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

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

8. 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.
Example:

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. Case-control studies A) Odds ratio of exposure and odds ratio of disease
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
Retrospective (case-control) studies can estimate the OR of disease because:
ORexposure = ORdisease
Because ORexp = ORdis, interpretation of the OR is always “prospective”.

12. Calculation of the Odds Ratios: Example of Use of Salicylates and Reye’s Syndrome
140 27
Total 87 1 No
(26/1) ÷ (53/87) = 43.0 53 26
Yes
Odds Ratios
Controls
Cases
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:
In a retrospective (case-control) study, an unbiased sample of the cases and controls yields an unbiased OR
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).

14. Case-control studies B) 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. 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).
Using a traditional case-control strategy, cases of recurrent MI can be compared to non-cases, i.e., individuals without recurrent MI:

17. 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).
Using a case-cohort strategy, the controls are formed by the total population:
Using a traditional case-control strategy, cases of recurrent MI are compared to non-cases, i.e., individuals without recurrent MI:

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:

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:
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
Prevalence Odds=
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.
Example?
Smoking and emphysema

23. Attributable risk in the exposed:
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
ARexp
Incidence (per 1000)
10/1000
Or, expressed as a proportion
(e.g., percentage):
Unexposed
Exposed
Alternative formula for the %ARexp:

24. 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).
Levin’s formula
(Levin: Acta Un Intern Cancer 1953;9:531-41)
Incidence (per 1000)
Unexposed
Exposed
ARexp
Population
Low exposure prevalence
Pop AR
Incidence (per 1000)
Unexposed
Population
Exposed
Pop AR
ARexp
High exposure prevalence

25. Dietary Calcium (mg/day)
Chu SP et al. Risk factors for proximal humerus fracture. Am J Epi 2004; 160:
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).
Dietary Calcium (mg/day)
Odds Ratios (95% CI)
Highest quartile (≥970)
1.0 (reference)
Third quartile ( )
1.36 (0.96, 1.91)
Second quartile ( )
1.11 (0.81, 1.52)
Lowest quartile (≤495)
1.54 (1.14, 2.07)
What is the %AR in those exposed to the lowest quartile?
More or less 1.0
Percent ARexposed ~
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?
Levin’s formula for the Percent ARpopulation
RR estimate ~ 1.54
Pexp ~ 0.25
Percent Population AR ~
Interpretation: The exposure to the lowest quartile is responsible for about 12% of the total incidence of humerus fracture in the Kaiser permanente population