We continue work from our previous proposal in developing new Bayesian methodology for longitudinal cancer data with missingness. In the presence of missing data that is related to observed or unobserved responses, it is known that mis-specifying the dependence will most often result in biased estimates of mean parameters. In addition, in such settings, flexible, parsimonious dependence models are often necessary. Such models are not currently available for correlation matrices (which form an integral part of many longitudinal models).
The first aim of this proposal will introduce a new parameterization for a correlation matrix for longitudinal responses that offers considerable benefits with respect to prior specification and modeling. We will explore several models and priors and their associated properties, computational issues and strategies both with respect to automated parsimonious modeling, posterior sampling, and high-dimensional problems, and their implementation in a wide array of longitudinal models with applications.
The second aim will explore the extension of these models to multivariate longitudinal data. In particular, we will explore the 'ordering'of the multivariate longitudinal response vector with regards to parsimonious models and prior specification and correlation/covariance structures for which this ordering is not an issue. In the third aim, we will develop new Bayesian approaches for causal inference in longitudinal cancer studies in which repeatedly measured outcomes may be informatively missing due to loss to follow-up or protocol-defined events (progression or death). In seeking to draw inference about causal estimands, non-identifiable assumptions are required. We will introduce low-dimensional, interpretable parameterizations of these assumptions and elicit priors for these parameters from scientific experts. These methods will be used to answer questions of interest from several recent cancer clinical trials including assessing potential surrogate markers (Specific Aim 1), exploring the relationship between patient reported (quality of life) and physician reported (toxicity) outcomes (Specific Aim 2), and making inference at the end of quality of life studies when subjects have dropped out due to cancer progression or death (Specific Aim 3).
The new methods proposed in this application will have important public health benefits. They will facilitate drawing correct inferences from quality of life studies for late stage cancers, understanding the relationship between physician reported and patient reported outcomes, and making earlier determinations of treatment effects.
|Daniels, M J; Wang, C; Marcus, B H (2014) Fully Bayesian inference under ignorable missingness in the presence of auxiliary covariates. Biometrics 70:62-72|
|Wang, Y; Daniels, M J (2014) Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor. J Multivar Anal 130:21-26|
|Gaskins, J T; Daniels, M J; Marcus, B H (2014) Sparsity Inducing Prior Distributions for Correlation Matrices of Longitudinal Data. J Comput Graph Stat 23:966-984|
|Das, Kiranmoy; Daniels, Michael J (2014) A semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data. Biometrics 70:33-43|
|Gaskins, Jeremy T; Daniels, Michael J (2013) A Nonparametric Prior for Simultaneous Covariance Estimation. Biometrika 100:|
|Wang, Y; Daniels, M J (2013) Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances. J Multivar Anal 116:130-140|
|Lee, Keunbaik; Daniels, Michael J; Joo, Yongsung (2013) Flexible marginalized models for bivariate longitudinal ordinal data. Biostatistics 14:462-76|
|Li, Ning; Daniels, Michael J; Li, Gang et al. (2013) An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout. Biom J 55:17-37|
|Daniels, Michael J; Chatterjee, Arkendu S; Wang, Chenguang (2012) Bayesian model selection for incomplete data using the posterior predictive distribution. Biometrics 68:1055-63|
|Wang, Weiwei; Scharfstein, Daniel; Wang, Chenguang et al. (2011) Estimating the Causal Effect of Low Tidal Volume Ventilation on Survival in Patients with Acute Lung Injury. J R Stat Soc Ser C Appl Stat 60:475-496|
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