Table 4.

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 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=200 and 400.

		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=200
Change point model	0%	0.656	0.659	−0.003	5.1%	9.9%	0.660	0.658	0.002	5.0%	9.9%
	10%	0.662	0.646	0.016	6.5%	12.8%	0.660	0.658	0.002	4.8%	8.9%
	20%	0.668	0.631	0.037	15.8%	25.7%	0.660	0.657	0.003	3.9%	7.6%
	33%	0.679	0.609	0.070	37.6%	51.2%	0.660	0.658	0.002	3.5%	7.1%
	50%	0.695	0.576	0.119	68.5%	78.0%	0.661	0.657	0.003	2.3%	5.5%
	65%	0.709	0.551	0.158	80.0%	87.5%	0.661	0.656	0.005	2.0%	4.0%
	80%	0.718	0.545	0.173	69.4%	80.5%	0.664	0.653	0.010	1.0%	2.1%
Threshold model	0%	0.803	0.802	0.001	4.8%	10.3%	0.803	0.802	0.001	4.5%	9.9%
	10%	0.817	0.803	0.013	8.0%	14.2%	0.803	0.802	0.001	3.9%	8.9%
	20%	0.831	0.805	0.026	16.3%	25.2%	0.804	0.802	0.002	3.4%	7.7%
	33%	0.852	0.808	0.044	36.9%	48.8%	0.804	0.802	0.002	3.1%	6.5%
	50%	0.885	0.817	0.068	68.9%	79.1%	0.807	0.803	0.004	2.6%	5.6%
	65%	0.919	0.834	0.085	87.6%	92.7%	0.815	0.803	0.013	4.0%	7.0%
	80%	0.956	0.866	0.090	94.3%	97.2%	0.849	0.799	0.050	12.6%	20.7%
n=400
Change point model	0%	0.656	0.656	0.000	4.8%	9.6%	0.660	0.655	0.005	5.9%	10.8%
	10%	0.662	0.643	0.019	11.2%	18.4%	0.660	0.655	0.006	4.9%	9.5%
	20%	0.668	0.628	0.041	30.4%	42.2%	0.660	0.655	0.005	4.2%	8.4%
	33%	0.679	0.605	0.074	61.3%	71.3%	0.660	0.655	0.006	3.4%	7.5%
	50%	0.694	0.570	0.124	54.8%	57.4%	0.660	0.654	0.006	3.6%	7.2%
	65%	0.709	0.541	0.168	37.5%	38.3%	0.661	0.654	0.007	2.3%	5.7%
	80%	0.719	0.532	0.187	55.3%	57.2%	0.662	0.653	0.010	0.8%	1.7%
Threshold model	0%	0.803	0.802	0.000	5.7%	10.1%	0.803	0.802	0.000	5.6%	9.6%
	10%	0.816	0.803	0.013	10.3%	17.7%	0.803	0.803	0.000	5.0%	9.2%
	20%	0.830	0.805	0.025	26.0%	37.5%	0.803	0.803	0.000	4.4%	8.6%
	33%	0.852	0.809	0.044	60.2%	71.5%	0.803	0.803	0.001	2.9%	6.1%
	50%	0.884	0.817	0.067	92.7%	95.8%	0.805	0.803	0.002	2.7%	5.4%
	65%	0.919	0.834	0.085	99.3%	99.7%	0.811	0.803	0.007	3.0%	5.8%
	80%	0.956	0.866	0.090	99.9%	100.0%	0.838	0.800	0.038	14.6%	20.8%