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Abstract:
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Powering a study to address its research aims requires accurate determination of the sample size. A primary hypothesis often asserts a relationship between a main variable of interest and an outcome. Regression permits more precise evaluation of this relationship through covariate adjustment at the cost of increased complexity in sample size estimation. Correlation between the main variable and other covariates, commonly seen in non-randomized clinical trials and observational studies, further complicates this process. Many existing sample size methods rely on either simple approximations lacking theoretical support or complex procedures that are difficult to apply at the design stage. Methods are available for specific covariate distributions and regression models, but the current literature lacks a coherent theory applicable to a broader class of models. We propose succinct sample size formulas for the logistic, Poisson, Cox, and Fine-Gray models that account for correlation between covariates. Extensive simulations confirm that this method produces studies with the targeted power and provides a suitable adjustment of the sample size in the presence of correlated covariates.
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