Joint Models for Recurrent Event data Combining with a Longitudinal Internal Covariate
Date
2023-09-01
Authors
Journal Title
Journal ISSN
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Type
Thesis
Degree Level
Masters
Abstract
In many clinical trials, both longitudinal measurements and time-to-event data are frequently observed
and collected within the same study. However, they are typically analyzed separately, which can lead to
biased results due to measurement errors and missing information. The modern approach to analyze such
data when both longitudinal and time-to-event responses are available is to jointly model the two processes, a
framework in which potential underlying relationships between the two processes are explicitly acknowledged.
Combining the two processes also enables us to mutually borrow information from each process and gain
efficiency in statistical inference. For this reason, the joint modeling approach has gained considerable
attention in recent years. The primary goal is to investigate the relationship between the two processes, and
ultimately to estimate the effects of the longitudinal response on the survival outcomes.
A typical joint modeling setup involves describing the longitudinal process by a linear mixed-effects model,
and the time-to-event process by a parametric survival model. The motivating concept behind the joint modeling
technique is to connect the time-to-event model with the longitudinal process through shared random
effects. Note that a non-parametric method for the time-to-event process often leads to an underestimation
of the standard errors of the parameter estimates. Therefore, joint models based on parametric response distributions
are typically considered in the literature. The parametric methods for time-to-event data analysis
broadly fall into two families: proportional hazards (PH) and the accelerated failure time (AFT) models. In
this thesis, we focus on modeling the time-to-event process using an AFT model (the use of a PH model is a
topic for future research). Note that although a PH model is widely used to describe a time-to-event process
because of its relative risk interpretation, an AFT model is particularly useful when the PH assumption is
violated.
While most studies on joint modeling focus on a single outcome event for the survival process (e.g.,
death or recovery from a disease), some literature extends this method to multiple events. For example,
in a long-term follow-up study the occurrence of the event of interest may not necessarily be a one-time
event but rather an individual can experience the event multiple times over a specified period of time (e.g.,
recurrent asthma attacks). Such processes are called recurrent event processes, and the data generated by
these processes are called recurrent event data. In this thesis, we propose a joint modeling approach that
combines recurrent event data with a longitudinal response (the longitudinal response serves as a covariate
for the recurrent event process, commonly called an internal time-dependent covariate). For example, serum
bilirubin is a surrogate marker (longitudinal response) for time to blood vessel malformations in the skin
(recurrent event process), and we would like to model the time-to-event to investigate the effects of serum bilirunbin on the risk of blood vessel malformations in the skin. As mentioned above, we focus on AFT models
to describe the recurrent event process. We propose a general framework for joint models, and develop a
Bayesian method for statistical inference. We also propose generalized residuals for goodness-of-fit of a joint
model, and develop computational algorithms for data analysis. Our simulation study demonstrates that
the proposed methodology performs well for joint analysis of recurrent event and longitudinal data. We also
demonstrate the application of the proposed methodology with two real data examples of scientific interest:
(1) colorectal cancer data to investigate the effects of tumor size (internal covariate) on the occurrences of
new lesions (recurrent events), and (2) primary biliary cirrhosis (PBC) of the liver data to investigate the
association between serum bilirubin and blood vessel malformations in the skin.
Overall, our work holds significant value in the joint model of recurrent events, both in theory and applications.
The proposed joint model offers a versatile approach for modeling recurrent events by accommodating
various distributions within the AFT framework.
Description
Keywords
Joint Models, Time-to-Event data, Longitudinal Data, Bayesian Inference, AFT model
Citation
Degree
Master of Mathematics (M.Math)
Department
Mathematics and Statistics
Program
Mathematics