Question

A meta analysis compared aspirin with placebo on incidence of heart attack and of stroke, separately for men and for women. For the Women’s Heal Study, heart attacks were reported for 198 of 19,934 taking aspirin and for 193 of 19,942 taking placebo.

(a) Estimate the odds ratio. Interpret.

(b) Find a 95% confidence interval for the population odds ratio for women. Interpret. (as of 2006, results suggested that for women, aspirin was helpful for reducing risk of stroke but not necessarily risk of heart attack).

Answer 1

SOLUTION-

A.) LET US FIRST CONSTRUCT A 2*2 CONTINGENCY TABLE-

TREATMENT	HEART ATTACK(YES)	HEART ATTACK(NO)	TOTAL
ASPIRIN	198	19736	19934
PLACEBO	193	19749	19942
TOTAL	391	39485	39876

THE ODDS RATIO IS ESTIMATED AS,

HENCE THE ESTIMATED ODDS OF A HEART ATTACK OF A WOMAN TAKING ASPIRIN IS 1.03 TIMES THAT OF A WOMAN TAKING PLACEBO.

B.) THE 95% CONFIDENCE INTERVAL FOR LOG THETA IS GIVEN AS,

WE KNOW,

ALSO,

HENCE THE CONFIDENCE INTERVAL OBTAINED FOR IS

HERE THE ESTIMATED ODDS RATIO IS WITHIN THE CONFIDENCE LIMIT. HENCE ODDS RATIO AND INTERVAL ESTIMATION DEPICTS THAT MOST WOMEN PRONE TO HEART ATTACK ARE THE ONE USING ASPIRIN