Biased estimation with shared parameter models in the presence of competing dropout mechanisms

Recently, Thomadakis et al. quantified potential sources of bias that can occur when shared parameter (SP) models are used to jointly model longitudinal trends of a biomarker over time (e.g., a slope) and time-to-dropout in an effort to address concerns over possible informative censoring. Although SP models induce no bias under a missingness completely at random dropout mechanism, the authors demonstrate that bias can occur under a missingness at random (MAR) dropout mechanism wherein dropout depends on the observed biomarker data. To address this, the authors propose including the most recent observed marker value within the hazard function for the time-to-dropout portion of an SP model. They demonstrate via a limited simulation that the proposed model minimizes bias under a specific MAR dropout mechanism and a specific missingness not-at-random dropout mechanism. In the present article, we compare and contrast their work with that of previous authors by illustrating via simulation and an example the degree of bias or lack thereof that can occur when applying SP models, particularly, in the presence of competing dropout mechanisms. We propose the use of a competing risk SP model as a means to minimize bias whenever competing dropout mechanisms are suspected assuming the competing mechanisms result from distinct observable causes of dropout.