1. Relative Risk, Increased Risk, and Odds Ratios Measures that allow us to compare two groups...

2. Example: Plaque Breaks and Heart Attacks

3. The comparison 0.68/0.21 = 3.24 “Men who died during strenuous activity were more than 3 times as likely to have ruptured plaque than men who engaged in normal activity.”

4. Relative risk Relative Risk = P(Diseased|Exposed) ÷ P(Diseased|Unexposed)

5. Example: Gender and Tattoos Rows: gender Columns: tattoo N Y All M 74 16 90 82.22 17.78 100.00 F 79 8 87 90.80 9.20 100.00 All 153 24 177 86.44 13.56 100.00 Cell Contents -- Count % of Row

6. The comparison 0.1778/0.0920 = 1.93 “Males in Fall 1998 Stat 250 classes were almost twice (“2 times”) as likely to have a tattoo than females in Fall 1998 Stat 250 classes.”

7. Interpretation of relative risk Relative risk of 1 means that each “exposed” group is equally likely to have the “disease.” 10% of students who take Stat 250 appreciate statistics 10% of students who don’t take Stat 250 appreciate statistics RR of appreciating statistics = 0.10 /0.10 = 1

8. Interpretation of relative risk If RR = 1, the exposed and unexposed groups are equally likely to get the disease. If RR < 1, the exposed group is less likely to get the disease than the unexposed group. If RR > 1, the exposed group is more likely to get the disease than the unexposed group.

9. Increased Risk as an alternative to Relative Risk Relative risk is the “number of times more likely” one event is to occur over another. Alternatively, can report the amount as a “percent more likely”. In this case, called “the increased risk.” RR of 1 means a 0 percent increased risk. To find increased (or decreased) risk, find percentage above (or below) 1.

10. Increased Risk 1.93 - 1.00 = 0.93  100 = 93% Males in Fall 1998 Stat 250 classes are 93 percent more likely to have a tattoo than females in Fall 1998 Stat 250 classes. What is the increased risk of male Stat 250 students having a tattoo over female Stat 250 students?

11. Increased risk Increased risk = (Relative Risk - 1.00)  100

12. Increased risk “The researchers found that even occasional exercisers, were 30 percent less likely to die than their sedentary twins.” Increased risk can be negative! If so, it is a “decreased” risk. Increased Risk = (0.70 - 1.00) × 100 = -30% “Researchers found that occasional exercisers, those who did less than the equivalent of six brisk half-hour walks a month, were 0.70 times as likely to die than their sedentary twins.” Relative Risk = 0.70

13. Caution! Relative risk and increased risk by themselves are not sufficient. Critical that you also know the conditional probabilities that went into calculating them. RR = 0.005/0.001 = 5 RR = 0.5/0.1 = 5 Relative risk of 5 means two very different things in these two cases.

14. Odds If P(event) is p, then odds of an event happening is “p/(1-p) to 1”. That is, the probability of the event happening over the probability of the event not happening. Or, if m = # with a trait and n = # without the trait, then the odds of an event happening is “m/n to 1”. That is, the # with the trait over the # without the trait.

15. Interpreting odds Odds = 10 to 1 For every 10 students who didn’t sleep enough last night, I’ll find 1 who did sleep enough. Odds = 3 to 2 For every 3 students who do their homework daily, I’ll find 2 students who don’t do their homework daily.

16. Example: Gender and Tattoos Rows: gender Columns: tattoo N Y All M 74 16 90 82.22 17.78 100.00 F 79 8 87 90.80 9.20 100.00 All 153 24 177 86.44 13.56 100.00 Cell Contents -- Count % of Row

17. Odds of Not Having a Tattoo For males 0.8222/0.1778 to 1 = 74/16 to 1 = 4.6 to 1 For every 4.6 males I find without a tattoo, I’ll find one male with a tattoo. For females 0.9080/0.0920 to 1 = 79/8 to 1 = 9.9 to 1 For every 9.9 females I find without a tattoo, I’ll find one female with a tattoo.

18. Odds ratio The ratio of two odds, that is, the odds for one group divided by the odds for another group.

19. The comparison The odds of finding a female without a tattoo is 2.15 times that of the odds of finding a male without a tattoo. Odds ratio = (79/8)/(74/16) = 9.9/4.6 = 2.15

20. What to know? Calculation of RR, IR, odds, OR Interpretation of RR, IR, odds, OR Relationship between RR and IR Relationship between probability and odds Importance of knowing probabilities and not just RR and IR