Table 2.

Estimated cut-points when (k₁, k₂, a) equals (−8/5, 8/3, 1/2) in simulation data

Method	Pc = 0%			Pc = 20%			Pc = 50%
	Median	Mean	Sim SE	Median	Mean	Sim SE	Median	Mean	Sim SE
Median ‘	−0.01	0.00	0.05	− 0.01	0.00	0.05	−0.01	0.00	0.05
Q1Q3_1	−0.68	−0.68	0.06	−0.68	− 0.68	0.06	− 0.68	−0.68	0.06
Q1Q3_2	0.67	0.67	0.07	0.67	0.67	0.07	0.67	0.67	0.07
MinP	−0.42	−0.40	0.13	−0.47	−0.48	0.15	−0.73	− 0.74	0.16
OEHR_1	−0.58	− 0.61	0.20	−0.65	− 0.65	0.19	− 0.80	− 0.77	0.22
OEHR_2	1.17	1.18	0.11	1.21	1.21	0.10	1.30	1.29	0.13

P_c = censoring proportion; Sim SE = simulation standard error; Median ‘= using the median value of the continuous covariate as a cut-point; Q1Q3 = using the upper and lower quartiles values as cut-points, Q1Q3_1 is the upper quartile value and Q1Q3_2 is the lower quantile value; MinP = the single cut-point minimum p-value method with log-rank test; OHER = the optimal equal-HR method proposed in this study, OEHR_1 is the left estimated cut-point and OEHR_2 is the right estimated cut-point