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Recurrent Event Models with Time-Dependent Covariates and Informative Censoring

 Xianghua Luo, PhD Candidate, Johns Hopkins Department of Biostatistics

Many longitudinal follow-up studies record recurrent event data and treat recurrent events as the major outcomes of interest. Examples of recurrent event data are frequently encountered in biomedical, behavioral and social sciences, such as relapses of diseases, hospitalizations, emergency room visits, drug abuses and violent behaviors. In many studies, the occurrence of subsequent recurrent events may be precluded by a terminal event. For example, for AIDS patients the possibility of opportunistic diseases occurring could be precluded by death.  Usually, the terminal events or other censoring events are not independent of the recurrent events. Under this situation, assuming independent censoring like most statistical analyses would be more or less inappropriate.

In the first part of this dissertation, we propose a semiparametric regression model for informatively censored recurrent event data with time-dependent covariates. We know that time-dependent covariates carry more updated information than time-independent ones. Existing statistical methods for Cox-type regression models inherit the feature of dealing with time-dependent covariates, but they typically require independent censoring in the data collecting process. In our approach, subject-specific nonstationary Poisson processes are assumed to be the underlying model, which implies a proportional rate model, so that the regression coefficients have the desirable marginal interpretations. Informative censoring is characterized by a latent variable (frailty), which is treated as a nuisance.  Bias-correction technique through a weighted nonhomogeneous Poisson process is used to circumvent the estimation of the latent variable. A profile estimating function is proposed to estimate regression coefficients. Large sample properties of the proposed estimator are established. The estimating procedures are illustrated by simulation studies and data collected in a juvenile violent behavior study.

The second part of the dissertation is concerned with statistical implications of proportional rate models for recurrent event data in the presence of an explicit terminal event. In such circumstances, various definitions of the rate function have been adopted in the proportional rate models. While these rate functions have quite different interpretations, the recognition of the differences has been lacking theoretically and practically. We carefully compare three types of rate functions for recurrent events from both conceptual and quantitative perspectives, and reach the conclusion that careless use of a certain rate function may lead to misleading scientific conclusions. Simulations are conducted for comparisons of the  focused models. A data analysis of a clinical trial conducted by the Community Programs for Clinical Research on AIDS (CPCRA) is presented to illustrate the analytical results.

In the third part of this dissertation, the focus is placed on time between consecutive recurrent events, i.e., gap time. A set of one-sample semiparametric estimators of the marginal survival function of the gap times is proposed for the focused data. The inverse weighting technique is used to correct the bias caused by informative censoring, and the techniques of within-cluster averaging and within-cluster resampling are adopted to correct the bias caused by informative cluster size (number of observed recurrent events within each subject). The proposed method allows the censoring time to depend on the gap times. The performance of the proposed estimators and an existing method are compared by a sequence of simulation studies.

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