Longitudinal data arise frequently in the analysis of cancer studies. The goal of this proposal will be to develop new Bayesian models and methods to assist in the analysis of, and inference from, longitudinal cancer studies. These new developments can be categorized into four aims.
The first aim will be to develop new (Bayesian) models for the analysis of discrete multivariate longitudinal data.
This aim will build on recent innovative work by Heagerty and others for univariate longitudinal binary data by developing models for multivariate discrete longitudinal data that model marginal covariate effects directly and provide natural ways to model both temporal and multivariate dependence.
The second aim will be to develop flexible and automated methods for subject specific and overall curve fitting in hierarchical models using free knots splines. Methods and RJMCMC algorithms will be proposed that extend and improve current methods in at least three ways: 1) allow different knots for the fixed and random components of the subject-specific curves, 2) properly account for the variability of the between subject covariance matrix, and 3) provide a natural setup for dimension reduction for the random components of the subject-specific curves. Several applications of these methods will be developed, including using this methodology to evaluate cancer biomarkers through joint longitudinal/survival models.
The third aim will address modeling dependence across groups and these ideas will be combined with those in aim 1 to construct models for mixed multivariate longitudinal data. Modeling dependence correctly is very important for inference in the presence of missing data that is missing at random and/or non-ignorable.
The fourth aim will develop flexible Bayesian semi-parametric selection models for longitudinal data with non-ignorable missingness. This will build on recent work by the Principal Investigator's who constructed such models in the non-longitudinal setting without covariates. An important feature of these models will be the preservation of the marginal distribution of the observed data. Many of the methods proposed here are partially motivated by two recently completed cancer clinical trials; a large colorectal cancer clinical trial and a large breast cancer prevention trial. These methods will be illustrated on the data from these trials and will allow specific questions from these trials to be answered, including a comparison of the longitudinal trajectories of quality of life across treatments in both trials, with the breast cancer trial offering the additional complication of having a lot of dropout, thought to be informative. ? ? ? ? ? ?
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