Adapting a method for applying the Cox proportional hazards model when the change time of a binary time-varying covariate is interval censored

This dissertation adapts a method for applying the Cox proportional hazards model when the change time of a binary time-varying covariate is interval censored. The bivariate case was motivated by the relationship between cardiovascular disease events and first occurrence of hypertension in males at the Framingham Heart Study. The Heart Study has regularly scheduled examinations every two to four years depending on the cohort. The change time from non-hypertensive to hypertensive state is known only to lie between the last non-hypertensive exam and the first hypertensive exam. A time-dependent Cox model uses the timing of the covariate change relative to event times to assess the effect of the covariate with the event of interest. The hypertension change time is unknown in our data. Our methodology employs the same Monte Carlo EM algorithm as does the original method by Goggins in Biometrics (1999), but introduces a new sampling technique that replaces the Gibbs sampler used in the original. The differences in computing time are analyzed. Along with the new sampling technique, the original method is adapted to allow for two covariates, a multivariable model. The relationship between cardiovascular disease with first occurrences of both hypertension and diabetes prompted this extension. The change times of these two binary time-varying covariates are interval censored, since both hypertension and diabetes statuses are evaluated at each attended examination. Simulations are run to test the validity of our new approach.