Robustness of the Pairwise-Fitting Approach Under Missing at Random Dropout: A Case and Simulation Study

Abstract

In many studies, multiple longitudinal outcomes are collected, and interest lies in studying the association between these outcomes. Joint modeling is then required, but full likelihood estimation becomes infeasible as the number of outcomes increases. To address this, the pairwise-fitting approach was developed. However, the robustness of this pseudo-likelihood-based approach under missing at random (MAR) remains unclear. We investigate the impact of MAR dropout on the pairwise-fitting approach through a case and simulation study and compare the results to full likelihood estimation. In the simulation study, we simulate three continuous longitudinal outcomes so that full likelihood estimation remains computationally feasible, allowing a comparison with the pairwise fitting approach. Various settings are examined, including random intercept and random intercept-and-slope models, in which we vary the standard deviation of the error terms and the degree of correlation between random effects. Our results show that bias remains limited in random intercept models and in most random intercept-and-slope models. However, when the standard deviation of the error terms becomes large compared to that of the random effects, some bias appears in the covariances between the random effects of the outcomes not driving dropout. This bias is mitigated using multiple imputation. As a case study, we analyzed data from a schizophrenia study using both full likelihood and pseudo-likelihood approaches and compared the results.