When a joint model should be preferred over a linear mixed model for analysis of longitudinal health-related quality of life data in cancer clinical trials

Abstract

Background Patient-reported outcomes such as health-related quality of life (HRQoL) are increasingly used as endpoints in randomized cancer clinical trials. However, the patients often drop out so that observation of the HRQoL longitudinal outcome ends prematurely, leading to monotone missing data. The patients may drop out for various reasons including occurrence of toxicities, disease progression, or may die. In case of informative dropout, the usual linear mixed model analysis will produce biased estimates. Unbiased estimates cannot be obtained unless the dropout is jointly modeled with the longitudinal outcome, for instance by using a joint model composed of a linear mixed (sub)model linked to a survival (sub)model. Our objective was to investigate in a clinical trial context the consequences of using the most frequently used linear mixed model, the random intercept and slope model, rather than its corresponding joint model. Methods We first illustrate and compare the models on data of patients with metastatic pancreatic cancer. We then perform a more formal comparison through a simulation study. Results From the application, we derived hypotheses on the situations in which biases arise and on their nature. Through the simulation study, we confirmed and complemented these hypotheses and provided general explanations of the bias mechanisms. Conclusions In particular, this article reveals how the linear mixed model fails in the typical situation where poor HRQoL is associated with an increased risk of dropout and the experimental treatment improves survival. Unlike the joint model, in this situation the linear mixed model will overestimate the HRQoL in both arms, but not equally, misestimating the difference between the HRQoL trajectories of the two arms to the disadvantage of the experimental arm.

Bayesian Joint Model with Latent Time Shifts for Multivariate Longitudinal Data with Informative Dropout

“…Our findings were consistent with prior studies. First, most of the previous studies on joint models, both linear and nonlinear, showed that joint models outperformed separate models in the presence of informative dropout [24–28, 30, 32], which was consistent with our key findings. Second, the mix-effects model in the separate models that ignored informative dropout showed over-optimistic estimates for the disease progression trend, corresponding to conclusions drawn in previous studies [26–28].…”

“…First, most of the previous studies on joint models, both linear and nonlinear, showed that joint models outperformed separate models in the presence of informative dropout [24–28, 30, 32], which was consistent with our key findings. Second, the mix-effects model in the separate models that ignored informative dropout showed over-optimistic estimates for the disease progression trend, corresponding to conclusions drawn in previous studies [26–28]. It was shown that subjects who dropped out due to excessively high or low longitudinal measures were downweighed during the estimation procedure, so they contributed weakly to the likelihood function in the mixed-effects models.…”

“…Another commonly used association structure is the current value structure, where dropouts are linked to the true unobserved values of the longitudinal trajectories [18,[28][29][30][31][32]. Notably, Vonesh et al ( 2006) investigated both association structures, comparing them with separate models under various assumptions of missing mechanism [17].…”

“…All studies showed that joint models improve over linear mixed models or separate models regarding bias and model fit. In addition, it has been shown that linear mixed models tend to provide overly optimistic estimates for longitudinal outcomes, while joint models are able to recover the true longitudinal estimates with low bias [26][27][28]. When dropouts occur due to different reasons, joint models with competing risks have been developed to account for various types of dropouts.…”