Nonparametric Estimation of a Recurrent Survival Function

Mei-Cheng Wang, Shu-Hui Chang, Mei-Cheng Wang, Shu-Hui Chang

Abstract

Recurrent event data are frequently encountered in studies with longitudinal designs. Let the recurrence time be the time between two successive recurrent events. Recurrence times can be treated as a type of correlated survival data in statistical analysis. In general, because of the ordinal nature of recurrence times, statistical methods that are appropriate for standard correlated survival data in marginal models may not be applicable to recurrence time data. Specifically, for estimating the marginal survival function, the Kaplan-Meier estimator derived from the pooled recurrence times serves as a consistent estimator for standard correlated survival data but not for recurrence time data. In this article we consider the problem of how to estimate the marginal survival function in nonparametric models. A class of nonparametric estimators is introduced. The appropriateness of the estimators is confirmed by statistical theory and simulations. Simulation and analysis from schizophrenia data are presented to illustrate the estimators' performance.

Keywords: Correlated survival data; Frailty; Kaplan-Meier estimate; Longitudinal designs; Recurrent event.

Figures

Figure 1
Figure 1
Survival Function Estimates From Simulated Data With Gamma(a, b) Frailty, (a) Frailty = gamma(1/.75, .75); (b) frailty = gamma(1, 1); (c) frailty = gamma(1/1.5, 1.5); (d) frailty = gamma(1/2, 2).—, true curve; (x025D6) (x025D6) (x025D6), proposed curve;– -– - –, Kaplan-Meier estimate I; &22EF;, Kaplan-Meier estimate II.
Figure 2
Figure 2
Relative Efficiency Plot. —, censoring time = 2; ---, censoring time = 4; ---, censoring time = 6.
Figure 3
Figure 3
Relative Efficiency Plot. ——, a = 1 and Ci is Uniform(0, 4); ---, a = c and Ci, is Uniform(0, 4); ---, a = 1 and Ci is Uniform(0, 8); …, a = c and Ci Uniform(0, 8).
Figure 4
Figure 4
Recurrent Survival Function Estimates From Schizophrenic Data. —, estimate for onset age ≤ 20 years;---, 95% confidence interval;– - ;– - ;–, estimate for onset age > 20 years; - - -, 95% confidence interval.

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Source: PubMed

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