Baseline hazard function

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)

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.

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.

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.

Author

Greg Ridgeway gregridgeway@gmail.com