Mantel-Haenszel method

We consider hypothetical data from a case-control study for coronary heart disease (CHD) and oral contraceptive use (modeled after an example from Koepsell and Weis). Assume that physical activity status is thought to be associated with OC use as well as the occurrence of CHD. Thus, physical activity status is a potential confounder in the relationship between OC use and CHD. Below is a table presenting the case-control data stratified by physical activity status (sedentary versus active).

	Sedentary			Active
	CHD Case	Control	Total	CHD Case	Control	Total
OC User	48	29	77	28	57	85
Non-OC User	24	44	68	5	33	38
Total	72	73	145	33	90	123

1. Calculate the OR for CHD according to OC use (NOT stratified by physical activity status).
2. Calculate the OR for CHD according to OC use within each physical activity stratum.

3. Based on the ORs obtained in questions a and b, what is the best way to present the OR for CHD according to OC use in order to appropriately illustrate the etiologic relationship between the risk factor and the disease outcome? That is, should one us one overall unadjusted OR, two stratified (physical-activity specific) ORs, or one OR adjusted for physical activity? Briefly state why. ( Hints: (a). if no confounding and/or interaction, one overall unadjusted OR should be used; (b). if there is interaction, two stratified Ors should be used; (c). if there is only confounding, an adjusted OR should be used)

4. Assume that physical activity is a confounder; we will use the Mantel-Haenszel method of weighing the relative odds from a small series of 2x2 tables to calculate a summary the relative odds. Please complete the following table and calculate a Mantel-Haenszel adjusted OR.

Strata	Physical Activity	OC Use	Cases	Controls	Ni	ai di / Ni	ci bi / Ni
1	Sedentary	OC Use	a=48	b=29	145	14.57	4.8
		No OC Use	c=24	d=44
2	Active	OC Use	a=28	b=57	123	7.51	2.32
		No OC Use	c=5	d=33
	Total ()	--	--	--	--	22.08	7.12

5. Please use a full sentence to interpret the Mantel-Haenszel adjusted OR from Part d