Review and Comparison of Computational Approaches for Joint Longitudinal and Time‐to‐Event Models

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/1/insr12322.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/2/insr12322_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/3/Supplement_ReviewComputationalJointModels_final.pd

Bayesian Models for Joint Longitudinal and Multi-State Survival Data

Biomedical data commonly include repeated measures of biomarkers and disease states over time. When the processes determining the biomarker levels and disease states are related, a joint longitudinal and survival model is needed to properly handle the data. In a recent study of adrenal cancer patients at the University of Michigan, their tumors were monitored with repeated radiography scans. Other body measurements, called morphomics, were also measured from these scans. At each scan, it was noted whether the patient's disease was stable, progressing or regressing. In addition, the data include time to death or end of follow-up. Motivated by this data we explore joint models for longitudinal and survival data of several types. In Chapter 2 we compare computational approaches to joint longitudinal and survival models with a single type of event. We examine different joint model formulations especially those most often implemented in software available to statisticians and clinicians. We apply and compare several models to the adrenal data and perform a simulation study to further evaluate each model and software. In Chapter 3 we examine the relationship between a morphomic variable and time to first disease state change which can be either cancer progression or regression, in the adrenal cancer data. We develop Bayesian joint models for longitudinal and competing risks survival data. A seldom considered aspect of competing risk joint models is the relationship between the two competing outcomes. This cannot be examined when using the most common technique, cause-specific hazards models. With that motivation for our future projects, we work under the assumption that each risk has a latent failure time for each individual. We begin with the simple case of conditionally independent risks and model the survival times using parametric distributions. We apply our models to the adrenal data and examine the performance via simulations. In Chapter 4 we extend our joint longitudinal and competing risks models for dependent competing risks. We begin with a discussion of survival copulas and the general joint survival function we will use which is based on an Archimedean copula model. We prove that dependent variables with this joint survival function can be written in terms of independent variables which is useful for simulating data. We develop the model with Weibull marginals. We fit this model to the adrenal data and examine the models using a simulation study. We discuss interpretations of the model and how it can be used to learn about the dependence between risks. Finally, in Chapter 5 we will develop a joint model that incorporates multiple longitudinal outcomes and multistate survival data. We will develop an appropriate model and apply it to the adrenal cancer data.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169659/1/acullen_1.pd