those polymorphisms with higher variant allele frequencies (>15%).

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