Measures used to compare groups

1. Summer Course:Introduction to Epidemiology August 26, 1330-1500 Measures used to compare groups Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

2. Session Overview Methods of comparing studies • Risk/rate ratios • Odd ratios • Difference measures • Number needed to treat • Attributable risk

3. ONE BIG WARNING!!!!! The textbook has rotated their 2X2 tables from the normal approach. That is, they have the outcomes as the rows and the exposure as the columns. BE WARNED. This could cause confusion with my tables which use the more common approach.

4. Comparing studies (1) • Two main types of outcome measures • Incidence (either risk or rate) • Prevalence • How do you determine if an exposure is related to an outcome? • Study 2 groups • Need to compare the measure in the two groups. • Differences • Ratios (we’ll start with this one).

5. Comparing studies (2) • Ratios (we’ll start with this one). • Ratio measures have NO units. • All ratio measures have the same interpretation • 1.0 = no effect • < 1.0  protective effect • > 1.0  increased risk • Values over 2.0 are of strong interest

6. Comparing studies: Cohorts (3) RISK RATIO Risk in exposed: = 1,000/10,000 Risk in Non-exposed = 100/10,000 If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the ratio of one to the other: Disease Exp

7. Comparing studies: Cohorts (4) RISK RATIO Risk in exposed: = a/(a+b) Risk in Non-exposed = c/(c+d) If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the ratio of one to the other: Disease Exp

8. Comparing studies: Cohorts (5) RISK RATIO Risk in exposed: = 42/122 = 0.344 Risk in Non-exposed = 43/345 = 0.125 Death Apgar

9. Comparing studies: Cohorts (6) RISK DIFFERENCE Risk in exposed: = 1,000/10,000 Risk in Non-exposed = 100/10,000 If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the difference between the two: Disease Exp

10. Comparing studies: Cohorts (7) RISK DIFFERENCE Risk in exposed: = a/(a+b) Risk in Non-exposed = c/(c+d) If exposure increases risk, you would expect the risk in the exposed to be larger than risk in the unexposed. How much larger can be assessed by the difference between the two: Disease Exp

11. Comparing studies: Cohorts (8) RISK DIFFERENCE Risk in exposed: = 42/122 = 0.344 Risk in Non-exposed = 43/345 = 0.125 Death Apgar

12. Comparing studies: Cohorts (9) Which comparative measure do you use? • Depends on the circumstances. • Risk Ratio  RELATIVE risk measure • Risk Difference  ABSOLUTE risk measure • Post-menopausal estrogens & endometrial cancer • RR = 2.3 • RD = 2/10,000

13. Comparing studies: Cohorts (10) RATE RATIO Rate in exposed: = 1,000/9,500 Rate in Non-exposed = 100/9,950 If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the ratio of one to the other: Exp

14. Comparing studies: Cohorts (11) RATE RATIO Rate in exposed: = A/Y1 Rate in Non-exposed = B/Y2 If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the ratio of one to the other: Exp

15. Comparing studies: Cohorts (12) RATE RATIO Rate in exposed: = 42/101 = 0.416 Rate in Non-exposed = 43/323.5 = 0.133 Apgar

16. Comparing studies: Cohorts (13) RATE DIFFERENCE Rate in exposed: = 1,000/9,500 Rate in Non-exposed = 100/9,950 If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the difference between the two: Exp

17. Comparing studies: Cohorts (14) RATE DIFFERENCE Rate in exposed: = A/Y1 Rate in Non-exposed = B/Y2 If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the difference between the two: Exp

18. Comparing studies: Cohorts (15) RATE DIFFERENCE Rate in exposed: = 42/101 = 0.416 Rate in Non-exposed = 43/323.5 = 0.133 Apgar

19. Comparing studies: Cohorts (16) Some Issues • What does RR mean • Can mean either • risk ratio or • rate ratio. • Some people think this is pedantic rather than correct  • Need to tell which from context. • Sometimes referred to as Relative Risk (generic term). • Are risk differences or ratios preferred? • RR’s are much more common • Both have a role to play.

20. Comparing studies: Case-control (1) CAN NOT COMPUTE A RISK RATIO! • Can not estimate incidence from a case-control study. • Can not directly compute risk differences. • Why? We choose the subjects based on their outcome status. Usually, that means making the number of cases and controls equal. Hence, the ‘incidence’ in the case-control study is fixed at 0.50. In real world, it is most likely much lower (1/100,000). So, what do we do? • Cornfield & Haenzel provided solution in 1960. • They looked at the ODDS of exposure. • The ratio of the odds of exposure in the cases and controls is almost the same as the RR, if the disease is rare.

21. Comparing studies: Case-control (2) ODDS RATIO Odds of exposure in cases: = 900/100 Odds of exposure in controls: = 400/600 If exposure increases rate of getting disease, you would to find more exposed cases than exposed controls. That is, the odds of exposure for cases would be higher. How much higher can be assessed by the ratio of one to the other: Disease Exp

22. Comparing studies: Case-control (3) ODDS RATIO Odds of exposure in cases: = a/c Odds of exposure in controls: = b/d If exposure increases rate of getting disease, you would to find more exposed cases than exposed controls. That is, the odds of exposure for case would be higher. How much higher can be assessed by the ratio of one to the other: Disease Exp

23. Comparing studies: Case-control (4) ODDS RATIO Odds of exposure in cases: = 42/43 = 0.977 Odds of exposure in controls: = 18/67 = 0.269 Death Apgar NOTE: Risk ratio = 2.76 Rate ratio = 3.13

24. Comparing studies: Case-control (5) Cohort aside: • You can compute an OR for a cohort. Why would you do so? • OR’s are the key outcome measure for logistic regression, one of the most common analysis methods used in epidemiology • Unless disease is common, the OR and the RR from the cohort will be very similar. • But, where possible, rate ratios are preferred.

25. Number needed to treat (1) Consider a clinical trial of a new drug. How many people do we need to treat to prevent one death? • Incidence rate for the control group is 2 cases per 5 person years. • Incidence rate for the experimental group is 1 case per 5 person years.

26. Number needed to treat (2) • Treat five people for one year: • Control therapy: 2 deaths • Exp therapy: 1 death • PREVENTED = 1 death NNT = 5. • What is the risk difference: • 2/5 – 1/5 = 1/5

27. Number needed to treat (3) For diseases with rare outcomes, you will need to treat many people to prevent one outcome, even if the reduction in risk is high: Relative risk reduction = 0.1 IR (Old Rx) = 10/1,000 IR (New Rx) = 1/1,000 RD = 9/1,000 NNT = 1000/9 = 111

28. Attributable risks (1) • How much lung cancer can be attributed to smoking? • Measure of exposure IMPACT rather than strength. • There are many AR measures, often with similar names. Makes things confusing. One book used the same abbreviation for 4 different measures in five pages!

29. Attributable risks (2) In exposed subjects RD or Attributable Risk Iexp Iunexp Unexp Exp

30. Attributable risks (3) • In the exposed group, the impact of the exposure on outcome depends on RR only: • A value of ‘0’ shows no impact. • You shouldn’t compute AR’s unless causation has been established.

31. Attributable risks (4) However, my actual interest was: In the general population, how much lung cancer was due to smoking? Depends on two factors: • Strength of the smoking/lung cancer relationship (RR). • How common smoking is in the population (exposure prevalence).

32. Attributable risks (5) Iexp Attributable Risk, population Ipop Iunexp Exp Unexp Population

33. Attributable risks (5) Exposure is uncommon Iexp Attributable Risk, population Ipop Iunexp Exp Unexp Population

34. Attributable risks (5) Exposure is common Iexp Attributable Risk, population Ipop Iunexp Exp Unexp Population

35. Attributable risks (6) • Risk in the population is a weighted average of • risk in exposed people • risk in unexposed people. • The weight is the prevalence of the risk factor in the population:

36. Attributable risks (6) Formulae for Population Attributable Risk (PAR) • Usually expressed as a % • The percent reduction in risk in the population if the risk factor could be completely eliminated:

37. Summary: comparisons • Cohort studies • Relative risk • Relative rate • Risk/rate differences • Case-control study • Odds-ratio • Number needed to treat • Attributable risk/fraction • Measure of the impact of exposure to exposed people or to general population.