Table 1.

Simulated data for a randomized study of 1,000 participants where 30% of participants are diabetics. Diabetes increases the risk of death, but the treatment reduces mortality by 50% (on a multiplicative scale) in both diabetics and non-diabetics. The relative risk is collapsible. The crude odds ratio is a population weighted average of the odds ratio in the two strata (population standardized odds ratio).

	Dead	Alive	Total	Risk	Relative Risk (95%CI)	Odds Ratio (95%CI)
All Patients
Treated	130	370	500	26%	0.50 (0.42 to 0.59)	0.32 (0.25 to 0.43)
Control	260	240	500	52%
Total	390	610	1000
Non-Diabetic Patients
Treated	70	280	350	20%	0.50 (0.39 to 0.64)	0.38 (0.26 to 0.53)
Control	140	210	350	40%
Total	210	490	700
Diabetic Patients
Treated	60	90	150	40%	0.50 (0.40 to 0.62)	0.17 (0.10 to 0.29)
Control	120	30	150	80%
Total	180	120	300