An Introspective Overview of the Dynamics of Recurrent Events Data Analysis

A recurrent event remains the outcome variable of interest in many biometric studies. Recurrent events can be explained as events of defined interest that can occur to same person more than once during the study period. This study presents an overview of different pertinent recurrent models for analyzing recurrent events. Aims: To introduce, compare, evaluate and discuss pros and cons of four models in analyzing recurrent events, so as to validate previous findings in respect of the superiority or appropriateness of these models. Study Design: A comparative studies based on simulation of recurrent event models applied to a tertiary data on cancer studies. Methodology: Codes in R were implemented for simulating four recurrent event models, namely; The Andersen and Gill model; Prentice, Williams and Peterson models; Wei, Lin and Weissferd; and Cox frailty model. Finally, these models were applied to analyze the first forty subjects from a study of Bladder Cancer Tumors. The data set contained the first four repetitions of the tumor for each patient, and each recurrence time was recorded from the entry time of the patient into the study. An isolated risk interval is defined by each time to an event or censoring. Results: The choice and usage of any of the models lead to different conclusions, but the choice depends on: risk intervals; baseline hazard; risk set; and correlation adjustment or simplistically, type of data and research question. The PWP-GT model could be used if the research question is focused on whether treatment was effective for the event since the previous event happened. However, if the research question is designed to find out whether treatment was effective for the event since the start of treatment, then we could use the PWP- TT. The AG model will be adequate if a common baseline hazard could be assumed, but the model lacks the details and versatility of the event-specific models. The WLW model is very suitable for data with diverse events for the same person, which underscores a potentially different baseline hazard for each type. Conclusion: PWP-GT has proven to be the most useful model for analyzing recurrent event data.

Maximum Likelihood Estimation for an Inhomogeneous Gamma Process with a Log-linear Rate Function

An inhomogeneous gamma process is a compromise between a renewal process and a nonhomogeneous Poisson process, since its failure probability at a given time depends both on the age of the system and on the distance from the last failure time. The inhomogeneous gamma process with a log-linear rate function is often used in modelling of recurrent event data. In this paper, it is proved that the suitably non-uniform scaled maximum likelihood estimator of the three-dimensional parameter of this model is asymptotically normal, but it enjoys the curious property that the covariance matrix of the asymptotic distribution is singular. A simulation study is presented to illustrate the behaviour of the maximum likelihood estimators in finite samples. Obtained results are also applied to real data analysis.

Additive rates model for recurrent event data with intermittently observed time-dependent covariates

Various regression methods have been proposed for analyzing recurrent event data. Among them, the semiparametric additive rates model is particularly appealing because the regression coefficients quantify the absolute difference in the occurrence rate of the recurrent events between different groups. Estimation of the additive rates model requires the values of time-dependent covariates being observed throughout the entire follow-up period. In practice, however, the time-dependent covariates are usually only measured at intermittent follow-up visits. In this paper, we propose to kernel smooth functions involving time-dependent covariates across subjects in the estimating function, as opposed to imputing individual covariate trajectories. Simulation studies show that the proposed method outperforms simple imputation methods. The proposed method is illustrated with data from an epidemiologic study of the effect of streptococcal infections on recurrent pharyngitis episodes.

Semiparametric estimation of the proportional rates model for recurrent events data with missing event category

Proportional rates models are frequently used for the analysis of recurrent event data with multiple event categories. When some of the event categories are missing, a conventional approach is to either exclude the missing data for a complete-case analysis or employ a parametric model for the missing event type. It is well known that the complete-case analysis is inconsistent when the missingness depends on covariates, and the parametric approach may incur bias when the model is misspecified. In this paper, we aim to provide a more robust approach using a rate proportion method for the imputation of missing event types. We show that the log-odds of the event type can be written as a semiparametric generalized linear model, facilitating a theoretically justified estimation framework. Comprehensive simulation studies were conducted demonstrating the improved performance of the semiparametric method over parametric procedures. Multiple types of Pseudomonas aeruginosa infections of young cystic fibrosis patients were analyzed to demonstrate the feasibility of our proposed approach.