Statistical analysis of mixed recurrent event data with application to cancer survivor study

Abstract

Event history studies occur in many fields including economics, medical studies and social science. In such studies concerning some recurrent events, two types of data have been extensively discussed in the literature. One is recurrent event data that arise if study subjects are monitored or observed continuously. In this case, the observed information provides the times of all occurrences of the recurrent events of interest. The other is panel count data, which occur if the subjects are monitored or observed only periodically. This can happen if the continuous observation is too expensive or not practical and in this case, only the numbers of occurrences of the events between subsequent observation times are available. In this paper, we discuss a third type of data, which is a mixture of recurrent event and panel count data and for which there exists little literature. For regression analysis of such data, a marginal mean model is presented and we propose an estimating equation-based approach for estimation of regression parameters. A simulation study is conducted to assess the finite sample performance of the proposed methodology and indicates that it works well for practical situations. Finally it is applied to a motivating study on childhood cancer survivors.

Regression analysis of incomplete data from event history studies with the proportional rates model

“…To generate the simulated data, following [3], we assumed below that there was one covariate X i following the Bernoulli distribution with the success probability 0.5 and generated the follow-up time $C_i^{\ast }$ from the uniform distribution over ( τ /2, τ ) with τ = 1. For the underlying recurrent event process $N_i^{\ast }(t)$, we considered two situations.…”

“…In Section 4, we report some results obtained from a simulation study conducted to assess the performance of the multiple imputation procedure. They indicate that the proposed approach performs well for practical situations and can be more efficient than that given in [3]. The method is applied to the Children Cancer Survivor Study (CCSS) mentioned above in Section 5 and Section 6 contains some discussion and concluding remarks.…”

“…Note that both these time periods and discrete time points may be different for different subjects. If each subject gives either complete or incomplete sample path over the whole study period, the observed data are commonly referred to as type I mixed data and other-wise, they are usually referred to as type II mixed data [3]. It is apparent that the latter is much more complicated than the former.…”

“…Among others, one major problem with respect to the analysis of mixed data is to combine the two different types of data structures together. The first paper that discussed statistical analysis of such data was given by [3], which proposed some estimating equation-based methods under the proportional means model. In particular, they presented a set of mixed recurrent event and panel count data arising from a multi-center longitudinal cohort study, the Childhood Cancer Survivor Study (CCSS), of childhood cancer survivors (http://ccss.stjude.org; [4]).…”

“…One of the major goals of the study is to assess the long-term effects, if any, of childhood cancer and cancer treatments on the subsequent reproductive function and more details will be provided below. Following [3], [5] considered the same problem but only for type I mixed data, while [6] investigated regression analysis of mixed recurrent event and panel count data arising from the additive rates model.…”