CoxPh model described as $h(t|X)=h_{0}(t)e^{\beta X}$ where $h_{0}(t)$ is the baseline hazard function and is non-parametric. If you have the following model,
require(survival)
surv_object <- Surv(time = ovarian$futime, event = ovarian$fustat)
fit.coxph <- coxph(surv_object ~ rx + resid.ds + age_group + ecog.ps,
data = ovarian)
(fit.coxph)
The cumulative hazard function of the above model $H_{0}(t)$ can be obtained in this manner cumulativeHazard<- basehaz(fit.coxph)
and the smooth baseline hazard function can also be obtained using the method described by Royston
But, assuming you neither have the access to the fitted model (in this case fit.coxph
) nor the data used in modeling (in this case ovarian
), instead you have access to the model's exponentiated coefficients $\beta$ (hazard ratios), sample size $n$ (in this case n=26
), and the number of events $\delta$ (in this case $\delta$=12). Typically, this is what is found in the results of the most published papers(data is never published)
To my question, how can one estimate/approximate the cumulative hazard function $H_{0}(t)$ or even baseline hazard function $h_{0}(t)$ from the available information.
Many thanks
mean(ovarian$futime[ovarian$fustat==1])
$\endgroup$ – Smock Sep 15 '18 at 13:47