Instrumental Variable Modeling in a Survival Analysis Framework.

Open Access
Author:
Atiyat, Muhammad
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 21, 2011
Committee Members:
  • Dr. Debashis Ghosh, Committee Chair
  • Dr. Bruce Lindsay, Committee Member
  • Dr. Bing Li, Committee Member
  • Dr. Christopher Zorn, Committee Member
Keywords:
  • survival analysis
  • endogeneity
  • instrumental variable
  • proportional hazards model
  • additive hazards model
  • AFT model.
Abstract:
Often we are interested in examining whether the time until a particular event occurs depends on explanatory variables. For example, does an individual's survival time from cancer depend on the treatment that is given? Studies involving event times, such as death time due to cancer, are usually subject to censoring. In the cancer example, censoring refers to the fact that we are unable to observe all death times from cancer before our data analysis. This could be due to the patient being alive by the end of the study, the patient died from another cause, or another reason. Some of the well known models used to examine relationships between an event time and explanatory variables are the Cox proportional hazards model (PH) (Cox, 1972), the additive hazards model for right censored data (AHRC) (Lin and Ying, 1994), and the accelerated failure time (AFT) model. A common situation that analysts run into is that the explanatory variables used in examining potential relationships are a ffected by unobserved variables which in turn aff ect the event time of interest. This situation is referred to as endogeneity. Currently, there are no methods addressing endogeneity in the context of the PH, AHRC, and AFT models. Methods addressing endogeneity commonly use instrumental variables; some of these methods are two-stage predictor substitution (2SPS) (Terza et al., 2008), two-stage residual inclusion (2SRI) (Terza et al., 2008), and jackknife instrumental variable estimators (Angrist et al., 1999). In this work, I examine the performances of 2SPS and 2SRI in terms of adjusting for endogeneity in the context of the PH, AHRC, and AFT models. In addition, by combining the methodology of Angrist et al. (1999) with that of Buckley and James (1979), Koul et al. (1981), and an idea from Fygenson and Zhou (1992), I propose three methods which enable us to adjust for endogeneity in the AFT model. The performances of the proposed methods are compared with the original methods. We illustrate our methods on liver disease data.