Bayesian approaches to the regression analysis for longitudinal measurements are
considered. The history of measurements from a subject may convey characteristics
of the subject. Hence, in a regression analysis with longitudinal measurements, the
characteristics of each subject can be served as covariates, in addition to possible other
covariates. Also, the longitudinal measurements may lead to complicated covariance
structures within each subject and they should be modeled properly.
When covariates are some unobservable characteristics of each subject, Bayesian
parametric and nonparametric regressions have been considered. Although covariates
are not observable directly, by virtue of longitudinal measurements, the covariates
can be estimated. In this case, the measurement error problem is inevitable. Hence,
a classical measurement error model is established. In the Bayesian framework, the
regression function as well as all the unobservable covariates and nuisance parameters
are estimated. As multiple covariates are involved, a generalized additive model is
adopted, and the Bayesian backfitting algorithm is utilized for each component of the
additive model. For the binary response, the logistic regression has been proposed,
where the link function is estimated by the Bayesian parametric and nonparametric
regressions. For the link function, introduction of latent variables make the computing
fast.
In the next part, each subject is assumed to be observed not at the prespecifiedtime-points. Furthermore, the time of next measurement from a subject is supposed to
be dependent on the previous measurement history of the subject. For this outcome-
dependent follow-up times, various modeling options and the associated analyses
have been examined to investigate how outcome-dependent follow-up times affect
the estimation, within the frameworks of Bayesian parametric and nonparametric
regressions. Correlation structures of outcomes are based on different correlation
coefficients for different subjects. First, by assuming a Poisson process for the follow-
up times, regression models have been constructed. To interpret the subject-specific
random effects, more flexible models are considered by introducing a latent variable
for the subject-specific random effect and a survival distribution for the follow-up
times. The performance of each model has been evaluated by utilizing Bayesian
model assessments.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2398 |
| Date | 29 August 2005 |
| Creators | Ryu, Duchwan |
| Contributors | Carroll, Raymond J., Mallick, Bani K. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 648666 bytes, electronic, application/pdf, born digital |
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