CONDITIONAL LOGISTIC-REGRESSION WITH SANDWICH ESTIMATORS - APPLICATION TO A METAANALYSIS

Motivated by a meta-analysis of animal experiments on the effect of di etary fat and total caloric intake on mammary tumorigenesis, we explor e the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that th e parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or ra ndom effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using in formation from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald te st. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardized residuals. Second, we a pproximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators e ven when some parameters are estimated from a small number of clusters .