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Disease Association I Main points to be covered

Disease Association I Main points to be covered. Measures of association compare measures of disease occurrence between levels of an exposure variable Cross-sectional study Introducing: The 2 X 2 table Prevalence ratio Odds ratio Cohort study Risk ratio (cumulative incidence ratio)

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Disease Association I Main points to be covered

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  1. Disease Association IMain points to be covered • Measures of association compare measures of disease occurrence between levels of an exposure variable • Cross-sectional study • Introducing: The 2 X 2 table • Prevalence ratio • Odds ratio • Cohort study • Risk ratio (cumulative incidence ratio) • Rate ratio (incidence rate ratio and hazard rate ratio) • Risk difference • Rate difference

  2. Measures of Disease Association • Measuring occurrence of new events can be an aim by itself, but usually we want to look at the relationship between an exposure (risk factor, predictor) and the outcome • Measures of association compare measures of disease (incident or prevalent) between levels of a predictor variable • The type of measure showing an association between an exposure and an outcome event is dictated by the study design

  3. Cross-Sectional Study Design: A Prevalent Sample CE

  4. Measures of Association in a Cross-Sectional Study • Simplest case is to have a dichotomous outcome and dichotomous exposure variable • Everyone in the sample is classified as diseased or not and having the exposure or not, making a 2 x 2 table • The proportions with disease are compared among those with and without the exposure • NB: Exposure = risk factor = predictor = predictor variable = independent variable

  5. 2 x 2 table for association of disease and exposure Disease Yes No Yes a + b a b Exposure c + d c d No N = a+b+c+d a + c b + d Note: data may not always come to you arranged as above. STATA puts exposure across the top, disease on the side.

  6. Prevalence ratio of disease in exposed vs unexposed Disease Yes No a a Yes b a + b PR = Exposure c c d c + d No PR is a point estimate of association between exposure and disease in cross-sectional design.

  7. Prevalence Ratio • Text refers to Point Prevalence Rate Ratio in setting of cross-sectional studies • We like to keep the concepts of rate and prevalence separate, and so prefer to use prevalence ratio

  8. Calculating Prevalence Ratio

  9. Describing a PR < 1 (e.g., PR = 0.74) • Importance of understandable interpretation • * “Those who are exposed are 0.74 times as likely to have the disease than those who are not exposed.” • “Being exposed is associated with a lower prevalence of the outcome compared with being unexposed (PR = 0.74).” • Avoid: “The exposed have 26% less prevalence of the disease than the unexposed.” • Could be misinterpreted as the difference in prevalence between exposed and unexposed. In this example the difference is in fact: • 45% in exposed – 61% in unexposed = -16% • We are ignoring issues of statistical significance for now • * Preferred description

  10. Describing a PR > 1 (e.g., PR = 1.5) * “Those who are exposed are 1.5 times as likely to have the disease than those who are not exposed.” * “Prevalence of disease in exposed is 1.5 times as high as in unexposed.“ • “There is a 1.5 fold higher prevalence of disease among exposed compared to unexposed.” • “Being exposed is associated with a higher prevalence of disease compared with being unexposed (PR = 1.5).” • Avoid: “50% more likely to have disease” • Open to misinterpretation as the difference in prevalence in the exposed and unexposed

  11. PR > 1 often easier to describe • Prevalence ratio (and other ratio measures) > 1 are typically easier to explain than PR < 1. • If appropriate, switch the reference group

  12. Re-calculating to report Prevalence Ratio > 1

  13. Example of 2 x 2 Table Layout in STATA Exposed Unexposed | Total --------------------------------------------------- Cases | 14 388 | 402 Noncases | 17 248 | 265 --------------------------------------------------- Total | 31 636 | 667 | | STATA puts exposure across the top (as columns), disease on the side (as rows).

  14. Prevalence ratio (STATA output) Exposed Unexposed | Total --------------------------------------------------- Cases | 14 388 | 402 Noncases | 17 248 | 265 --------------------------------------------------- Total | 31 636 | 667 | | Risk | .4516129 .6100629 | .6026987 Point estimate [95% Conf. Interval] --------------------------------------------- Risk ratio .7402727 | .4997794 1.096491 ----------------------------------------------- chi2(1) = 3.10 Pr>chi2 = 0.0783 STATA uses “risk” and “risk ratio” by default

  15. Study Reporting Prevalence Ratios Prevalence of hip osteoarthritis among Chinese elderly in Beijing, China, compared with whites in the United States Abstract:The crude prevalence of radiographic hip OA in Chinese ages 60–89 years was 0.9% in women and 1.1% in men; it did not increase with age. Chinese women had a lower age-standardized prevalence of radiographic hip OA compared with white women in the SOF (age-standardized prevalence ratio = 0.07) and the NHANES-I (prevalence ratio = 0.22). Chinese men had a lower prevalence of radiographic hip OA compared with white men of the same age in the NHANES-I (prevalence ratio = 0.19). Nevitt et al, 2002 Arthritis & Rheumatism

  16. Vitamin D and PAD • Objective – The purpose of this study was to determine the association between the 25-hydroxyvitamin D (25(OH)D) levels and the prevalence of peripheral arterial disease (PAD) in the general United States population. • Methods and Results – We analyzed data from 4839 participants of the National Health and Nutrition Examination Survey. After multivariate adjustment for demographics, comorbidities, physical activity level, and laboratory measures, the prevalence ratio of PAD for the lower, compared to the highest, 25(OH)D quartile (<17.8 and ≥29.2 ng/mL, respectively) was 1.80 (95% CI: 1.19, 2.74) • Log binomial regression model to estimate adjusted PR Melamed et. al. Arterioscler Throm Basc Biol 2010

  17. Example: Adjusted prevalence ratio Log binomial regression used for multivariable model 4-level exposure: How to describe?

  18. Alternative in cross-sectional study: Odds Ratio • Many cross-sectional studies report an odds ratio rather than a prevalence ratio. • Odds of disease provide a legitimate statistical description but are not as intuitive as prevalence of disease. • Popularity of odds ratio (OR) based on availability of statistical software for adjusted models via logistic regression. • Adjusted models for prevalence ratio are now available, and use of PR is increasing. • We introduce odds in the context of cross-sectional design, where use of OR is an option. OR is required for analysis of disease association in case-control studies (next week).

  19. Summary: Prevalence ratio of disease in exp and unexp Disease Yes No Prevalence Ratio = a a Yes b a + b Exposure c c d c + d No a/(a+b) and c/(c+d) = probabilities of disease and PR is ratio of two probabilities

  20. Probability and Odds • Odds another way to express occurrence of an event • Rarely used for occurrence. Discussing today because used for ratio measure of association – the odds ratio. • Odds = # events # non-events • Probability = # events # events + # non-events = # events # subjects

  21. Probability and Odds • Probability = # events # subjects • Odds = # events # subjects = probability # non-events (1 – probability) # subjects • Odds = p / (1 - p) [ratio of two probabilities: unlike probability, can be greater than 1]

  22. Probability and Odds • If event occurs 1 of 5 times, probability = 1/5 = 0.2 • Out of the 5 times, 1 time will be the event and 4 times will be the non-event, odds = 1 / 4 = 0.25 • To calculate probability given the odds: probability = odds / 1+ odds

  23. Understanding Odds • To express odds in words, think of it as frequency of the event compared to the frequency of the non-event • “For every time the event occurs, there will be 3 times when the event does not occur” • In words: “Odds are 1 to 3” • Written as 1:3 or 1/3 or 0.33

  24. Odds • Less intuitive than probability (wouldn’t say “my odds of dying are 1 to 4”) • unless you are a professional gambler • No less legitimate mathematically, just not so easily understood

  25. Odds (continued) • Used in epidemiology because the measure of association available in case-control design is the odds ratio (more on this next week) • And logistic regression often used to obtain adjusted measures of association in cross-sectional design. Logistic regression provides odds ratio. • Less important now that adjusted models for prevalence ratio are possible.

  26. Odds ratio • As odds are just an alternative way of expressing the occurrence of an outcome, odds ratio (OR) is an alternative to the ratio of two probabilities (prevalence ratio) in cross-sectional studies • Odds ratio = ratio of two odds

  27. Probability and odds in a 2 x 2 table Disease Yes No What is p of disease in exposed? What are odds of disease in exposed? And the same for the un-exposed? 2 Yes 3 5 Exposure 1 4 5 No 7 10 3

  28. Prevalence ratio and odds ratio in a 2 x 2 table Disease Yes No PR = 2/5 1/5 = 2 2 3 Yes 5 OR = 2/3 1/4 Exposure = 2.67 1 4 5 No 7 10 3

  29. Odds ratio of disease in exposed and unexposed Disease a Yes No a + b a b a Yes 1 - a + b OR = Exposure c d c c + d No c 1 - c + d Formula: (p / 1-p in exposed) / (p / 1-p in unexposed)

  30. Odds ratio of disease in exposed and unexposed a a + b b a + b c c + d d c + d a a b c d a + b a 1 - a + b ad bc = OR = = = c c + d c 1 - c + d OR is often described as the “cross-product.”Better to calculate as odds of disease in exposed/ odds of disease in unexposed to keep track of what you are comparing.

  31. Odds Ratio in Cross-Sectional Study • Study design affects not just the measure of disease occurrence but also measure of association • Cross-sectional design uses prevalent cases of disease, so Odds Ratio in a cross-sectional study is a Prevalence Odds Ratio • Many authors do not use but we encourage • Promotes clarity of thought and presentation to be as accurate as possible about measures

  32. Odd Ratio compared to Prevalence Ratio If Prevalence Ratio = 1.0, OR = 1.0; otherwise OR farther from 1.0 than PR 0 1 ∞ Stronger effect Prev Ratio OR Stronger effect OR Prev Ratio

  33. Prevalence ratio and Odds ratio If Prevalence Ratio > 1, then OR farther from 1 than Prevalence Ratio: PR = 0.4 = 2 0.2 OR = 0.4 0.6 = 0.67 = 2.7 0.2 0.25 0.8

  34. Prevalence ratio and Odds ratio If Prevalence Ratio < 1, then OR farther from 1 than PR: PR = 0.2 = 0.67 0.3 OR = 0.2 0.8 = 0.25 = 0.58 0.3 0.43 0.7

  35. Odds ratio (STATA output) Exposed Unexposed | Total --------------------------------------------------- Cases | 14 388 | 402 Noncases | 17 248 | 265 --------------------------------------------------- Total | 31 636 | 667 | | Risk | .4516129 .6100629 | .6026987 Point estimate [95% Conf. Interval] --------------------------------------------- Risk ratio .7402727 | .4997794 1.096491 Odds ratio .5263796 | .2583209 1.072801 ----------------------------------------------- chi2(1) = 3.10 Pr>chi2 = 0.0783

  36. Describing an OR < 1 (e.g., OR = 0.53) • * “Those who are exposed have 0.53 times the odds of having the disease than those who are not exposed.” • * “The exposed have 47% lower odds of the disease than the unexposed.” • “Being exposed is associated with lower odds of the outcome compared with being unexposed (OR = 0.53).” • Avoid: “Those who are exposed are 0.53 times as likely to have the disease as those who are not exposed.” • Odds ratio, not a prevalence ratio

  37. Describing an OR > 1 (e.g., OR = 1.5) • *“Those who are exposed have 1.5 times the odds of having the disease than those who are not exposed.” • * “The odds of disease in exposed are 1.5 times as high as in unexposed." • “There is a 1.5 fold higher odds of disease among exposed compared to unexposed.” • “Being exposed is associated with higher odds of disease compared with being unexposed (OR = 1.5).” • Avoid: “1.5 times more likely” or “1.5 times higher risk”

  38. Important property of odds ratio #1 • OR approximates Prevalence Ratio only if disease prevalence is low in both the exposed and the unexposed group

  39. Prevalence ratio and Odds ratio If risk of disease is low in both exposed and unexposed, PR and OR approximately equal. Text example: prevalence of MI in high bp group is 0.018 and in low bp group is 0.003: Prev Ratio = 0.018/0.003 = 6.0 OR = 0.01833/0.00301 = 6.09

  40. Prevalence ratio and Odds ratio If prevalence of disease is high in either or both exposed and unexposed, PR and OR differ. Example, if prevalence in exposed is 0.6 and 0.1 in unexposed: PR = 0.6/0.1 = 6.0 OR = 0.6/0.4 / 0.1/0.9 = 13.5 OR approximates PR only if disease prevalence islow in both exposed and unexposed group

  41. “Bias” in OR as estimate of PR • Text refers to “bias” in OR as estimate of Prevalence Ratio • Not “bias” in usual sense because both OR and PR are mathematically valid and use the same numbers • Simply that OR is not equal to PR. • OR can be a “close approximation” for the PR, but only if outcome prevalence is low

  42. Table 2—Prevalence and odds of falling according to diabetes status (NHANES) – 60+ years old Gregg et al. Diabetes Care (2000) 23: 1272

  43. Prevalence Ratio vs Odds Ratio Prevalence Ratio Zocchetti et al. 1997

  44. Relative Measures of Association: Interpreting the Magnitude • One gauge of the strength of an association between risk factor and disease is the size of the relative measure • In practice, many risk factors have a relative measure (prevalence ratio, risk ratio, rate ratio, or odds ratio) in the range of 2 to 5 • Some very strong risk factors may have a relative measure in the range of 10 or more • Asbestos and lung cancer • Relative measures < 2.0 may still be valid but are more likely to be the result of bias • Second-hand smoke risk ratio < 1.5 • Caution: If disease prevalence (incidence) is high, can’t use this same yardstick to assess the size/strength of the Odds Ratio.

  45. Important property of odds ratio #2 • Unlike Prevalence Ratio, OR is symmetrical: OR of event = 1 / OR of non-event

  46. Symmetry of odds ratio versus non-symmetry of prevalence ratio OR of non-event is 1/OR of event PR of non-event = 1/PR of event

  47. Example: Prevalence ratio not symmetrical

  48. Example: OR is symmetrical

  49. Important property of odds ratio #3 • OR's obtained from common model used to manage confounding -- logistic regression. • ecoefficient of exposure variable = OR for one unit change in exposure (e.g. exposed vs unexposed) • Logistic regression. Commonly used for multivariable analysis in cross-sectional studies. Now possible to obtain adjusted models for prevalence ratio.

  50. Smoking and Tooth loss – Example of prevalence odds ratio Methods. The authors collected information about tooth loss and other health-related characteristics from a questionnaire administered to 103,042 participants in the 45 and Up Study conducted in New South Wales, Australia. The authors used logistic regression analyses to determine associations of cigarette smoking history and ETS with edentulism (all teeth lost), and they adjusted for age, sex, income and education. Results. Current and former smokers had significantly higher odds of experiencing edentulism compared with never smokers (prevalence odds ratio [OR], 2.51; 95 percent confidence interval [CI], 2.31-2.73 and OR, 1.50; 95 percent CI, 1.43-1.58, respectively). Arora et al. JADA 2010

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