Breslow estimator of the baseline cumulative hazard — morie_cox_breslow

The Cox partial likelihood throws the baseline away; this puts it back, as a step function jumping at each event time by \(d_j / \sum_{i \in R_j} \exp(x_i'\beta)\).

Usage

morie_cox_breslow_step(time, event, X, beta = NULL, ties = "efron")

Arguments

time: follow-up times, non-negative.
event: 1 for an event, 0 for right-censored.
X: covariate matrix, one row per subject.
beta: coefficient vector. Fitted internally when NULL.
ties: tie correction used for the internal fit.

Value

list with times, hazard, cumhazard, survival.

Details

"Baseline" means x = 0, which for uncentred covariates is a subject who does not exist – centre the covariates or the curve is not interpretable. The curve is also undefined past the last event time; it is drawn flat there by convention, not by evidence.

References

Breslow, N. (1972). Discussion of Professor Cox's paper. JRSS-B, 34(2), 216-217.

Examples

set.seed(1)
X <- matrix(rnorm(60), ncol = 1)
tt <- rexp(60, exp(X * 0.5))
tail(morie_cox_breslow_step(tt, rep(1, 60), X)$cumhazard, 1)
#> [1] 5.495108