Baseline hazard function

Computes the Breslow estimator of the baseline hazard function for a proportional hazard regression model - only for censored survival data.

Usage

baseline_hazard(surv_times, delta, coxph_preds, eval_times=NULL, smooth=FALSE,
cumulative=TRUE)

Arguments

surv_times

the survival times - an atomic vector of doubles

delta

the censoring indicator - a vector same length as surv_times

coxph_preds

the predicted values of the regression model on the log hazard scale

eval_times

values at which the baseline hazard will be evaluated

smooth

if TRUE baseline_hazard 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 surv_times (or of length eval_times if eval_times is not NULL) containing the baseline hazard evaluated at t (or at eval_times if eval_times 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)). gbmt can estimate the f(x) component via partial likelihood. After estimating f(x), baseline_hazard can compute 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.

See also

survfit, gbmt

Author

James Hickey, Greg Ridgeway gregridgeway@gmail.com