Simulation Program to Determine Sample Size and Power for a Multiple Logistic Regression Model with Unspecified Covariate Distributions

Abstract

Binary logistic regression models are commonly used to assess the association between outcomes and covariates. Many covariates are inherently continuous, and have a variety of distributions, including those that are heavily skewed to the left or right. Existing theoretical formulas, criteria, and simulation programs cannot accurately estimate the sample size and power of non-standard distributions. Therefore, we have developed a simulation program that uses Monte Carlo methods to estimate the exact power of a binary logistic regression model. This power calculation can be used for distributions of any shape and covariates of any type (continuous, ordinal, and nominal), and can account for nonlinear relationships between covariates and outcomes. For illustrative purposes, this simulation program is applied to real data obtained from a study on the influence of smoking on 90-day outcomes after acute atherothrombotic stroke. Our program is applicable to all effect sizes and makes it possible to apply various statistical methods, logistic regression and related simulations such as Bayesian inference with some modifications.