Measures of association

1. Measures of association

2. Intermediate methods in observational epidemiology 2008 Measures of Association

3. 1) Measures of association based on ratios • Cohort studies • Relative risk (RR) • Odds ratio (OR) • Case control studies • OR of exposure and OR of disease • OR when the controls are a sample of the total population • Prevalence ratio (or Prevalence OR) as an estimate of the RR 2) Measures of association based on absolute differences: attributable risk

4. Cohort studies Hypothetical cohort study of the one-year incidence (q) of acute myocardial infarction for individuals with severe systolic hypertension (HTN, ≥180 mm Hg) or normal systolic blood pressure (<120 mm Hg).

5. The OR can also be calculated from the “cross-products ratio” if the table is organized exactly as above :

6. RR “bias” Example: RR=6.0 OR=6.09 When (and only when) the OR is used to estimate the RR, there is a “built-in” bias:

7. IN GENERAL: • The OR is always further away from 1.0 than the RR. • The higher the incidence, the higher the discrepancy.

8. Example: Relationship between RR and OR … when probability of the event (q) is low: or, in other words, (1-q) 1, and thus, the “built-in bias” term, and OR  RR.

9. Relationship between RR and OR … when probability of the event (q) is high: Example: Cohort study of the one-year recurrence of acute myocardial infarction (MI) among MI survivors with severe systolic hypertension (HTN, ≥180 mm Hg) and normal systolic blood pressure (<120 mm Hg). q 0.36 0.06

10. OR vs. RR: Advantages • OR can be estimated from logistic regression. • OR can be estimated from a case-control study

11. Hypothetical cohort study of the one-year incidence of acute myocardial infarction for individuals with severe systolic hypertension (HTN, 180 mm Hg) and normal systolic blood pressure (<120 mm Hg). same Hypothetical case-control study assuming that all members of the cohort (cases and non cases) were identified Case-control studiesA) Odds ratio of exposure and odds ratio of disease Retrospective (case-control) studies can estimate the OR of disease because: ORexposure = ORdisease Because ORexp = ORdis, interpretation of the OR is always “prospective”.

12. Cases Controls Odds Ratios Yes 26 53 (26/1) ÷ (53/87) = 43.0 No 1 87 Total 27 140 Calculation of the Odds Ratios: Example of Use of Salicylates and Reye’s Syndrome Past use of salicylates Preferred Interpretation: Children using salicylates have an odds (≈risk) of Reye’s syndrome 43 times higher than that of non-users. Another interpretation (less useful): Odds of past salicylate use is 43 times greater in cases than in controls. (Hurwitz et al, 1987, cited by Lilienfeld & Stolley, 1994)

13. Cohort study: It is not necessary that the sampling fraction be the same in both cases and controls. For example, a majority of cases (e.g., 90%) and a small sample of controls (e.g., 20%) could be chosen (assume no random variability).(As cases are less frequent, the sampling fraction for cases is usually greater than that for controls). In a retrospective (case-control) study, an unbiased sample of the cases and controls yields an unbiased OR

14. Case-control studiesB) OR when controls are a sample of the total population In a case-control study, when the control group is a sample of the total population (rather than only of the non-cases), the odds ratio of exposure is an unbiased estimate of the RELATIVE RISK

15. Example: Hypothetical cohort study of the one-year recurrence of acute myocardial infarction (MI) among MI survivors with severe systolic hypertension (HTN, ≥180 mm Hg) or normal systolic blood pressure (<120 mm Hg).

16. Using a traditional case-control strategy, cases of recurrent MI can be compared to non-cases, i.e., individuals without recurrent MI: Example: Hypothetical cohort study of the one-year recurrence of acute myocardial infarction (MI) among MI survivors with severe systolic hypertension (HTN, 180+ mm Hg) or normal systolic blood pressure (<120 mm Hg).

17. Using a traditional case-control strategy, cases of recurrent MI are compared to non-cases, i.e., individuals without recurrent MI: • Using a case-cohort strategy, the controls are formed by the total population: Example: Hypothetical cohort study of the one-year recurrence of acute myocardial infarction (MI) among MI survivors with severe systolic hypertension (HTN, 180+ mm Hg) or normal systolic blood pressure (<120 mm Hg).

18. Note that it is not necessary to have a total group of cases and non-cases or the total population to assess an association in a case-control study. What is needed is a sample estimate of cases and either non-cases (to obtain the odds ratio of disease) or the total population (to obtain the relative risk). Example: samples of 20% cases and 10% total population: Thus… RR= unbiased exposure odds estimate in cases divided by unbiased exposure odds estimate in the total population.

19. To summarize, in a case-control study:

20. How to calculate the OR when there are more than two exposure categories Example: Univariate analysis of the relationship between parity and eclampsia.* 1.0 (Reference) (21/11)÷(27/40)=2.9 (68/11)÷(33/40)=7.5 * Abi-Said et al: Am J Epidemiol 1995;142:437-41.

21. How to calculate the OR when there are more than two exposure categories Example: Univariate analysis of the relationship between parity and eclampsia.* * Abi-Said et al: Am J Epidemiol 1995;142:437-41. Correct display: Log scale Baseline is 1.0

22. A note on the use of estimates from a cross-sectional study (prevalence ratio, OR) to estimate the RR If the prevalence is low (~≤5%)  If this ratio= 1.0 Duration (prognosis) of the disease after onset is independent of exposure (similar in exposed and unexposed)... However, if exposure is also associated with shorter survival (D+ < D-), D+/D- <1  the prevalence ratio will underestimate the RR. Prevalence Odds= Example? Smoking and emphysema

23. ARexp Or, expressed as a proportion (e.g., percentage): Alternative formula for the %ARexp: Measures of association based on absolute differences(absolute measures of “effect”) • Attributable risk in the exposed: • The excess risk (e.g., incidence) among individuals exposed to a certain risk factor that can be attributed to the risk factor per se: 20/1000 Incidence (per 1000) 10/1000 Unexposed Exposed

24. Levin’s formula (Levin: Acta Un Intern Cancer 1953;9:531-41) High exposure prevalence Low exposure prevalence Pop AR Pop AR ARexp ARexp Incidence (per 1000) Incidence (per 1000) Population Unexposed Exposed Population Unexposed Exposed • Population attributable risk: • The excess risk in the population that can be attributed to a given risk factor. Usually expressed as a percentage: • The Pop AR will depend not only on the RR, but also on the prevalence of the risk factor (pe).

25. More or less 1.0 ~ Percent ARexposed Levin’s formula for the Percent ARpopulation Percent Population AR ~ Chu SP et al. Risk factors for proximal humerus fracture. Am J Epi 2004; 160:360-367 Cases: 448 incident cases identified at Kaiser Permanente. 45+ yrs old, identified through radiology reports and outpatient records, confirmed by radiography, bone scan or MRI. Pathologic fractures excluded (e.g., metastatic cancer). Controls: 2,023 controls sampled from Kaiser Permanente membership (random sample). What is the %AR in those exposed to the lowest quartile? Interpretation: If those exposed to values in the lowest quartile had been exposed to other values, their odds (risk) would have been 35% lower. What is the Percent AR in the total population due to exposure in the lowest quartile? RR estimate ~ 1.54 Pexp~ 0.25 Interpretation: The exposure to the lowest quartile is responsible for about 12% of the total incidence of humerus fracture in the Kaiser permanente population