TABLE 4.

The National Wilms Tumor Study data example

		Estimation performance by regressor					Sum of squares
Method	Criterion	Hstga	Stageb	Agec	Diamd	H*Se
MLE	$\sqrt{\text{MSE}}$	1.765	0.776	0.014	0.014	0.602	4.080
	Bias	−1.765	−0.776	−0.007	−0.012	0.600	4.076
	$\sqrt{\text{Var}}$	0.031	0.023	0.012	0.008	0.050	0.004
Raking	$\sqrt{\text{MSE}}$	0.132	0.021	0.006	0.003	0.205	0.060
	Bias	0.032	0.000	0.000	0.001	−0.064	0.005
	$\sqrt{\text{Var}}$	0.128	0.021	0.006	0.003	0.195	0.055
RC	$\sqrt{\text{MSE}}$	0.040	0.004	0.004	0.002	0.183	0.196
	Bias	0.403	0.003	0.004	0.002	−0.179	0.195
	$\sqrt{\text{Var}}$	0.022	0.003	0.001	0.001	0.036	0.001
MI	$\sqrt{\text{MSE}}$	0.148	0.015	0.003	0.002	0.173	0.052
	Bias	0.062	−0.003	0.002	0.002	−0.050	0.006
	$\sqrt{\text{Var}}$	0.134	0.014	0.002	0.001	0.166	0.046
MIR	$\sqrt{\text{MSE}}$	0.125	0.019	0.006	0.003	0.182	0.049
	Bias	0.032	0.004	0.001	0.001	−0.047	0.003
	$\sqrt{\text{Var}}$	0.121	0.019	0.006	0.003	0.175	0.046
Full cohort	Estimate	1.193	0.285	0.089	0.028	0.816	−
	SE	0.156	0.105	0.017	0.012	0.227	−

Note: We compare relative performance of the semiparametric efficient maximum likelihood (MLE), standard raking, regression calibration (RC), multiple imputation using the bootstrap (MI), and the proposed multiple imputation with raking (MIR) estimators for a two-phase design with cohort size N = 3915, phase 2 subset $\left|S_2\right|$ = 1338, M = 100 imputations, and 1000 Monte Carlo runs. We report the root-mean squared error ($\sqrt{\text{MSE}}$) for the parameter estimate obtained from the full cohort analysis of the outcome model (13), and its bias and variance decomposition (10).

^aUnfavorable histology vs favorable.

^bDisease stage III/IV vs I/II.

^cYear at diagnosis.

^dTumor diameter (cm).

^eHistology*Stage.