basehaz.gbm: Baseline hazard function

Description

Computes the Breslow estimator of the baseline hazard function for a proportional hazard regression model.

Usage

basehaz.gbm(t, delta, f.x, t.eval = NULL, smooth = FALSE, cumulative = TRUE)

Value

A vector of length equal to the length of t (or of length

t.eval if t.eval is not NULL) containing the baseline hazard evaluated at t (or at t.eval if t.eval is not

NULL). If cumulative is set to TRUE then the returned vector evaluates the cumulative hazard function at those values.

Arguments

t: The survival times.
delta: The censoring indicator.
f.x: The predicted values of the regression model on the log hazard scale.
t.eval: Values at which the baseline hazard will be evaluated.
smooth: If TRUE basehaz.gbm will smooth the estimated baseline hazard using Friedman's super smoother supsmu.
cumulative: If TRUE the cumulative survival function will be computed.

Author

Greg Ridgeway gregridgeway@gmail.com

Details

The proportional hazard model assumes h(t|x)=lambda(t)*exp(f(x)). gbm can estimate the f(x) component via partial likelihood. After estimating f(x), basehaz.gbm can compute the a nonparametric estimate of lambda(t).

References

N. Breslow (1972). "Discussion of `Regression Models and Life-Tables' by D.R. Cox," Journal of the Royal Statistical Society, Series B, 34(2):216-217.

N. Breslow (1974). "Covariance analysis of censored survival data," Biometrics 30:89-99.