Table 4.

Performance of the two-phase continuous-time Cox model analysis of time to relapse in the National Wilms Tumor Study.

Sampling	Criterion	Estimation performance by regressor
		UHa	Stageb	Agec	dTmrd	U*Se
Full cohort analysis	Ref.	1.027	0.292	0.064	0.022	0.620
SRS	$\sqrt{\mathsf{MSE}}$	0.388	0.313	0.046	0.033	0.600
	Bias	−0.018	0.014	−0.002	0.001	0.028
	$\sqrt{\mathsf{Var}}$	0.387	0.312	0.046	0.033	0.599
Balanced	$\sqrt{\mathsf{MSE}}$	0.413	0.421	0.061	0.043	0.622
	Bias	0.057	0.020	0.010	0.006	−0.008
	$\sqrt{\mathsf{Var}}$	0.409	0.420	0.060	0.042	0.622
Adaptive	$\sqrt{\mathsf{MSE}}$	0.308	0.297	0.048	0.030	0.461
	Bias	−0.000	−0.006	0.007	0.003	0.039
	$\sqrt{\mathsf{Var}}$	0.308	0.296	0.048	0.029	0.459
Oracle	$\sqrt{\mathsf{MSE}}$	0.313	0.332	0.046	0.031	0.477
	Bias	−0.001	0.001	0.000	0.000	0.035
	$\sqrt{\mathsf{Var}}$	0.313	0.332	0.046	0.031	0.476

Note: We used inverse probability weights (IPW) for the two-phase analysis for four different sampling designs for the second phase; (i) simple random sampling (SRS), (ii) balanced sampling, (iii, iv) the proposed adaptive and oracle sampling designs, respectively, determined by the mean score method for the discrete-time survival analysis. We took equal proportions for the pilot and adaptive samples. The target parameter for the mean score design was the interaction between unfavorable histology and late stage disease. Mean squared error and its bias-variance decomposition are estimated from 1000 phase two subsamples of n = 400 from the reduced full cohort (N = 3757). Reference parameters estimates are from the full cohort analysis using the continuous-time Cox model with complete data on all subjects.

^aUnfavorable histology versus favorable.

^bDisease stage III/IV versus I/II.

^cYear at diagnosis.

^dTumor diameter (cm).

^eInteraction effect between UH and Stage.