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.