THESIS DEFENSE ABSTRACT
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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