Joint Models for Longitudinal Analysis and Competing Risks in Survival Analysis

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Abstract

In longitudinal studies involving assessing ordinal disease(s) outcome across multiple time points, ignoring the correlations between the development and transition of the disease status and any informative potential censoring event(s) may lead to bias in the estimation of covariate effects. To address the problems created by these dependencies, we propose and apply several models:

  1. Linking the Cause-specific Hazards Model for competing risks analyses with a model for longitudinal ordinal measurements through a correlated random effects structure. To do this, we apply a 2009 approach by Li et al. (2009), and use this as the baseline model.
  2. Developing a joint longitudinal competing risks survival model in which previous wave disease status history is an additional time-varying covariate in the survival component, through the same linkage mechanism as in the baseline model.
  3. Applying the same linkage mechanism as in the baseline model, we model the longitudinal outcome using a continuous time Markov chain model.
  4. Comparing the application results from applying the baseline approach to those obtained using available software. To assess the properties of these models and their effectiveness, we conduct simulation studies, in which we compare performance (likelihood and covariate parameter estimate accuracy) against the baseline model. The Aim 2 model achieves smaller bias in the estimation of the intercepts compared to separate model estimates, as well as estimates from the baseline approach when the speed of the change of the longitudinal ordinal outcome is appropriately estimable. Model 3 achieves more accurate estimates of the baseline transition probabilities and covariate effects, compared to the separate models, when the association between two sub-models is large. To assess the practical effects of these model modifications, we demonstrate the fit of these models for estimating measures of frailty (treated as a three-level factor) in the Hispanic Established Populations for the Epidemiologic Study of the Elderly data, which is a longitudinal survey study to estimate the prevalence of and risk factors for key health conditions in older Mexican Americans. Death and loss to follow-up are occurrences with potential to add bias to covariate effect estimates. We applied the baseline approach and available software to the working data, and covariate estimates and model fit were compared.
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Joint model, longitudinal analysis, survival analysis, frailty, continuous time Markov chain, competing risks.
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