Questions 1-8: An investigator is interested in understanding the association between relative abundance of bacteria of the genus Fusobacterium in the gut and colon cancer. Over a 20-year period she follows-up 7,175 individuals, and follows them up for the development of colon cancer. Her results are shown below in Table A.

Table A: Crude Association
	Colon Cancer (+)	Colon Cancer (-)
High abundance of Fusobacterium	545	961	1506
Low abundance of Fusobacterium	1668	4001	5669
	2213	4962	7175

Question 1. Calculate the crude OR and crude RR for the association between abundance of Fusobacterium in the gut and colon cancer.

Question 2. Interpret the crude RR association.

Concerned that her association may be confounded by total dietary fiber intake, a factor known to be associated with both the relative abundance of Fusobacterium in the gut and colon cancer, she stratifies her results by high and low fiber intake and decides to calculate a Mantel-Haenszel adjusted estimate.

Table B: Association in those with Low Fiber Intake
	Colon Cancer (+)	Colon Cancer (-)
High abundance of Fusobacterium	245	850	1095
Low abundance of Fusobacterium	532	2,894	3426
	777	3744	4,521

Table C: Association in those with High Fiber Intake
	Colon Cancer (+)	Colon Cancer (-)
High abundance of Fusobacterium	300	111	411
Low abundance of Fusobacterium	1,136	1,107	2243
	1436	1218	2,654

Question 3. Calculate the stratum-specific associations (both RR and OR).

Question 4. Calculate the Mantel-Haenszel adjusted OR.

Question 5. Interpret your Mantel-Haenszel adjusted estimate.

Question 6. Calculate the magnitude or percent of confounding using the equation we discussed in lecture (based on the OR).

Question 7. What would you expect the Mantel-Haenszel adjusted Risk Ratio to be? How different is it going to be from the crude?

You can use the following formula to calculate the Mantel-Haenszel adjusted Risk Ratio, but it is not required for this question:

(c; + d; 11 RR CMH