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.

Keywords: Cancer; Clinical trials; Health-related quality of life; Informative dropout; Joint model; Linear mixed model; Longitudinal outcome; Random intercept and slope model.

Fig. 1

Predicted mean HRQoL score trajectories in the experimental (solid lines) and control (dotted lines) arms from the LMM and the JM fitting to the clinical trial PRODIGE 4/ACCORD 11 data for the six scales of interest. HRQoL, health-related quality of life; JM, joint model; LMM, linear mixed model

Fig. 2

Mean trajectories of the true HRQoL score value in both arms considered in the simulation study (i.e., representation of $\mathbb{E}\left(\left(Y^{\star },(,t\right)\right)={\beta }_0+{\beta }_{1}t+{\beta }_2\left\{a,r,m,\times ,t\right\}$ according to t with t the time in months and arm the treatment arm indicator). HRQoL, health-related quality of life

Fig. 3

Representation of the hazard functions considered in the simulation study for both arms where the current HRQoL true value is set to its theoretical mean, i.e., $\lambda \left(t|arm,\mathbb{E},\left(\left(Y^{\star },(,t\right)\right)\right)={\lambda }_0(t)exp\left\{{\gamma }_1,,a,r,m,+,\alpha ,,\left({\beta }_0,+,{\beta }_1,t,+,{\beta }_2,\left\{a,r,m,\times ,t\right\}\right)\right\}$ where λ₀(t) = ϕt^ϕ − 1 exp(γ₀) with ϕ and exp(γ₀) the shape and scale parameters, respectively, according to t with t the time in months and arm the treatment arm indicator. HRQoL, health-related quality of life

Fig. 4

HRQoL theoretical mean trajectories (in black) and mean of the HRQoL predicted mean trajectories over the simulations (in color) in the control arm (dashed lines) and the experimental arm (solid lines), i.e., representation of the functions given by, respectively, β₀ + β₁t + β₂{arm × t} and $\overline{{\widehat{\beta }}_0}+\overline{{\widehat{\beta }}_1}t+\overline{{\widehat{\beta }}_2}\left\{a,r,m,\times ,t\right\}$, according to t with t the time in months and arm the treatment arm indicator. HRQoL, health-related quality of life; JM, joint model; LMM, linear mixed model