A joint model for longitudinal measurements and survival data in the presence of multiple failure types

Abstract

In this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause-specific hazards frailty submodel (Prentice et al., 1978, Biometrics 34, 541-554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease.

Figures

Figure 1

(a)-(b) Profile plots of %FVC for CYC group versus the placebo group: ○ for treatment failure or death; + for informative censoring without %FVC measurements after the events; △ for informative censoring with %FVC measurements after the events; □for noninformatively censored events.