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Chapter 11 Estimating Risk: Is There an Association?

Chapter 11 Estimating Risk: Is There an Association?. Measurements of disease occurrence Incidence (new cases; absolute risk) - Cumulative incidence - Incidence density Odds (P/1-P) Prevalence (existing cases; not a risk). Measures of Association

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Chapter 11 Estimating Risk: Is There an Association?

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  1. Chapter 11Estimating Risk: Is There an Association?

  2. Measurements of • disease occurrence • Incidence (new cases; absolute risk) - Cumulative incidence - Incidence density • Odds (P/1-P) • Prevalence (existing cases; not a risk)

  3. Measures of Association • Measurements of disease occurrence (incidence, prevalence) are the basis for comparison between groups. • Two measurements are combined into a single summary parameter that estimates the association between exposure and outcome. • Summary can be: - ratio: how much more likely is one group to develop the disease relative to the other? - difference: how much greater on an absolute scale is the frequency of disease in one group compared to another?

  4. Relative Risk • What is the ratio of the risk of disease in exposed individuals to the risk of disease in nonexposed individuals? • Or, what is the probability of an event (e.g., developing a disease) occurring in exposed people compared to the probability of the event in nonexposed people? • Relative Risk (RR) = Risk in exposed • Risk in nonexposed • In a cohort study, the relative risk can be calculated directly. • In a case-control study, the RR can NOT be calculated directly.

  5. 2×2 Table for calculating relative risk (RR) Exposure Status Disease Status Disease No disease TOTAL Positive a b a+b Negative c d c+d TOTAL a+c b+d a+b+c+d

  6. Measure of disease association: cohort study with count data Exposure Disease TOTAL Diseased Not Diseased 1137 409 Exposed 409 Women 1137 1,982 845 193 Not Exposed 193 845 Men What is the measure of disease occurrence in the exposed? What is the measure of disease occurrence in the unexposed? What is the relative risk of exposure?

  7. Interpreting the relative risk • RR < 1; RR = 1; RR > 1 • Example, RR=1.56: women are 56% more likely than men to develop the disease or women are about one and a half times as likely to develop the disease than men. • State magnitude, direction, and to whom the comparison is being made (also statistical significance if you know it) • What if you want to compare men to women? (1/RR)

  8. Figure 11-4 Relative risk for myocardial infarction and death from coronary heart disease in men aged 30 to 62 years by serum cholesterol (left) and blood pressure levels (right) in relation to cigarette smoking. High cholesterol levels are defined as 220 mg/dL or greater. (Data from Doyle JT, Dawber TR, Kannel WB, et al: The relationship of cigarette smoking to coronary heart disease. JAMA 190:886, 1964.)

  9. Relative Odds (OR) • In case-control studies, RR can NOT be directly calculated because we can’t calculate risks in case-control studies. • Instead, we use relative odds or odds ratio as a proxy for RR in case-control studies. • Relative Odds (OR) = Odds in diseased Odds in nondiseased • OR=(p1/1-p1)/(p2/1-p2) (OR also called the cross-products ratio)

  10. 2×2 Table for calculating odds ratio (OR) Exposure Status Disease Status Disease No disease TOTAL Positive a b a+b Negative c d c+d TOTAL a+c b+d a+b+c+d

  11. Figure 11-5 A, Odds ratio (OR) in a cohort study. B, Odds ratio (OR) in a case-control study.

  12. Measure of disease association: case-control study Exposure Disease Disabled M=193 F=409 M=652 F=728 TOTAL Cases Controls 602 Exposed (women) 409 728 Not disabled 1380 Not Exposed (men) 193 652 What is the measure of disease occurrence in the exposed? What is the measure of disease occurrence in the unexposed? What is the relative risk of exposure?

  13. Relationship of the OR to the RR • When is the OR a good estimate of the RR?—When a and c are small due to infrequent disease (a/a+b) (a/b) (c/c+d) (c/d) (RR) (OR) • We use relative odds or odds ratio as a proxy for RR in case-control studies. • Relative Odds (OR) = Odds in diseased Odds in nondiseased • OR=(p1/1-p1)/(p2/1-p2)

  14. Figure 11-6 Example: The odds ratio is a good estimate of the relative risk when a disease is infrequent.

  15. Figure 11-7 Example: The odds ratio is not a good estimate of the relative risk when a disease is not infrequent.

  16. Summary • The relative odds (odds ratio) is a useful measure of association, in and of itself, in both case-control and cohort studies. • In a cohort study, the relative risk can be calculated directly. • In a case-control study, the relative risk cannot be calculated directly, so that the relative odds or odds ratio (cross-products ratio) is used as an estimate of the relative risk when the risk of the disease is low.

  17. Calculating the Odds Ratio in an Unmatched Case-Control Study Figure 11-8 A case-control study of 10 cases and 10 unmatched controls.

  18. 2×2 Table for calculating odds ratio (OR) Exposure Status Disease Status Disease No disease TOTAL Positive a b a+b Negative c d c+d TOTAL a+c b+d a+b+c+d

  19. 2×2 Table for calculating odds ratio (OR) in a non-matched case-control study Exposure Status Disease Status Disease No disease TOTAL Positive 6 3 9 Negative 4 7 11 TOTAL 10 10 20 Odds ratio = ad/bc = (6*7) / (4*3) = 42/12 = 3.5

  20. Calculating the OR in a matched-pairs case-control study Exposure Control Status Exposed Not Exposed TOTAL Exposed a b a+b Not Exposed c d c+d Case TOTAL a+c b+d a+b+c+d Concordant Pairs: a and d; Discordant pairs: b and c; Odds ratio (matched pairs) = b / c

  21. Figure 11-9 A case-control study of 10 cases and 10 matched controls.

  22. Controls • Exposed Not Exposed • Cases Exposed 2 4 • Not Exposed 1 3 • OR: b/c=4/1=4, the odds of having the exposure among the diseases are 4 times as likely as the odds of having the exposure among the nondiseased.

  23. Figure 11-10 Birth weight of index child: Matched-pairs comparison of cases and normal controls (&#8805;8 lbs vs. 8 lbs). (Data from Gold E, Gordis L, Tonascia J, Szklo M: Risk factors for brain tumors in children. Am J Epidemiol 109:309-319, 1979.)

  24. Figure 11-11 Exposure of index child to sick pets: Matched-pairs comparison of cases and normal controls. (Data from Gold E, Gordis L, Tonascia J, Szklo M: Risk factors for brain tumors in children. Am J Epidemiol 109:309-319, 1979.)

  25. Calculating the OR in a matched-pairs case-control study • Calculation of the odds ratio in such a matched-pair study is based on the discordant pairs only (b and c). The concordant pairs (a and d, in which cases and controls were either both exposed or both not exposed) are ignored, because they do not contribute to our knowledge of how cases and controls differ in regard to past history of exposure.

  26. Calculating the OR in a matched-pairs case-control study • Again, the matched-pairs odds ratio can be viewed as the ratio of the number of pairs that support the hypothesis of an association (pairs in which the case was exposed and the control was not) to the number of pairs that negate the hypothesis of an association (pairs in which the control was exposed and the case was not).

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