EBM Module 2: Measurement

1. EBM Module 2:Measurement

2. Objectives • At the completion of this module participants should be able to: • To enumerate and explain the various measures used to describe the frequency of exposure or disease within a population (prevalence, risk, rate, odds) • To enumerate and explain the various measures that are used to compare the frequency of exposure and disease between two populations • To compare and contrast ‘difference’ and ‘ratio’ measures of association • To define the concepts of ‘number needed to treat’ and ‘number needed to harm’

3. The 2 x 2 Table

4. The 2 x 2 Table Exposure Variable

5. The 2 x 2 Table Outcome Variable

6. Variable Types • Continuous variables • A variable that may assume any value within an interval (e.g. age, height, blood pressure, etc.) • Discrete (categorical) variables • A variable that may assume only values within a discrete set • Dichotomous (yes/no) • Ordinal - multiple ordered categories (e.g. MRC muscle strength scale) • Nominal - multiple non-ordered categories (e.g. race)

7. Measures of Frequency

8. Measures of Frequency The frequency of a Good Outcome within the population may be expressed as (a+c)/(a+b+c+d). In our example, this is (239/319) = 0.75 This means 75% of our entire population had a good outcome.

9. Measures of Frequency The frequency of an Exposure (e.g., steroids) within the population may be expressed as (a+b)/(a+b+c+d). In our example, this is (167/319) = 0.52 This means 52% of our entire population were given steroids.

10. Measures of Frequency • Prevalence - the amount of disease already present in a population • Risk (cumulative incidence) - the likelihood or probability than an individual will contract disease in a specified time frame • Rate (incidence density) - the speed with which new occurrences of disease arise in a population • Odds - a ratio of the probability than an event occurs divided by the probability that the event does not occur

11. Prevalence & Incidence • Prevalence and incidence are related concepts • They are connected by disease duration • Annual Incidence of ALS and MS - both ~2 per 100,000 • Prevalence of ALS ~6 per 100,000 • Prevalence of MS ~100 per 100,000

13. Risk • Describes the probability of some event (cumulative incidence) • It is a measure of the occurrence of new cases in the population • Quantified by measuring the frequency with which unaffected people develop disease • Assumes a value from 0 to 1 • Requires definition of the relevant time period over which risk is quantified • Formally defined:

14. Problems with Risk • Incident data is required • Necessary to follow subjects over a given period of time and to document the number of new instances of disease • Problem of the changing denominator due to competing risks and loss to follow-up

15. Rate

16. Rate • Another concept used to describe incidence (incidence density) • Describes the speed with which new cases develop • Rate is a measure of frequency that accommodates the problem of a changing denominator • In calculating rate, the numerator is the same as in calculating risk • The denominator is a composite of the number of subjects followed and the duration of time over which they are followed

17. Rate

18. Rate • Total follow-up time: Patient 1 = 5 years

19. Rate • Total follow-up time: Patient 1 = 5 years • Total follow-up time: Patient 2 = 3 years

20. Rate • Total follow-up time: Patient 1 = 5 years • Total follow-up time: Patient 2 = 3 years • Total follow-up time: Patient 3 = 4 years

21. Rate • Total follow-up time: Patient 1 = 5 years • Total follow-up time: Patient 2 = 3 years • Total follow-up time: Patient 3 = 4 years • Total follow-up time: Patient 4 = 2 years

22. Rate • Total follow-up time: Patient 1 = 5 years • Total follow-up time: Patient 2 = 3 years • Total follow-up time: Patient 3 = 4 years • Total follow-up time: Patient 4 = 2 years • Total follow-up time: Patient 5 = 3 years

23. Rate • Total follow-up time: Patient 1 = 5 years • Total follow-up time: Patient 2 = 3 years • Total follow-up time: Patient 3 = 4 years • Total follow-up time: Patient 4 = 2 years • Total follow-up time: Patient 5 = 3 years • TOTAL PATIENT FOLLOW-UP: 17 YEARS • Thus, if 2 new cases develop during this time, then the incidence rate is 2 per 17 person-years • Alternately expressed as 0.11 per person-year or 11 per 100 person-years

24. Rate • Assumes a value from 0 to infinity • Rate does NOT reflect the proportion of people who develop disease, but rather the speed with which new instances of disease accrue • The value rate assumes depends on the unit of time used in the denominator

25. A Chicken and a Half If a chicken and a half lay an egg and a half in a day and a half, then how many eggs does a chicken lay in one day? This riddle is essentially a rate problem. See if you can answer the riddle.

26. A Chicken and a Half Rate = Cases = Eggs = 1.5 = 0.67 eggs/chicken days Persons x Time Chickens x Days 1.5 x 1.5 • The number of eggs represents the number of cases (1.5) • The “person-time” at risk is represented by the 1.5 chickens who lay eggs over a period of 1.5 days (i.e. 1.5 x 1.5 chicken-egg laying days) • The rate of egg laying is 1.5 eggs / (1.5 x 1.5 chicken-egg laying days) = 0.67 • Therefore, a chicken laying eggs at this rate would lay two-third of an egg each day

27. Odds

28. Odds • What does it mean to talk of the “odds of polyneuropathy amongst those with a history of statin use”? • How is this different from the “risk of polyneuropathy …”? • Like risk and rate, odds is also a measure of frequency • Unintuitive because it is a ratio rather than a proportion

29. Odds Probability of Disease (among exposed) = 20 / 25 = 0.8 (i.e., 80%) Probability of No Disease (among exposed) = 5 / 25 = 0.2 (i.e., 20%) Odds of Disease (among exposed) = 80% / 20% = 4

30. Odds Also expressed as: Odds of Disease (among exposed) = 20 / 5 = 4

31. Why the need for Odds ? • We are not always able to estimate risk • Measurement of risk requires incident data • When incident data is not available (e.g. case-control study), then we need to rely on odds as a surrogate measure for risk

32. Measures of Association Risk of Disease (among exposed) = 20 / 25 = 0.8 (i.e., 80%)

33. Measures of Association Risk of Disease (among non-exposed) = 40 / 100 = 0.4 (i.e., 40%)

34. Measures of Association Relative Risk of Disease = 0.8 / 0.4 = 2 (i.e., 80%/40% = 2)) Risk Difference of Disease = 0.8 - 0.4 = 0.4 (i.e., 80% - 40% = 40%)

35. Measures of Association • In order to quantify the determinants of disease we need tools to compare the frequency of exposure or disease between two populations • Two types of measures of association • Difference measures (additive scale) • Example 0.8 - 0.4 = 0.4 (or 80% - 40% = 40%) • Ratio measures (relative scale) • Example 0.8 / 0.4 = 2 (or 80% / 40% = 2)

37. Risk: Relative and Absolute • This means, the risk of a vascular event over 3 years was: • 5.83% in the group treated with aspirin • 5.32% in the group treated with clopidogrel • Both of these risk measures required incident data (i.e., following patients over the 3 years and recording how many had a vascular event) • Note that the absolute risk reduction is modest: 5.83% - 5.32% = 0.51% • That means the absolute advantage of clopidogrel over aspirin was only 0.51%

38. Risk: Relative and Absolute • However, the authors reported the relative risk difference: • Relative Risk Reduction = Risk (standard treatment group) – Risk (new treatment group) Risk (standard treatment group) • Presenting the results in terms of relative risk (an 8.7% reduction in this case) is misleading in that it gives the impression of a more marked difference in outcome between the two treatment groups.

39. Risk: Relative and Absolute In the aspirin / clopidogrel study, the relative risk difference is: 5.32% - 5.83% 5.83% Presenting the results in terms of relative risk (an 8.7% reduction in this case) is misleading in that it gives the impression of a more marked difference in outcome between the two treatment groups. = 0.087 = 8.7%

40. Number Needed to Treat / Harm (NNT / NNH) • Number needed to treat or harm • How many patients must I treat to see one better (or worse) outcome? • NNT = 1 / absolute risk difference • NNH is 1/absolute difference in risk of adverse event

41. Number Needed to Treat / Harm (NNT / NNH) • Thus is the clopidogrel vs aspirin trial • The absolute risk difference of a benefit was 0.51% (0.0051) • NNT = 1 / absolute risk difference • NNT = 1 / 0.0051 = 200 • That means, one would need to treat 200 patients with clopidogrel as opposed to aspirin for 3 years to prevent one vascular event.

42. Number Needed to Treat / Harm (NNT / NNH) • In the same study, the risk of GI hemorrhage was higher in the aspirin group: • 0.52% in the clopidogrel group • 0.72% in the aspirin group • The absolute risk difference was 0.20% (0.0020) • NNH = 1 / absolute risk difference • NNH = 1 / 0.0020 = 500 • That means, one would need to treat 500 patients with aspirin instead of clopidogrel for 3 years to cause one additional GI hemorrhage.

43. Odds Ratio Odds ratio = Oddspopulation-1/Oddspopulation-2 • Since odds is the ratio of two probabilities, the odds ratio is a ratio of two ratios • The odds ratio and the risk ratio are related, but not the same • Under certain circumstances (when the outcome is rare), the odds ratio provides a close estimate of the risk ratio • Also known as the “cross-products” ratio

44. Odds of Disease (exposed) = 50:50 = 1 Odds of Disease (not exposed) = 5:95 =0.0526 Odds Ratio = 19 Risk of Disease (exposed) = 50 / 100 = 0.5 Risk of Disease (not exposed) = 5 / 100 = 0.05 Risk Ratio = 10

45. Odds Disease (exposed) = 5:95 = 0.0526 Odds Disease (not exposed) = 2:98 = 0.0204 Odds Ratio = 2.58 Risk Disease (exposed) = 5 / 100 = 0.05 Risk Disease (not exposed) = 2 / 100 = 0.02 Risk Ratio = 2.5

46. Summary (1) • Prevalence describes the amount of exposure or disease in a population at a single time • Incidence (risk and rate) describes the occurrence of new disease in a population • Risk and Rate are appropriate measures only when incident data is available

47. Summary (2) • Odds should be used when incident data is not available (e.g. case-control study) • For example, in module 1, we collected cases of Bell’s palsy from hospital records, and compared the group of patient who received steroids and those who did not. This is a case-control series. In a case control study, we do not know any incident data.

48. Summary (3) • Risk ratio describes the relative difference in risk between 2 populations • Risk difference describes the difference in risk between 2 populations. Risk difference can be either absolute or relative. Using relative risk, although correct, may be misleading in that it gives the impression of a more marked difference in outcome between the two treatment groups • Odds ratio (a ratio of ratios) describes the relative difference in odds of exposure (or disease) between 2 populations

49. References • A randomized, blinded, trial of clopidogrel versus aspirin in patients at risk of ischaemic events (CAPRIE). Lancet 1996 348:1329-1339 • The epidemiology of multiple sclerosis in Europe. Eur J Neurol 2006 13:700-722 • The worldwide prevalence of multiple sclerosis. Clin Neurol Neurosurg 2002 104:182-191 • Incidence of multiple sclerosis in the United Kingdom. J Neurol 2007 254:1736-1741 • Epidemiology of motor neuron disease in Northern Sweden. Acta Neurol Scand 1983 68:20-29 • The incidence and survival of amyotrophic lateral sclerosis in Saskatoon, Saskatchewan, Canada. Neurology 2007 69:1224-1229

50. References • Epidemiological survey of amyotrophic lateral sclerosis in the province of Reggio Emilia, Italy: influence of environmental exposure to lead. Neuroepi 1996 15:301-312 • Medical Epidemiology (Lange Basic Science). Raymond Greenberg, Stephen Daniels, Dana Flanders and John Eley. McGraw Hill, 2001 • Epidemiology: An Introduction. Kenneth Rothman, Oxford University Press, 2002 • Higgins JPT, Green S (Editors). Cochrane Handbook for Systematic Reviews of Interventions 4.2.5 (updated May 2005). In The Cochrane Library, Issue 3, 2005, Chichester, UK. John Wiley & Sons Ltd (http://www.cochrane.dk/cochrane/handbook/hbook.htm)