A unified approach to sample size and power determination for testing parameters in generalized linear and time-to-event regression models

To ensure that a study can properly address its research aims, the sample size and power must be determined appropriately. Covariate adjustment via regression modeling permits more precise estimation of the effect of a primary variable of interest at the expense of increased complexity in sample size/power calculation. The presence of correlation between the main variable and other covariates, commonly seen in observational studies and non-randomized clinical trials, further complicates this process. Though sample size and power specification methods have been obtained to accommodate specific covariate distributions and models, most existing approaches rely on either simple approximations lacking theoretical support or complex procedures that are difficult to apply at the design stage. The current literature lacks a general, coherent theory applicable to a broader class of regression models and covariate distributions. We introduce succinct formulas for sample size and power determination with the generalized linear, Cox, and Fine-Gray models that account for correlation between a main effect and other covariates. Extensive simulations demonstrate that this method produces studies that are appropriately sized to meet their type I error rate and power specifications, particularly offering accurate sample size/power estimation in the presence of correlated covariates.