Table 3.

Compare one-shot nonparametric method and IPCW method. Change point Cox PH model: covariates X and Y are generated from Uniform[0, 1]. Parameters in hazard function are λ₀ = 0.01, β₁ = 3, β₂₀ = 0.1, and β₂₁ = 15. The change point τ = 8.59 is selected such that C_TX = C_TY = 0.655 based on 100,000 simulations. The values of parameter λ for exponential censoring is chosen to achieve the desired censoring proportions. Threshold model: event time T is generated from exponential distribution with the rate λ =1. Two risk scores X and Y are generated from a mixture of bivariate normal distribution described in equation (7), with parameters μ₀ = 2, ρ = 0, ${\sigma }_1^2=9$ and ${\sigma }_2^2=0.25$. The cut point τ = 0.718 is selected such that C_TX = C_TY = 0.803 based on 100,000 simulations. Parameters λ for exponential censoring is chosen to achieve the desired censoring proportions. Sample size n=100.

		The one-shot nonparametric method					The IPCW method
	% Censor	ĈTX	ĈTY	ĈTX − ĈTY	% Reject H0 at α = 5%	% Reject H0 at α = 10%	C̃TX	C̃TY	C̃TX − C̃TY	% Reject H0 at α = 5%	% Reject H0 at α = 10%
n=100
Change point model	0%	0.657	0.660	−0.003	5.0%	9.8%	0.661	0.659	0.002	4.6%	9.1%
	10%	0.663	0.647	0.016	6.4%	11.8%	0.661	0.659	0.002	4.2%	8.3%
	20%	0.669	0.633	0.036	10.5%	18.0%	0.661	0.658	0.002	3.6%	7.3%
	33%	0.68	0.612	0.068	21.9%	31.6%	0.661	0.659	0.002	2.7%	5.7%
	50%	0.695	0.582	0.113	39.4%	51.6%	0.661	0.658	0.003	1.7%	4.1%
	65%	0.710	0.563	0.147	47.2%	59.5%	0.663	0.657	0.006	1.3%	3.1%
	80%	0.720	0.565	0.156	36.3%	48.4%	0.682	0.656	0.027	1.2%	2.7%
Threshold model	0%	0.802	0.802	0.000	5.4%	10.2%	0.803	0.802	0.001	4.9%	9.8%
	10%	0.816	0.803	0.013	7.2%	12.6%	0.803	0.802	0.001	4.5%	8.8%
	20%	0.830	0.805	0.025	10.7%	18.0%	0.803	0.802	0.001	3.8%	7.5%
	33%	0.852	0.808	0.044	20.9%	30.9%	0.805	0.802	0.003	3.3%	6.9%
	50%	0.884	0.818	0.066	40.0%	52.4%	0.809	0.803	0.006	2.1%	5.2%
	65%	0.918	0.834	0.083	57.1%	69.7%	0.821	0.803	0.018	4.7%	8.0%
	80%	0.955	0.865	0.090	65.5%	77.8%	0.863	0.802	0.061	10.2%	17.6%