Table 1.

Estimated cut-points when (k₁, k₂, a) equals (− 2, 2, 0) 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	0.60	0.06	0.77	0.00	−0.02	0.84	−0.76	− 0.01	1.03
OEHR_1	−0.90	− 0.89	0.15	−0.93	− 0.93	0.16	−1.02	−1.03	0.17
OEHR_2	0.90	0.90	0.15	0.94	0.93	0.15	1.01	1.03	0.17

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