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Dang, Qianyu (2004) USING TRAJECTORIES FROM A BIVARIATEGROWTH CURVE OF COVARIATES IN A COXMODEL ANALYSIS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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PDF (Modelling Unequally Spaced Bivariate Growth Curve with Kalman Filter Approach)
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In many maintenance treatment trials, patients are first enrolled into an open treatmentbefore they are randomized into treatment groups. During this period, patients are followedover time with their responses measured longitudinally. This design is very common intoday's public health studies of the prevention of many diseases. Using mixed model theory, onecan characterize these data using a wide array of across subject models. A state-spacerepresentation of the mixed model and use of the Kalman filter allow more fexibility inchoosing the within error correlation structure even in the presence of missing and unequallyspaced observations. Furthermore, using the state-space approach, one can avoid invertinglarge 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 firstorder autoregressive (CAR (1)) structure. A simulation study was conducted to validatethe model. We developed a method where estimated random effects for each subject froma 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 thenave regression without accounting for estimation errors. These results hold true in Coxmodels 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.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Dang, Qianyuqidst1@pitt.eduQIDST1
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairMazumdar, Satimaz1@pitt.eduMAZ1
Committee CoChairAnderson, Stewartsja@nsabp.pitt.eduSJA
Committee MemberReynolds, Charles FReynoldsCF@upmc.eduCHIPR
Committee MemberRockette, Howard Eherbst@pitt.eduHERBST
Committee MemberWeissfeld, Lisa Alweis@pitt.eduLWEIS
Date: 27 August 2004
Date Type: Completion
Defense Date: 20 July 2004
Approval Date: 27 August 2004
Submission Date: 4 August 2004
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: School of Public Health > Biostatistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Cox model; estimation error; Kalman filter; longitudinal data; mixed model
Other ID:, etd-08042004-160209
Date Deposited: 10 Nov 2011 19:56
Last Modified: 19 Dec 2016 14:37


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