Joint scale-change models for recurrent events and failure time

Abstract

Recurrent event data arise frequently in various fields such as biomedical sciences, public health, engineering, and social sciences. In many instances, the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event, such as treatment failure and death. In this article, we propose a joint scale-change model for the recurrent event process and the failure time, where a shared frailty variable is used to model the association between the two types of outcomes. In contrast to the popular Cox-type joint modeling approaches, the regression parameters in the proposed joint scale-change model have marginal interpretations. The proposed approach is robust in the sense that no parametric assumption is imposed on the distribution of the unobserved frailty and that we do not need the strong Poisson-type assumption for the recurrent event process. We establish consistency and asymptotic normality of the proposed semiparametric estimators under suitable regularity conditions. To estimate the corresponding variances of the estimators, we develop a computationally efficient resampling-based procedure. Simulation studies and an analysis of hospitalization data from the Danish Psychiatric Central Register illustrate the performance of the proposed method.

Keywords: Accelerated failure time model; Frailty; Informative censoring; Marginal models; Semiparametric methods.

Figure 1

Plots of estimated Λ̂₀(t) and Ĥ₀(t) with pointwise 95% confidence intervals for n = 200 (—, true curve; - - -, empirical average; -----, pointwise 95% confidence intervals). Conditioning on Z, the recurrent process is a Poisson process and a non-Poisson process for Scenario I and Scenario II, respectively.

Figure 2

Plots of estimated Λ̂₀(t) and Ĥ₀(t) with pointwise 95% confidence intervals for n = 500 (—, true curve; - - -, empirical average; -----, pointwise 95% confidence intervals). Conditioning on Z, the recurrent process is a Poisson process and a non-Poisson process for Scenario I and Scenario II, respectively.

Figure 3

Plots of estimated Λ̂₀(t) and Ĥ₀(t) for the Danish Psychiatric Central Register data. (a) Baseline cumulative rate function; (b) baseline cumulative hazard function; (—, estimates; -----, pointwise 95% confidence intervals).