Table A.3.

Population log odds ratio (PLOR) in the overall population and in a case-control sample compared to two-stage (IV–risk factor association was taken both in the entire case-control sample using a weighted first-stage regression, and in the controls only) and adjusted two-stage estimates of log odds ratio for unit increase in risk factor from modelof confounded association in a case-control setting (Scenario 5). Median estimates across 250 000 simulations

Confounded association		β2 = −1.0	β2 = −0.6	β2 = −0.2	β2 =0	β2 = 0.2	β2 = 0.6	β2 = 1.0
β1 = 0.4	PLOR in population	0.393	0.398	0.398	0.396	0.393	0.377	0.347
	PLOR in sample	0.390	0.397	0.397	0.395	0.390	0.363	0.317
	Two-stage – sample	0.393	0.398	0.398	0.397	0.394	0.381	0.353
	Two-stage – controls	0.392	0.399	0.400	0.399	0.397	0.386	0.361
	Adjusted two-stage	0.395	0.400	0.417	0.428	0.443	0.468	0.474
β1 = 0.8	PLOR in population	−0.629	−0.700	−0.753	−0.769	−0.779	−0.789	−0.789
	PLOR in sample	−0.556	−0.635	−0.713	−0.743	−0.764	−0.783	−0.783
	Two-stage – sample	−0.611	−0.683	−0.741	−0.760	−0.773	−0.783	−0.784
	Two-stage – controls	−0.651	−0.718	−0.769	−0.783	−0.792	−0.795	−0.792
	Adjusted two-stage	−0.991	−1.028	−1.016	−0.988	−0.955	−0.878	−0.819