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Measures of association

Measures of association. Generic name: “Relative Risk”. 1) Measures of association based on ratios Cohort studies Rate ratio Incidence proportion ratio Hazard ratio Odds ratio (OR) Case control studies OR of exposure and OR of disease

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Measures of association

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  1. Measures of association

  2. Generic name: “Relative Risk” 1) Measures of association based on ratios • Cohort studies • Rate ratio • Incidence proportion ratio • Hazard ratio • 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 risk ratio 2) Measures of association based on absolute differences: attributable risk

  3. 1. Measures of association based on ratios (relative measures of “effect”) The relative measures of association should assume the names of the measures of disease frequency on which they are based. Examples: • Rate ratio: Ratio of two rates [denominator of rate: person-time] • Incidence proportion ratio: Ratio of two incidence proportions [denominator of rate: persons without adjustment for duration of follow-up] • Hazard ratio: Ratio of two hazards (cumulative incidences) [denominator of hazard: persons, with adjustment for duration of follow-up (time to event)] • Odds ratio (or relative odds): Ratio of two odds [usually based on incidence proportions] (Even though many of the concepts discussed in this lecture also apply to rate ratios and hazard ratios, for simplification purposes, the discussion is based on the ratio of incidence proportions, which is usually called “risk ratio” or “relative risk”)

  4. (Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer in men and women. Am J Epidemiol 2004;160:248-258)

  5. (Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer in men and women. Am J Epidemiol 2004;160:248-258)

  6. Adjusts for multiple variables in addition to duration of follow-up (time to event) (Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer in men and women. Am J Epidemiol 2004;160:248-258) =cumulative incidence

  7. ** ** ** Cases/Person-years= rates of pancreatic cancer (Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer in men and women. Am J Epidemiol 2004;160:248-258) “*Relative risks adjusted for potential confounders were approximated by Cox proportional hazards regression…”

  8. (Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer in men and women. Am J Epidemiol 2004;160:248-258)

  9. Jacobs EJ, Multivitamin use and colorectal incidence in a US cohort: does timing matter? Am J Epidemiol 2003;158:621-628)

  10. Jacobs EJ, Multivitamin use and colorectal incidence in a US cohort: does timing matter? Am J Epidemiol 2003;158:621-628) Correct terminology? Incidence proportion ratios? Rate ratios?

  11. Wrong! It should be “hazard ratio” Results

  12. q + - 1 . 0 q + = Odds Ratio q DISEASE - - 1 . 0 q - Cohort studies (assume that duration of follow-up is same in exposed and unexposed) Hypothetical cohort study (based on the Framingham study results) of the one-year incidence of acute myocardial infarction for individuals with severe systolic hypertension (HTN, ≥180 mm Hg) or normal systolic blood pressure (<120 mm Hg).

  13. The OR can also be calculated from the “cross-products ratio”:

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

  15. For risk factors (q+>q-, RR>1.0) as in the previous example: (1-q-)>(1-q+) and the resulting bias is, by definition, >1.0. Therefore, OR>RR. • For protective factors (q+<q-, RR<1.0) : (1-q-)<(1-q+) and the resulting bias is, by definition, <1.0. Therefore, OR<RR.

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

  17. Example: ~1.0 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.

  18. 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 = 1.47

  19. OR vs. RR: Advantages • OR can be estimated from logistic regression (to be discussed later in the course). • OR can be estimated from a case-control study because… …OR of exposure = Odds ratio of disease

  20. CASE-CONTROL STUDIES

  21. 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

  22. 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”.

  23. Cases Controls Odds Ratios Yes 26 53 (26/1) ÷ (53/87) = 42.7 No 1 87 Total 27 140 Calculation of the Odds Ratios: Example of Use of Salicylates and Reye’s Syndrome Past use of salicylates Interpretation: Always “prospective” Children using salicylates have an odds (≈risk) of Reye’s syndrome that is almost 43 times higher than that of non-users (Hurwitz et al, 1987, cited by Lilienfeld & Stolley, 1994)

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

  25. 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 INCIDENCE PROPORTION RATIO (or, if adjustment for duration of follow-up is done, of the HAZARD RATIO)

  26. 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).

  27. Using a traditional case-control strategy, cases of recurrent MI are 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).

  28. 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 cases are compared to 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).

  29. Note that it is not necessary to have the total groups of cases and non-cases or the total population to estimate the odds of exposure. It is sufficient to obtain sample estimates of the odds of exposure in cases and either non-cases (to obtain the odds ratio of disease) or the total reference population (to obtain the risk ratio). Example: samples of 20% cases and 5% total population: • Thus… Risk Ratio can be calculated in two ways: • Ratio of two incidence proportions, or • Exposure odds estimate in cases divided by exposure odds estimate in the total reference population (study base).

  30. Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in Busselton, Western Australia. Am J Epidemiol 2003;158:144-149

  31. Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in Busselton, Western Australia. Am J Epidemiol 2003;158:144-149

  32. Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in Busselton, Western Australia. Am J Epidemiol 2003;158:144-149

  33. Total cohort with serum samples: 1,612 individuals × 0.75= 1209 Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in Busselton, Western Australia. Am J Epidemiol 2003;158:144-149 * * Barlow WE. Robust variance estimation for the case-cohort design. Biometrics 1994;50:1064-1072

  34. Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in Busselton, Western Australia. Am J Epidemiol 2003;158:144-149 †Adjusted for age and other cardiovascular risk factors

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

  36. Recapitulation - I • Measures of association quantify a relationship between a potential risk factor and an outcome • Measures of association adopt the names of the measures of disease occurrence on which they are based: • Rate ratio: ratio of two rates (based on person-time) • Incidence proportion ratio: ratio of two incidence proportions (based on persons) • Hazard ratio or Cumulative incidence ratio: ratio of two hazards (based on persons, adjusted for time to event) • Odds ratio: ratio of two odds: • In a cohort study, ratio of the odds of disease in exposed and in unexposed • In a case-control study, ratio of the odds of exposure in cases and in controls Odds ratio of exposure = odds ratio of disease; thus, interpretation of odds ratio in a case-control study is always “predictive” or “prospective” NOTE: “RELATIVE RISK” IS A GENERIC NAME

  37. Recapitulation - II • The ideal ratio-based measure of association is the hazard ratio (cumulative incidence ratio): • Its analytic unit is person; • It adjusts for differential follow-up duration between the groups under comparison (e.g., exposed and unexposed, intervention and control); • Using the Cox regression model, additional variables (that is, other than duration of follow-up) can be adjusted for; • It can be estimated in a case-cohort study.

  38. Recapitulation- III • Rate (%) = (40 ÷ 27) × 100= 148/100 PY • PROBLEMS WITH RATES, AND THUS RATE RATIOS, BASED ON USING TIME UNITS (E.G., PERSON-YEARS) • 1) ASSUMPTION OF ACUTE (NON-CUMULATIVE) EFFECT: To follow N persons for t time is equivalent to following t persons for N time • Person-time= N× t • Example: 20 SMOKERS FOLLOWED FOR 1 YEAR = 1 SMOKER FOLLOWED FOR 20 YEARS= 20 PERSON-YEARS • 2) THEORETICALLY, RATES CAN RESULT IN IMPOSSIBLE VALUES • Example: • One wishes to obtain a one-year case-fatality rate of disease Y, which is highly lethal. • 50 persons are followed for up to one year: • Deaths are relatively uniform over the one-year follow-up. Average follow-up for 40 (out of the 50) patients who die is 6 months • 6 individuals are (also uniformly) lost to follow-up after an average of 6 months • No. of person-years= (40 × 6/12) + (6 × 6/12) + (4 × 1)= 27

  39. “traditional” case-control studies Recapitulation - IV • Case-control studies: Case-based case-control studies (control group is usually formed by non-cases) Odds ratio of exposure = odds ratio of disease • Case-cohort studies (control group is formed by a sample of the total cohort) • Odds ratio of exposure = relative risk (incidence proportion ratio or hazard ratio)

  40. CASE-COHORT STUDY USES A SAMPLE OF THE TOTAL COHORT (STUDY BASE): TO CALCULATE THE RISK RATIO VIA INCIDENCE PROPORTIONS (OR RATES, OR HAZARDS), A CLASSICAL COHORT ANALYSIS IS NEEDED CASE-BASED CASE-CONTROL STUDY USES A SAMPLE OF NON-CASES:

  41. TO CALCULATE THE RISK RATIO IN A CASE-COHORT STUDY, ONLY AN ESTIMATE OF THE ODDS OF EXPOSURE IN THE TOTAL COHORT (STUDY BASE) IS NEEDED. NOTE: IN A CASE-COHORT STUDY, BECAUSE THE OREXP = RR, THE “DISEASE RARITY” ASSUMPTION IS NOT NECESSARY CASE-BASED CASE-CONTROL STUDY USES A SAMPLE OF NON-CASES: CASE-COHORT STUDY USES A SAMPLE OF THE TOTAL COHORT (STUDY BASE):

  42. How to calculate the OR when there are more than two exposure categories

  43. 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) Unexposed: (21/11)÷(27/40)=2.9 (68/11)÷(33/40)=7.5 * Abi-Said et al: Am J Epidemiol 1995;142:437-41.

  44. 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

  45. OR Studies with small sample size may result in a NS trend test even though there appears to be a dose-response association N=80 P(trend)=0.07 1.0 Exposure level OR Studies with large samples size may result on a significant trend test even though there is no dose-response association (threshold effect) ? N=80,000 P(trend)=0.02 1.0 Exposure level Detour… A statistical significant (or non-significant) trend test should not be automatically interpreted as proof of (or automatically disprove) the presence of a dose-response association.

  46. OR Studies with small sample size may result in a NS trend test even though there appears to be a dose-response association N=80 P(trend)=0.07 1.0 Exposure level OR Studies with large samples size may result on a significant trend test even though there is no dose-response association (threshold effect) N=80,000 P(trend)=0.02 1.0 Exposure level Detour… A statistical significant (or non-significant) trend test should not be automatically interpreted as proof of (or automatically disprove) the presence of a dose-response association.

  47. A note on the use of estimates from a cross-sectional study (prevalence ratio, OR) to estimate the risk ratio 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. Hypothetical example: Prevalence Odds= Real life example? Smoking and emphysema

  48. Or, expressed as a percentage: 2. Measures of association based on absolute differences • 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: Pop AR ARexp Incidence (per 1000) Unexposed Exposed

  49. Levin’s formula:* *Levin: Acta Un Intern Cancer 1953;9:531-41. 2. Measures of association based on absolute differences • 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: Or, expressed as a percentage: • 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 (pexp) Advantage: In case-control studies, the RR can be replaced by the OR

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