gms | German Medical Science

Introduction: In observational studies, the effect of multiple risk factors on some binary response is typically analyzed by means of logistic regression. In contrast to its common use in the analysis of study data, sample size methods for logistic regression models are very rare and focus only on some specific study scenarios [1]. There are no adequate methods in the case of multiple risk factors of equal interest.

Methods: We developed a new approach for assessing the power of logistic regression models by approximating the common distribution of the Wald statistics used for testing the effect of the individual risk factors. Since this approach depends on the specification of a design matrix (with risk factors in its columns), we also propose a simulation method to determine the distribution of the conditional power. From this distribution one can determine also the unconditional power [2], which itself depends only on a certain class of design matrices. In addition, the quantile power can be determined from this distribution. To evaluate the performance of our methods, we simulate several study scenarios with either normally or dichotomous distributed risk factors, or with a mixture of both types of risk factors. In these simulations we determine the error of the power approximations with respect to the sample size, the correlation between risk factors, the number of risk factors and the number of events per risk factor.

Results: We found, that the approximation error was within an acceptable range (+/- 5%) in many of our simulated study scenarios. With normally distributed risk factors the error was smaller compared to the case of dichotomous risk factors.

Discussion: Our proposed methods appear to be useful in a variety of study scenarios with binary responses and multiple risk factors.