Psy 2003				Statistics				Risk and Odds

The data below appeared are from Prescott, Hippe, Schnor, and Vestbo (1998); see Utts and Heckard, 2002.

	Sample Size	Heart Attacks	Risk of Heart Attack	Odds of Heart
Attack	
Men					
     Smokers	8490	902	(902/8490) 10.62%	(902/7588) .12 to 1	
     Nonsmokers	4701	349	(349/4701) 7.38%	(349/4352) .08 to  1	
Women					
     Smokers	6461	380	(380/6461)  5.88%	(380/6081) .06 to 1	
     Nonsmokers	5011	132	(132/5011) 2.63%	(132/4879) .027 to 1	

Risk= Number in Category / Total  ( usually expressed as a percentage but it is a probability)

Relative Risk= Risk in Category 1 / Risk in Category 2

Percentage Increase in Risk = (Relative Risk –1) X 100%

Risk of heart attack for men who smoke = 10.62%

Relative Risk of heart attack for men that smoke =  10.62 / 7.38 = 1.43

Percentage Increase in Risk for men who smoke = (1.43 –1) x 100% = 43%

Risk of heart attack for women that smoke = 5.88%  

Relative Risk of heart attack for women that smoke =  5.88 / 2.63 = 2.24

Percentage Increase in Risk for women who smoke = (2.24 –1) x 100% =124%

The important point here is that relative risk is affected by baseline risk, so it is important to know the baseline risk. 

Odds = Number in Category 1 / Number in Category 2

Odds Ratio = Odds of heart attack for smokers / Odds of heart attack for nonsmokers