Longitudinal and Time-to-Drop-Out Joint Models Can Lead to Seriously Biased Estimates When the Drop-Out Mechanism is at Random

Abstract

Missing data are common in longitudinal studies. Likelihood-based methods ignoring the missingness mechanism are unbiased provided missingness is at random (MAR);under not-at-random missingness (MNAR), joint modeling is commonly used, often as part of sensitivity analyses. In our motivating example of modeling CD4 count trajectories during untreated HIV infection, CD4 counts are mainly censored due to treatment initiation, with the nature of this mechanism remaining debatable. Here, we evaluate the bias in the disease progression marker's change over time (slope) of a specific class of joint models, termed shared-random-effects-models (SREMs), under MAR drop-out and propose an alternative SREM model. Our proposed model relates drop-out to both the observed marker's data and the corresponding random effects, in contrast to most SREMs, which assume that the marker and the drop-out processes are independent given the random effects. We analytically calculate the asymptotic bias in two SREMs under specific MAR drop-out mechanisms, showing that the bias in marker's slope increases as the drop-out probability increases. The performance of the proposed model, and other commonly used SREMs, is evaluated under specific MAR and MNAR scenarios through simulation studies. Under MAR, the proposed model yields nearly unbiased slope estimates, whereas the other SREMs yield seriously biased estimates. Under MNAR, the proposed model estimates are approximately unbiased, whereas those from the other SREMs are moderately to heavily biased, depending on the parameterization used. The examined models are also fitted to real data and results are compared/discussed in the light of our analytical and simulation-based findings.

MMRM vs joint modeling of longitudinal responses and time to study drug discontinuation in clinical trials using a “de jure” estimand

“…Our simulations task has illustrated that MMRM are preferred over SPM when the association mechanism follows TVC model as SPM lead to bias in that situation. This finding aligns with a recent work from Thomadakis et al showing that fitting SPM on datasets where the event process does not depend on the random effects, but on the full last observation of the longitudinal response (ie, the TVC model) may lead to serious bias 17 . The way that work overcame this issue differs from our approach.…”

“…In this context, JM is used to handle endogenous error‐prone time‐dependent covariates in contrast with classical approaches such as the extension of the Cox model using the counting process formulation 16 . In addition, JM has also been studied in the missing data framework, being often referred in here as SPM 17‐20 …”

“…Several simulation studies have already studied the performance of the models evaluated in this paper when missingness follows the TVC model. While MMRM provides unbiased estimates, 6,10 SPM have been shown to lead to considerable bias 17 . On the performance of SPM under the TVC model, the existing paper focused on a single‐arm random intercepts and slopes model only 17 .…”

“…While MMRM provides unbiased estimates, 6,10 SPM have been shown to lead to considerable bias 17 . On the performance of SPM under the TVC model, the existing paper focused on a single‐arm random intercepts and slopes model only 17 . In contrast, we have studied the between‐arms treatment difference and covered not only random intercepts and slopes models, but also the more complex covariance pattern used in the standard MMRM specification.…”

Joint analysis of longitudinal measurements and spatially clustered competing risks HIV/AIDS data

“…The proposed model relates drop-out to both the longitudinal data and the random effects. 47 In HIV disease, when the response is a survival of the patient, there is a terminal outcome (death), and an intermediate nonterminal outcome (AIDS) for a patient. When there is an intermediate nonterminal event in data we are faced with the semi-competing risks data.…”