A novel approach to determine two optimal cut-points of a continuous predictor with a U-shaped relationship to hazard ratio in survival data: simulation and application

Table 3 Estimated cut-points when (k₁, k₂, a) equals (−4/3, 4, 1) in simulation data

Method	P_c = 0%			P_c = 20%			P_c = 50%
Method	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	−0.08	−0.08	0.15	−0.19	−0.20	0.17	−0.51	− 0.51	0.20
OEHR_1	−0.41	−0.39	0.23	−0.45	− 0.46	0.24	− 0.60	−0.59	0.26
OEHR_2	1.49	1.49	0.08	1.51	1.52	0.08	1.55	1.55	0.10

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

ISSN: 1471-2288