1. R Programming Risk & Relative Risk 1

2. Session 2 Overview 1.Risk 2.Relative Risk 3.Percent Increase/Decrease Risk 2

3. Risk The risk that a randomly selected individual within a group falls into a undesirable category is simply the proportion of individuals in that category. 3

4. Risk 4 The risk of divorce for a smoker is 238/485 =.4907

5. Risk 5 Risk can be expressed as a percentage or a proportion. Ex: Within a group of 200 individuals, asthma affects 24. Therefore, the risk of asthma is 24/200 =.12 = 12%.

6. Relative Risk 6 Often, we, as data analysts and statisticians, are interested in how the risk of an outcome relates to a categorical explanatory variable.

7. Relative Risk 7 Is the risk of some undesirable event substantially higher for one group of individuals than another? Ex: Is the risk of lung cancer higher for men than for women? The relative risk statistic is one way to accomplish this end.

8. Relative Risk 8 The relative risk is the ratio of the risks in two different categories of a categorical explanatory variable.

9. Relative Risk 9 The relative risk (RR) describes the risk in one group as a multiple of the risk in another group.

10. Relative Risk 10 When 2 risks are the same, than the RR = 1. When the category (i.e., group) in the numerator has higher risk, than the RR > 1 and vice versa. The category in the denominator is often the baseline group where no additional treatment or behavior is present.

11. Relative Risk 11 Ex: To compute the RR of divorce for smokers vs. nonsmokers.

12. Relative Risk 12 Risk(Smokers) = 238/485 =.491 Risk(Nonsmokers) = 374/1184 =.316 RR =.491/.316 = 1.53 The risk of divorce for smokers is 1.53 times greater than the risk of divorce for nonsmokers.

13. Percent Increase/Decrease Risk 13 Sometimes an increase or decrease in risk is presented as a percent change instead of a multiple.

14. Percent Increase/Decrease Risk 14 The percent increase (or decrease) in risk can be calculated as: Or or

15. Percent Increase/Decrease Risk 15 NOTE: When a risk is smaller than the baseline risk, the RR < 1, and the percent “increase” will be negative. Therefore, this really a percent decrease.

16. Percent Increase/Decrease Risk 16 Therefore, the risk of divorce is 53% higher for smokers than for nonsmokers.

17. Ex: The Respiratory Data 17 The Respiratory data were collected during a randomized clinical trial that compared two treatments (test, placebo) for a respiratory disorder.

18. R 18 We can often obtain the necessary calculations to compute risk and relative risk in either R.