Transient effects in the Cox regression model.

Semi-parametric hazard function regression models with time-dependent covariates are developed to model the hazard for the second treatment, relative to the first, in a cross-over experiment. These models characterize the relative hazard of the second treatment versus the first as a transient increase at time of change followed by a long term decrease. Two models are developed for the relative hazard over time: a discrete step function and a smooth exponential decay. The models are used to compare mortality rates for kidney failure patients as they switch from dialysis to transplant therapy. The hazard functions for these two treatments are shown to cross at some time after transplant. The parameter estimates from the exponential decay model are used to estimate the times at which the hazard and survival functions cross, and to estimate truncated expected remaining lifetimes for the two treatments. Several methods are compared for computing confidence intervals and standard errors for the resulting estimators. Non-identifiability problems are documented at the boundary of the parameter space for the exponential decay model. These result in problems related both to computation, which are addressed, and to asymptotic properties of the estimators, which are reviewed. These issues are particularly relevant to the test of the null hypothesis of no transient effect. Two bootstrap methods to carry out a likelihood ratio test for this hypothesis are proposed and are studied through simulation. One method estimates the null hypothesis distribution of the likelihood ratio test statistic based on its distribution at a different, data-based, null hypothesis. Another method uses semi-parametric bootstrap techniques to generate data under the null hypothesis. In the situations examined, the semi-parametric bootstrap approach yields a more accurate estimate of the distribution of the likelihood ratio test statistic. The simulation results are compared to chi-square mixture distributions.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104988/1/9624681.pdfDescription of 9624681.pdf : Restricted to UM users only