Appendix.

We generated data with no association between the exposures and the disease. More specifically, we let the probabilities of being exposed in both case and control to be 0.4, thus the OR of exposure comparing cases and controls are 1. Sensitivities are set to be 0.60, 0.65, and 0.55 for controls; while 0.65, 0.70, and 0.60 for cases. Specificities are set to be 0.85, 0.80, and 0.75 for controls; while 0.90, 0.90, and 0.90 for cases. The following results show that our approach provided less-biased estimate than individual measurements.

True OR	Our method OR	Next-of-kin OR	Expert OR	JEM OR
1.00	1.05	0.95	0.85	0.73