Joint modeling of longitudinal measurements and survival data with competing risks: application to HIV/AIDS study
Date
2017-06-07
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Type
Thesis
Degree Level
Doctoral
Abstract
Joint modeling of longitudinal measurements and survival data is a popular modeling technique in biomedical research (Wulfsohn and Tsiatis, 1997). Most of the studies in joint modeling consider only one failure type for the time-to-event outcome and an assumption of independent censoring. Some literature extends the methodology to allow for the multiple failures (also regarded as competing risks event) that frequently occur in clinical studies. However, only the Cox or other parametric cause-specific hazards (CSH) proportional survival submodels were used in those studies (Cox, 1972).
In this thesis, I study shared random effects joint models that consist of a linear mixed submodel for the longitudinal outcome, and Cox proportional CSH and proportional subdistribution hazards (SDH) submodels for the competing risks events (Fine and Gray, 1999; Laird and Ware, 1982; Rizopoulos, 2012). The longitudinal and the survival outcomes are linked together by latent random effects. To obtain estimates of the parameters, the joint likelihood of the longitudinal process and the survival process is used. The Expectation-Maximization (EM) algorithm was deployed to obtain maximum likelihood estimates of the parameters (Dempster, Laird, and Rubin, 1977).
I applied the methodology to a real HIV dataset that consisted of longitudinal biomarker CD4+ counts and cancer-related AIDS (cancer AIDS), and non-cancer AIDS as time-to-event outcomes. When cancer AIDS is the main event of interest, then non-cancer AIDS is a competing risk and vice versa. I compared results between joint models with the CSH and SDH submodels. For cancer AIDS, results in both the longitudinal and survival submodels varied between the CSH-based and SDH-based joint models. However, for non-cancer AIDS, results were different in the longitudinal submodels but similar in the survival submodels. In my study population, proportions of individuals experiencing cancer AIDS and non-cancer AIDS were 2.7% and 15.0%, respectively. Thus, when non-cancer AIDS was the main event of interest, the proportion of competing event (cancer AIDS) was very low relative to non-cancer AIDS. Previous studies reported that if the proportion of individuals experiencing a competing risk is low, the CSH and SDH models may not provide different results. Hence, I conducted simulation studies to check the performance of the CSH and SDH models for different proportions of events and competing events. I observed that the results between CSH and SDH models are different if the proportion of individuals experiencing a competing risk is not much lower than the proportion experiencing the event of interest.
I also performed simulation study on the joint model to investigate how magnitudes of association parameter between longitudinal and survival outcomes influence the parameter estimates in separate Cox proportional hazards and linear mixed models. I observed that the bias of the estimate in separate Cox regression analysis increases as the magnitude of the association increases.
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Keywords
AIDS, Aids-Defining Illness, Antiretroviral Therapy, Cancer AIDS, Cause-specific Hazards, CD4+ count, Competing risks, HIV, Injection Drug User, Joint model, Kaposi’s Sarcoma, Men who have Sex with Men, Non-cancer AIDS, Non-Hodgkin Lymphoma, Opportunistic Infection, Subdistribution Hazards
Citation
Degree
Doctor of Philosophy (Ph.D.)
Department
School of Public Health
Program
Biostatistics