Estimation for recurrent events through conditional estimating equations

TL;DR

This paper introduces new statistical estimators for analyzing the dependence of mean gap times between recurrent events on covariates, accounting for right censoring, with proven asymptotic properties.

Contribution

It develops conditional estimating equations for recurrent event data, providing consistent and asymptotically normal estimators under censoring conditions.

Findings

Estimators are asymptotically unbiased and normal.

Simulations show effectiveness with small sample sizes.

Method handles dependence and censoring in recurrent events.

Abstract

We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is expressed through regression-like and overdispersion parameters, estimated via conditional estimating equations. The mean and variance of the length of each gap time, conditioned on the observed history of prior events and other covariates, are known functions of parameters and covariates. Under certain conditions on censoring, we construct normalized estimating functions that are asymptotically unbiased and contain only observed data. We discuss the existence, consistency and asymptotic normality of a sequence of estimators of the parameters, which are roots of these estimating equations. Simulations suggest that our estimators could be used successfully with a relatively small sample size in a study of short duration.