Analysis of an Incomplete Binary Outcome Dichotomized From an Underlying Continuous Variable in Clinical Trials

In many clinical trials, outcomes of interest include binary-valued endpoints. It is not uncommon that a binary-valued outcome is dichotomized from a continuous outcome at a threshold of clinical interest. To reach the objective, common approaches include (a) fitting the generalized linear mixed model (GLMM) to the dichotomized longitudinal binary outcome and (b) imputation method (MI): imputing the missing values in the continuous outcome, dichotomizing it into a binary outcome, and then fitting the generalized linear model for the "complete" data. We conducted comprehensive simulation studies to compare the performance of GLMM with MI for estimating risk difference and logarithm of odds ratio between two treatment arms at the end of study. In those simulation studies, we considered a range of multivariate distribution options for the continuous outcome (including a multivariate normal distribution, a multivariate t-distribution, a multivariate log-normal distribution, and the empirical distribution from a real clinical trial data) to evaluate the robustness of the estimators to various data-generating models. Simulation results demonstrate that both methods work well under those considered distribution options, but MI is more efficient with smaller mean squared errors compared to GLMM. We further applied both the GLMM and MI to 29 phase 3 diabetes clinical trials, and found that the MI method generally led to smaller variance estimates compared to GLMM.