In our analysis of 500 subjects, the differences among the variances of the sandwich estimators for the covariate of interest (β1) from equation (6) are very small. This is not surprising as the simulation results reported that the sandwich estimator’s coverage probabilities converge to the same values in large sample sizes, even with outcome prevalence values as low as 1%. When we analyze the sample of 30 subjects, the variability of the sandwich estimators’ variance is even larger, as reflected in their values differing from one another by several magnitudes of 10. When performing statistical hypothesis testing in a situation where the outcome is of low prevalence and the sample size is small, the choice of sandwich estimator affects the outcome of hypothesis testing concerning the regression coefficients. The estimated odds ratio for a 100-hour increase of flight time (β^1) in the sample of 30 subjects is 1.1664. The associated 95% confidence intervals for the Liang-Zeger and Rogers sandwich estimators are (1.0374, 1.3120) and (0.6016, 2.2625), respectively. For the purposes of this question, the use of the Liang-Zeger or Rogers sandwich estimator impacted the statistical significance of the covariate of interest.
