Result Discrepancy between lifelines CoxTimeVaryingFitter and R survival

[opendataminer]

A very simple test case that illustrate the result discrepancy, the param for x are identical for both cases, but the baseline cumulative hazard are different, especially the index t are of different values! My fault if it is due to any misusage of the 2 packages.

Python Version

from lifelines import CoxTimeVaryingFitter

test2 = pd.DataFrame(dict(
    start=[1, 2, 5, 2, 1, 7, 3, 4, 8, 8],
    stop =[2, 3, 6, 7, 8, 9, 9, 9,14,17],
    event=[1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
    x    =[1, 0, 0, 1, 0, 1, 1, 1, 0, 0 ]
))

s_model = CoxTimeVaryingFitter(penalizer=0)
s_model.fit(test2, event_col='event', start_col='start', stop_col='stop', 
            formula=' ~ x', show_progress=False, robust=False)

s_model.baseline_cumulative_hazard_

Output

R Version

library(survival)

test2 <- list(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8),
                   stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17),
                   event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0),
                   x    =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) )

cox_pp_00 <- coxph( Surv(start, stop, event) ~ x, test2, robust = FALSE, ties = 'efron', method = 'efron')

basehaz(cox_pp_00, centered=FALSE)

Output

[MetzgerSK]

For what it's worth: the apparent R/Python mismatch might have the source as the R/Stata mismatch, as described here.

I mention it only because when I flipped basehaz(cox_pp_00, centered=FALSE) in your MWE to basehaz(cox_pp_00, centered=TRUE), the output was identical to centered=FALSE:

> basehaz(cox_pp_00, centered=FALSE)
     hazard time
1 0.5052761    2
2 0.8409462    3
3 1.0434840    6
4 1.2974621    7
5 1.5514402    8
6 2.0066161    9
7 2.0066161   14
8 2.0066161   17
> basehaz(cox_pp_00, centered=TRUE)
     hazard time
1 0.5052761    2
2 0.8409462    3
3 1.0434840    6
4 1.2974621    7
5 1.5514402    8
6 2.0066161    9
7 2.0066161   14
8 2.0066161   17

The identical output, to me, suggests that centered isn't touching the part of survival's behavior that gives rise to the R/Stata differences, meaning that behavior's still in play to explain the R/Python discrepency.