Rosenberg et al 1980 studied the relationship between coffee

Rosenberg et al. [1980] studied the relationship between coffee drinking and myocardial infarction in young women aged 30-49 years. This retrospective study included 487 cases hospitalized for the occurrence of a myocardial infarction (MI). Nine hundred eighty controls hospitalized for an acute condition (trauma, acute cholecystitis, acute respiratory diseases, and appendicitis) were selected. Data for consumption of five or more cups of coffee containing caffeine were: Compute the odds ratio of a MI for heavy (=>5 cups per day) coffee drinkers vs. nonheavy coffee drinkers. Find the 90% confidence interval for the odds ratio.

Solution

Here is a table that has the vaues of Odds of MI happening to the heavy drinkers vs non-heavy drinkers calculated

Thus, Odds ratio = 1.976

The confidence interval of the odds ratio is calculated on a log scale and reversed back to original

SE of ln(OR)= sqrt ( 1/152 + 1/183 + 1/335 + 1/797)

=0.1276

ln (OR) = ln (1.976) = 0.6810

confidence coeff. for 90% = 1.65

Thus, UL = 0.6810 + 1.65(0.1276) = .8916

LL = 0.6810 - 1.65(0.1276) = 0.4705

Thus, odds ratio confidence interval = ( e^0.4705 , e^0.8916 )

= (1.600 , 2.439 )

Hope this helps. Ask if you have doubts.

Cups	MI (Yes)	Control (No)	Odds
> 5	152	183	0.830601
< 5	335	797	0.420326
	Odds Ratio		1.976087