Fixed versus Mixed Parameterization in Logistic Regression Models: Application to Meta-Analysis

Three methods: fixed intercept generalized model (GLM), random intercept generalized mixed model (GLMM), and conditional logistic regression (clogit) are compared in a meta-analysis of 43 studies assessing the effect of diet on cancer incidence in rats. We also perform simulation studies to assess distributional behavior of regression estimates and tests of fit. Other simulations assess the effects of model misspecification, and increasing the sample size, either by adding additional studies or by increasing the sizes of a fixed number of studies. Estimates of fixed effects seem insensitive to increasing the sample sizes, but the deviance test of fit is biased. Conditional logistic regression avoids the possibility of bias when the number of studies is very large in a GLM analysis and also avoids effects of misspecification of the random effect distribution in a GLMM analysis, but at the cost of some information loss.