Longitudinal and time‐to‐drop‐out joint models can lead to seriously biased estimates when the drop‐out mechanism is at random

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.