Table 2.

The results from 1000 simulated case-control studies from a population under HWE, with independent distributions for haplotypes (H) and environmental covariates (X). Each replicate contains 1000 cases and 1000 controls and is analyzed using the proposed retrospective maximum-likelihood method assuming HWE and H-X independence. Estimates are shown (a) using the known probability of the disease in the population and (b) estimating the probability from the data using the grid-search method.

pr(D=1)	Parameter	Value	Bias	Observed Standard Error	Estimated Standard Error	Coverage Probability
Known	βX	0.10	−0.009	0.053	0.054	0.961
	βH	0.15	−0.013	0.119	0.122	0.945
		0	0.006	0.171	0.172	0.951
		0	−0.007	0.147	0.145	0.948
	βHX	0.20	0.009	0.036	0.037	0.939
		0	−0.001	0.049	0.050	0.953
		0	0.001	0.041	0.042	0.964
	θ	0.25	0.001	0.009	0.009	0.954
		.15	< 0.001	0.009	0.009	0.954
		.05	< 0.001	0.004	0.004	0.938
Unknown	βX	0.10	−0.006	0.054	0.056	0.961
	βH	0.15	−0.008	0.123	0.129	0.961
		0	0.006	0.171	0.172	0.951
		0	−0.007	0.147	0.145	0.949
	βHX	0.20	0.007	0.040	0.043	0.964
		0	−0.001	0.049	0.049	0.953
		0	0.001	0.041	0.042	0.963
	θ	0.25	< 0.001	0.010	0.011	0.967
		.15	< 0.001	0.009	0.009	0.956
		.05	< 0.001	0.004	0.004	0.939