In many maintenance treatment trials, patients are first enrolled into an open treatment
before they are randomized into treatment groups. During this period, patients are followed
over time with their responses measured longitudinally. This design is very common in
today's public health studies of the prevention of many diseases. Using mixed model theory, one
can characterize these data using a wide array of across subject models. A state-space
representation of the mixed model and use of the Kalman filter allow more fexibility in
choosing the within error correlation structure even in the presence of missing and unequally
spaced observations. Furthermore, using the state-space approach, one can avoid inverting
large matrices resulting in eficient computations. Estimated trajectories from these models can be used as predictors in a survival analysis in judging the efacacy of the maintenance treatments. The statistical problem lies in accounting for the estimation error in these predictors. We considered a bivariate growth curve where the longitudinal responses were unequally spaced and assumed that the within subject errors followed a continuous first
order autoregressive (CAR (1)) structure. A simulation study was conducted to validate
the model. We developed a method where estimated random effects for each subject from
a bivariate growth curve were used as predictors in the Cox proportional hazards model,
using the full likelihood based on the conditional expectation of covariates to adjust for the estimation errors in the predictor variables. Simulation studies indicated that error corrected estimators for model parameters are mostly less biased when compared with the
nave regression without accounting for estimation errors. These results hold true in Cox
models with one or two predictors. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. A Visual Fortran 90 and a SAS IML program are developed.
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-08042004-160209 |
| Date | 27 August 2004 |
| Creators | Dang, Qianyu |
| Contributors | Howard E. Rockette, Sati Mazumdar, Stewart Anderson, Lisa A. Weissfeld, Charles F. Reynolds |
| Publisher | University of Pittsburgh |
| Source Sets | University of Pittsburgh |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.pitt.edu/ETD/available/etd-08042004-160209/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Pittsburgh or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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