5. Hazard Regression

Birgit Grund and Lijian Yang
18 November 2003

Hazard regression models are convenient tools to discover the structure and dependencies in time-to-event data with covariates. In medical research, the influence of certain covariates on the length of patients' survival is often evaluated with hazard regression models, see, for instance, Cox and Oakes (1984). In econometrics, hazard regression is being used, among others, to model insurance industry and employment data; see, for example, Heckman and Singer (1985), Lancaster (1990).

The XploRe quantlib hazreg provides a number of quantlets for the analysis of right-censored time-to-event data. These include Kaplan-Meier estimates of the survival function and pointwise confidence intervals for the Kaplan-Meier estimates. For the Cox proportional hazards model, we provide estimates for the regression coefficients and their covariance matrix, significance tests for the regression coefficients, and estimates for the baseline hazard and conditional survival functions. This chapter is a tutorial for the quantlets in the hazreg quantlib. We provide the syntax, shortly describe the underlying statistical theory, and illustrate their use with examples. In Section 5.1, we introduce right-censored time-to-event data and present quantlets that arrange the data into a form suitable for analysis in XploRe . Section 5.2 is dedicated to Kaplan-Meier estimates and corresponding confidence intervals for the survival function. Section 5.3 describes semiparametric estimation and hypothesis testing in the Cox proportional hazards model. We apply these methods to a data set on the length of stay in nursing homes.