concordance_index_ipcw output inconsistent with survAUC package

[melodiemonod]

When there is a time-tie between an event and a censoring, the Uno C-index from sksurv-survival is not equal to that found with the survAUC package on R.

Reproducible example:

sksurv-survival with tie

import numpy as np
from sksurv.metrics import  concordance_index_ipcw

test_survival_time = np.array([11., 11., 26.,  89., 128., 299., 300.])
test_survival_status = np.array([1, 0, 0, 1, 0, 1, 0]) 
y_test = np.array(list(zip(test_survival_status, test_survival_time)), dtype=[('survival', '?'), ('futime', '<i8')])

risk_score = np.array([-0.02, 1.20, -0.56, -1.33, -0.81, 1.02, -1.29])

c_uno = concordance_index_ipcw(y_test, y_test, risk_score, tau= 299 )[0]
print(c_uno)

= 0.37426900584795325

survAUC with tie

library(survAUC)

futime = c(11,  11, 26,  89, 128, 299, 300)
fustat = c(1, 0, 0, 1, 0, 1, 0)
Surv.rsp.new = survival::Surv(futime, fustat)

lpnew = c(-0.02, 1.20, -0.56, -1.33, -0.81, 1.02, -1.29)

C_Uno = UnoC(Surv.rsp.new, Surv.rsp.new, lpnew, time =299)
print(C_Uno)

= 0.4129032

Note that without the tie, the results would be the same.

sksurv-survival without tie

test_survival_time_2 = np.array([11., 26.,  89., 128., 299., 300.])
test_survival_status_2 = np.array([1, 0, 1, 0, 1, 0]) 
y_test_2 = np.array(list(zip(test_survival_status_2, test_survival_time_2)), dtype=[('survival', '?'), ('futime', '<i8')])

risk_score_2 = np.array([-0.02, -0.56, -1.33, -0.81, 1.02, -1.29])

c_uno_2 = concordance_index_ipcw(y_test_2, y_test_2, risk_score_2, tau= 299 )[0]
print(c_uno_2)

= 0.4129032258064516

survAUC without tie

futime_2 = c(11, 26,  89, 128, 299, 300)
fustat_2 = c(1, 0, 1, 0, 1, 0)
Surv.rsp.new_2 = survival::Surv(futime_2, fustat_2)

lpnew = c(-0.02, -0.56, -1.33, -0.81, 1.02, -1.29)

C_Uno_2 = UnoC(Surv.rsp.new_2, Surv.rsp.new_2, lpnew, time =299)
print(C_Uno_2)

= 0.4129032

[sebp]

Thanks for reporting this issue.

Interestingly, the reference implementation in R by Hajime Uno gives yet another result:

library(survC1)

futime = c(11,  11, 26,  89, 128, 299, 300)
fustat = c(1, 0, 0, 1, 0, 1, 0)
lpnew = c(-0.02, 1.20, -0.56, -1.33, -0.81, 1.02, -1.29)

C_est = Est.Cval(cbind(futime, fustat, lpnew), tau = 299, nofit = TRUE)
print(C_est$Dhat)

= 0.3514874

If the tied time point consists only of events (fustat[2] = 1), all implementations agree (= 0.612766). Therefore, it seems that the estimator of the censoring distribution differs.