Table 1.

Simulation results for ${\beta }_1$ under scenario 1 where the model ${\pi }_1(\mathbf{W},\mathit{\gamma })$ was correctly specified

n	$p_m$ (%)	Method	Bias	MCSD	ASE	CP	MSE	RE
200	25	Proposed MPPLE	0.002	0.409	0.396	0.945	0.167	1.000
		AIPW	0.003	0.412	0.418	0.946	0.170	1.013
		MI(5)	0.009	0.424	0.419	0.941	0.180	1.074
	44	Proposed MPPLE	0.007	0.450	0.428	0.943	0.203	1.000
		AIPW	0.009	0.464	0.468	0.943	0.215	1.061
		MI(5)	0.004	0.460	0.461	0.946	0.211	1.043
	56	Proposed MPPLE	0.004	0.492	0.468	0.942	0.242	1.000
		AIPW	0.009	0.526	0.540	0.949	0.277	1.144
		MI(5)	$-$ 0.004	0.502	0.510	0.951	0.253	1.043
400	25	Proposed MPPLE	0.001	0.284	0.282	0.948	0.081	1.000
		AIPW	$-$ 0.001	0.289	0.288	0.949	0.084	1.038
		MI(5)	$-$ 0.004	0.290	0.290	0.948	0.084	1.046
	44	Proposed MPPLE	$-$ 0.001	0.308	0.305	0.949	0.095	1.000
		AIPW	$-$ 0.004	0.326	0.321	0.946	0.106	1.116
		MI(5)	$-$ 0.008	0.320	0.316	0.950	0.102	1.076
	56	Proposed MPPLE	$-$ 0.003	0.337	0.333	0.946	0.114	1.000
		AIPW	$-$ 0.008	0.368	0.364	0.937	0.135	1.191
		MI(5)	$-$ 0.006	0.350	0.346	0.940	0.122	1.077
2000	25	Proposed MPPLE	0.003	0.124	0.126	0.955	0.015	1.000
		AIPW	0.003	0.126	0.127	0.950	0.016	1.029
		MI(5)	0.003	0.127	0.127	0.955	0.016	1.045
	44	Proposed MPPLE	0.005	0.132	0.136	0.954	0.017	1.000
		AIPW	0.005	0.137	0.139	0.953	0.019	1.080
		MI(5)	0.003	0.139	0.138	0.950	0.019	1.119
	56	Proposed MPPLE	0.002	0.142	0.148	0.956	0.020	1.000
		AIPW	0.002	0.152	0.155	0.941	0.023	1.150
		MI(5)	0.003	0.153	0.150	0.946	0.023	1.164

$p_m$, percent of missingness; MCSD, Monte Carlo standard deviation; ASE, average estimated standard error; CP, coverage probability; MSE, mean squared error; RE, variance of the estimator to variance of the proposed MPPLE (relative efficiency); MPPLE, maximum partial pseudolikelihood estimator; AIPW, augmented inverse probability weighting estimator; MI(5), Lu and Tsiatis type B multiple imputation based on 5 imputations