Dear All,
I'm having just a little terminology problem, relating the language used in
the Hosmer and Lemeshow text on Applied Survival Analysis to that of the
help that comes with the survival package.
I am trying to back out the values for the baseline hazard, h_o(t_i), for
each event time or observation time.
Now survfit(fit)$surv gives me the value of the survival function,
S(t_i|X_i,B), using mean values of the covariates and the coxph() object
provides me with the estimate of the linear predictors, exp(X'B).
If S(t_i|X_i,B)=S_o(t_i)^exp(X_iB) is the expression for the survival
function
And
-ln(S_o(t_i) ) is the expression for the cumulative baseline hazard
function, H_o(t_i)
Then by rearranging the expression for the survival function I get the
following:
-ln(S_o(t_i) ) = -ln( S(t_i|X_i,B) ) / exp(X_iB)
= basehaz(fit)/exp(fit$linear.predictors)
Am I right so far and is there an easier way?
The plot of the cumulative baseline hazard function , H_o(t_i), should be
linear across time. Once I have, H_o(t_i), to get at h_o(t_i) I then need
to reverse the cumsum operation. The corresponding plot should have a
constant baseline hazard over time.
I am aware of cox.zph() for testing the proportionality of hazards
assumption.
Thanks
Alex
Alex Hanke
Department of Fisheries and Oceans
St. Andrews Biological Station
531 Brandy Cove Road
St. Andrews, NB
Canada
E5B 2L9
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