Last, we conducted a simulation to compute power for detecting various effect sizes with the constraints of our sample size and study design using SAS. These estimation results were critical in the interpretation of our results. We performed the power calculation for our sample size of 2,032 in three steps. First, a simulated dataset was produced under a logistic regression model with assumed proportions and effect sizes (odds radios) for the variables in the model (including the interaction term if it was included in the model). Next, the regression model was executed using the simulated data and subsequently tested to determine whether the assumed effect size was significantly different from zero. The Wald Chi-square statistic (including the degrees of freedom) resulting from the test was taken as a non-centrality parameter of the non-central Chi-square distribution. Finally, power was calculated by subtracting the probability of the non-central Chi-square distribution from 1. Type I error was set to 0.05.
