Multiple imputation for estimating hazard ratios and predictive abilities in case-cohort surveys

Marti, Helena; Carcaillon, Laure; Chavance, Michel

doi:10.1186/1471-2288-12-24

BMC Medical Research Methodology

Table 1 Mean of the log hazard ratio estimates (Est), mean of the standard error estimates $\overset{\land}{SE}$ , standard error of the estimates (SE) and mean of the mean square error (MSE). Results of 1,000 simulations.

From: Multiple imputation for estimating hazard ratios and predictive abilities in case-cohort surveys

		Full cohort				Multiple imputation ^a				Weighted estimator
	Est	$\overset{\land}{SE}$	SE	MSE	Est	$\overset{\land}{SE}$	SE	MSE	Est	$\overset{\land}{SE}$	SE	MSE
Z₂ normally distributed
β ₁ = β ₂ = β ₃ = 0
β ₁	-0.003	0.107	0.100	0.010	-0.003	0.107	0.110	0.010	-0.001	0.133	0.128	0.016
β ₂	-0.001	0.054	0.058	0.003	-0.001	0.060	0.062	0.004	0.001	0.065	0.068	0.005
β3	-0.004	0.053	0.056	0.003	-0.004	0.054	0.057	0.003	-0.003	0.058	0.060	0.004
β ₁ = β ₂ = β ₃ = log(2)
β ₁	0.689	0.118	0.113	0.013	0.676	0.119	0.112	0.013	0.696	0.168	0.165	0.027
β ₂	0.687	0.058	0.057	0.003	0.679	0.070	0.068	0.005	0.701	0.088	0.097	0.009
β ₃	0.683	0.057	0.057	0.003	0.679	0.058	0.058	0.004	0.689	0.080	0.090	0.007
Z₂ log normally distributed
β ₁ = β ₂ = β ₃ = 0
β ₁	-0.003	0.107	0.100	0.010	-0.003	0.107	0.100	0.010	-0.004	0.133	0.128	0.016
β2	-0.001	0.027	0.034	0.001	0.015	0.031	0.032	0.001	0.002	0.034	0.038	0.001
β ₃	-0.004	0.053	0.056	0.003	-0.004	0.054	0.058	0.004	-0.005	0.059	0.062	0.004
β ₁ = β ₂ = β ₃ = log(2)
β ₁	0.686	0.058	0.056	0.003	0.621	0.061	0.055	0.008	0.686	0.112	0.117	0.014
β ₂	0.692	0.013	0.015	2e0^-4	0.602	0.015	0.014	0.008	0.695	0.020	0.023	0.001
β ₃	0.685	0.029	0.031	0.001	0.686	0.032	0.031	0.001	0.687	0.049	0.053	0.003
Z₂ uniformly distributed
β ₁ = β ₂ = β ₃ = 0
β ₁	0.007	0.181	0.175	0.031	0.007	0.181	0.175	0.031	0.007	0.197	0.188	0.035
β ₂	-0.001	0.092	0.087	0.008	0.004	0.094	0.088	0.008	-0.002	0.098	0.095	0.009
β ₃	0.003	0.090	0.090	0.008	0.002	0.090	0.090	0.008	0.004	0.093	0.093	0.009
β ₁ = β ₂ = β ₃ = log(2)
β ₁	0.690	0.120	0.116	0.013	0.680	0.121	0.115	0.013	0.694	0.166	0.169	0.028
β ₂	0.695	0.069	0.063	0.004	0.656	0.075	0.066	0.006	0.698	0.087	0.082	0.007
β ₃	0.690	0.058	0.054	0.003	0.689	0.059	0.055	0.003	0.698	0.081	0.081	0.007

^a MI estimates with imputation model: Z ₂ = α ₀ + α ₁ Ind _case + α ₂ Strata + ε, ε ~ N(0, σ)

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ISSN: 1471-2288

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