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The strength of the association

The strength of the association . Measures of association FETP India. Competency to be gained from this lecture. Calculate correctly the measure of association that corresponds to a study design . Key areas. Cohort studies Case control studies Cross-sectional survey .

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The strength of the association

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  1. The strength of the association Measures of association FETP India

  2. Competency to be gained from this lecture Calculate correctly the measure of association that corresponds to a study design

  3. Key areas • Cohort studies • Case control studies • Cross-sectional survey

  4. Presentation of the data of an analytical study in a 2 x 2 table Ill Non-ill Total Exposed a b a+b Non-exposed c d c+d Total a+c b+d a+b+c+d

  5. Presentation of the data of an analytical cohort study in a 2 x 2 table Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 Cohorts

  6. Calculation of the risk for the whole population in a cohort study Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 R = (a+c)/(L1 + L0) Cohorts

  7. Risk among exposed and unexposed in a cohort study Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 Risk among exposed : R1 = a/L1 Risk among unexposed : R0 = c/L0 Cohorts

  8. Approaches that may be used to compare two risks in a cohort study • Additive approach • Risk difference • Multiplicative approach • Cumulative incidence • Relative risk • Person-time analysis • Relative rate • Alternative approach • Disease odds ratio Cohorts

  9. Calculation of a risk difference in a cohort study Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 Risk difference = R1- R0 = (a/L1) - (c/L0) Cohorts

  10. Risk of leishmaniasis according to water bodies within 25 metres of house, Chatrakhali, West Bengal, 2004-6 Leishmaniasis Non-ill Total Water bodies 139 487 626 No water bodies 11 114 125 Total 150 601 751 Risk difference = (139/626) - (11/125) = 22% - 9% = 13% Cohorts

  11. Calculation of a relative risk in a cohort study Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 Relative risk = R1/R0 = (a/L1) / (c/L0) Cohorts

  12. Risk of leishmaniasis according to water bodies within 25 metres of house, Chatrakhali, West Bengal, 2004-6 Leishmaniasis Non-ill Total Water bodies 139 487 626 No water bodies 11 114 125 Total 150 601 751 Relative risk = (139/626) / (11/125) = 22% / 9% = 2.5 Cohorts

  13. Calculation of a relative rate in a cohort study Events Person-time Rate Exposed a PT1 Rate1 Non-exposed c PT0 Rate0 Total a+c PT Rate Relative rate = Rate1/Rate0 = (a/PT1) / (c/PT0) Cohorts

  14. The odds Probability of occurrence of an event ______________________________________ Probability of non-occurrence of this event Cohorts

  15. Calculation of a disease odds ratioin a cohort study Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 Odds of disease in exposed: = (a/L1)/(b/L1)= a/b Odds of disease in unexposed = (a/L0)/(b/L0) = c/d Disease odds ratio (OR): (a/b) / (c/d) = ad/bc Cohorts

  16. Reasons to prefer relative risks to diseases odds ratios in cohort studies • The relative risk corresponds to an intuitive notion • The OR is less meaningful to most readers • The OR is larger than the relative risk Cohorts

  17. Calculation of an exposure-odds ratioin a cohort study Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d L1 + L0 Odds of exposure in ill: = (a/a+c)/(c/a+c)= a/c Odds of exposure in non-ill = (b/b+d)/(d/d+d0) = b/d Exposure odds ratio (OR): (a/c) / (b/d) = ad/bc Cohorts

  18. Magical trick #1 In a cohort study, the ratio of the odds of disease among exposed and unexposed is equal to the ratio of the odds of exposure among ill and non-ill Cohorts

  19. Calculation of a relative risk for a rare disease in a cohort study Ill Non-ill Total Exposeda b L1 Non-exposedc d L0 Totala+c b+d L1 + L0 b # a+b; d # c+d Relative risk = a (c+d)/c(a+b) # ad/bc Cohorts

  20. Magical trick #2 In a cohort study, when the disease is rare, the ratio of the odds of disease is almost equal to the relative risk Cohorts

  21. Impossibility to calculate a relative risk in a case control study Case Control Total Exposed a.f1 b.f2 N/A Non-exposed c.f1 d.f2 N/A Total C1.f1 C0.f2 N/A Cases are sampled from all cases (sampling fraction: f1) Controls are sampled from all controls (sampling fraction: f2) f1 and f2 are unknown, risks cannot be calculated Case control

  22. Calculation of the exposure-odds ratio in a case control study Case Control Total Exposed a.f1 b.f2 N/A Non-exposed c.f1 d.f2 N/A Total C1.f1 C0.f2 N/A Odds of exposure among cases= (a.f1)/(c.f1) Odds of exposure among controls = (b.f2)/(d.f2) Exposure odds ratio: ad/bc Case control

  23. Magical trick #3 In a case control study, the exposure-odds ratio is equal to the disease-odds ratio of the corresponding cohort Case control

  24. Magical trick #2 + #3 = #4 In a case control study, when the disease is rare, the exposure-odds ratio is almost equal to the relative risk in the corresponding cohort Case control

  25. Sleeping in work clothes and scrub typhus, Darjeeling, West Bengal, India, 2005-6 S. typhus Controls Total Sleeping in work clothes 66 13 79 Changing clothes to sleep 56 33 89 Total 122 46 168 Odds ratio = (66x33)/(56x13) =3.0 Case control

  26. Presentation of the data of an analytical cross-sectional study in a 2 x 2 table Ill Non-ill Total Exposed a b L1 Non-exposed c d L0 Total a+c b+d a+b+c+d Prevalence in exposed: P1, Prevalence in unexposed: P0 Prevalence ratio = P1/P0 = (a/L1) / (c/L0) Formula identical to the relative risk, but could be calculated both ways Cross sectional studies

  27. Prevalence of trachoma according to facial hygiene, Burkina Faso, 1991 Trachoma No trachoma Total Dirty face 54 337 391 Clean face 50 1459 1509 Total 104 1796 1900 Prevalence ratio = (54/391)/(50/1509) = 4.2 Cross sectional studies

  28. Limitations of causal inference in analytical cross-sectional studies • Prevalent cases • Exposure and outcome examined simultaneously Cross sectional studies

  29. Take-home messages • Calculate relative risks in cohort studies • Calculate odd ratio in case control studies, it will approximate the relative risk if the disease is rare • Calculate prevalence ratio in cross-sectional surveys and beware of chicken-and-egg causality issues

  30. Association does not systematically mean causation: Potential explanations for an association • Bias • Chance • Confounding factor • Causation • After the first three have been ruled out

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