Joint model robustness compared with the time-varying covariate Cox model to evaluate the association between a longitudinal marker and a time-to-event endpoint - PubMed (original) (raw)

Joint model robustness compared with the time-varying covariate Cox model to evaluate the association between a longitudinal marker and a time-to-event endpoint

Maeregu W Arisido et al. BMC Med Res Methodol. 2019.

Abstract

Background: The recent progress in medical research generates an increasing interest in the use of longitudinal biomarkers for characterizing the occurrence of an outcome. The present work is motivated by a study, where the objective was to explore the potential of the long pentraxin 3 (PTX3) as a prognostic marker of Acute Graft-versus-Host Disease (GvHD) after haematopoietic stem cell transplantation. Time-varying covariate Cox model was commonly used, despite its limiting assumptions that marker values are constant in time and measured without error. A joint model has been developed as a viable alternative; however, the approach is computationally intensive and requires additional strong assumptions, in which the impacts of their misspecification were not sufficiently studied.

Methods: We conduct an extensive simulation to clarify relevant assumptions for the understanding of joint models and assessment of its robustness under key model misspecifications. Further, we characterize the extent of bias introduced by the limiting assumptions of the time-varying covariate Cox model and compare its performance with a joint model in various contexts. We then present results of the two approaches to evaluate the potential of PTX3 as a prognostic marker of GvHD after haematopoietic stem cell transplantation.

Results: Overall, we illustrate that a joint model provides an unbiased estimate of the association between a longitudinal marker and the hazard of an event in the presence of measurement error, showing improvement over the time-varying Cox model. However, a joint model is severely biased when the baseline hazard or the shape of the longitudinal trajectories are misspecified. Both the Cox model and the joint model correctly specified indicated PTX3 as a potential prognostic marker of GvHD, with the joint model providing a higher hazard ratio estimate.

Conclusions: Joint models are beneficial to investigate the capability of the longitudinal marker to characterize time-to-event endpoint. However, the benefits are strictly linked to the correct specification of the longitudinal marker trajectory and the baseline hazard function, indicating a careful consideration of assumptions to avoid biased estimates.

Keywords: Cox model; Joint model simulation; Longitudinal biomarker; Random effects model; Time-varying covariate.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Fig. 1

Mean-squared error (MSE) of the association parameter α obtained from the joint model and TVCM to the data generated considering different sample sizes (n) and different probability distributions for the random effect b _i_0

Fig. 2

a Mean biomarker trajectory for the different scenarios: linearly decreasing (scenarios 2-6 and 9) and quadratic shape with slight (scenario 7) and gross (scenario 8) misspecifications with respect to the linear trend. b Baseline hazard function for the scenarios 1-8 (Weibull) and 9 (non-monotonic shape)

Fig. 3

a The distribution of PTX3 marker in time. b The shape of the distribution of the GvHD hazard estimate

Fig. 4

Observed Kaplan-Meier (KM) curve and predicted survival curves from the joint model assuming constant, Weibull and spline based hazards. A logarithmic transformation of PTX3 was used in the joint models

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Joint model robustness compared with the time-varying covariate Cox model to evaluate the association between a longitudinal marker and a time-to-event endpoint - PubMed (original) (raw)