Longitudinal AIDS Data AnalysisLongitudinal AIDS Data AnalysisLongitudinal AIDS Data AnalysisLongitudinal AIDS Data AnalysisOur data: the ddI/ddC studyOur data: the ddI/ddC studyOur data: the ddI/ddC studyOur data: the ddI/ddC studyOur data: the ddI/ddC studyGoal and Subplot of ddI/ddC studyGoal and Subplot of ddI/ddC studyModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsModeling of Longitudinal CD4 CountsPrior SelectionPrior SelectionPrior SelectionPrior SelectionPrior SelectionPrior SelectionExploratory plots of CD4 countMCMC convergence monitoring plotsFixed effect ($alpha $)priors and posteriorsPoint and interval estimatesPoint and interval estimatesFitted population model by drug and DxFitted population model by drug and DxFitted population model by drug and DxChangepoint vs. linear decay modelChangepoint vs. linear decay modelResidual and CPO comparisonResidual and CPO comparisonResidual and CPO comparisonCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsCD4 ``Boost'' at Two MonthsSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisSurvival AnalysisEstimated $S(t)$ and median survivalEstimated $S(t)$and median survivalEstimated $S(t)$and median survivalConclusionsConclusionsConclusionsConclusionsConclusionsConclusionsConclusionsMedical journal references:Medical journal references:Longitudinal AIDS Data AnalysisProblem: Lengthy follow-up times required to evaluateefficacy of a new treatment (e.g., survival time ofHIV-infected patients)Chapter 8.1 Case Study: Analysis of AIDS Data – p. 1/22Longitudinal AIDS Data AnalysisProblem: Lengthy follow-up times required to evaluateefficacy of a new treatment (e.g., survival time ofHIV-infected patients)Solution(?): Select an easily-measured biologicalmarker, known to be predictive of the clinical outcome,as a surrogate endpoint. In AIDS research, typically useCD4 count (number of lymphocytes/mm3blood).Chapter 8.1 Case Study: Analysis of AIDS Data – p. 1/22Longitudinal AIDS Data AnalysisProblem: Lengthy follow-up times required to evaluateefficacy of a new treatment (e.g., survival time ofHIV-infected patients)Solution(?): Select an easily-measured biologicalmarker, known to be predictive of the clinical outcome,as a surrogate endpoint. In AIDS research, typically useCD4 count (number of lymphocytes/mm3blood).BUT several studies have cast doubt on this approach...Chapter 8.1 Case Study: Analysis of AIDS Data – p. 1/22Longitudinal AIDS Data AnalysisProblem: Lengthy follow-up times required to evaluateefficacy of a new treatment (e.g., survival time ofHIV-infected patients)Solution(?): Select an easily-measured biologicalmarker, known to be predictive of the clinical outcome,as a surrogate endpoint. In AIDS research, typically useCD4 count (number of lymphocytes/mm3blood).BUT several studies have cast doubt on this approach...Example: Anglo-French “Concorde” trial showedimmediate AZT produces consistently higher CD4counts than deferred, but survival patterns in twogroups were nearly identical.Chapter 8.1 Case Study: Analysis of AIDS Data – p. 1/22Our data: the ddI/ddC study467 persons randomized to didanosine (ddI) orzalcitabine (ddC)Chapter 8.1 Case Study: Analysis of AIDS Data – p. 2/22Our data: the ddI/ddC study467 persons randomized to didanosine (ddI) orzalcitabine (ddC)HIV-infected patients with AIDS or two CD4 counts of300 or less, and who had failed or could not toleratezidovudine (AZT)⇒ all are very illChapter 8.1 Case Study: Analysis of AIDS Data – p. 2/22Our data: the ddI/ddC study467 persons randomized to didanosine (ddI) orzalcitabine (ddC)HIV-infected patients with AIDS or two CD4 counts of300 or less, and who had failed or could not toleratezidovudine (AZT)⇒ all are very illCD4 counts recorded at baseline, 2, 6, 12, and 18months (some missing)Chapter 8.1 Case Study: Analysis of AIDS Data – p. 2/22Our data: the ddI/ddC study467 persons randomized to didanosine (ddI) orzalcitabine (ddC)HIV-infected patients with AIDS or two CD4 counts of300 or less, and who had failed or could not toleratezidovudine (AZT)⇒ all are very illCD4 counts recorded at baseline, 2, 6, 12, and 18months (some missing)covariates: age, sex, baseline AIDS Dx, baselineKarnofsky score, etc.Chapter 8.1 Case Study: Analysis of AIDS Data – p. 2/22Our data: the ddI/ddC study467 persons randomized to didanosine (ddI) orzalcitabine (ddC)HIV-infected patients with AIDS or two CD4 counts of300 or less, and who had failed or could not toleratezidovudine (AZT)⇒ all are very illCD4 counts recorded at baseline, 2, 6, 12, and 18months (some missing)covariates: age, sex, baseline AIDS Dx, baselineKarnofsky score, etc.outcome variables: clinical disease progression, deathChapter 8.1 Case Study: Analysis of AIDS Data – p. 2/22Goal and Subplot of ddI/ddC studyGoal: Analyze the association among CD4 count,survival time, drug group, and AIDS diagnosis at studyentry (an indicator of disease progression status). Makerecommendations for clinical practice and use of CD4as surrogate marker for death in end-stage patients.Chapter 8.1 Case Study: Analysis of AIDS Data – p. 3/22Goal and Subplot of ddI/ddC studyGoal: Analyze the association among CD4 count,survival time, drug group, and AIDS diagnosis at studyentry (an indicator of disease progression status). Makerecommendations for clinical practice and use of CD4as surrogate marker for death in end-stage patients.Subplot: ddI granted preliminary license in USA basedprimarily on its ability to “boost” CD4 count at 2 months.ddC makers would like to show a similar boost and/orcomparable survival time (“equivalency trial").Chapter 8.1 Case Study: Analysis of AIDS Data – p. 3/22Modeling of Longitudinal CD4 CountsWrite vector of CD4 counts for