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Disease Association I Main points to be covered Fall 2010

Disease Association I Main points to be covered Fall 2010. Measures of association compare measures of disease between levels of a predictor variable Cross-sectional study Introducing: The 2 X 2 table Prevalence ratio Odds ratio Cohort study Risk ratio (cumulative incidence)

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Disease Association I Main points to be covered Fall 2010

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  1. Disease Association IMain points to be coveredFall 2010 • Measures of association compare measures of disease between levels of a predictor variable • Cross-sectional study • Introducing: The 2 X 2 table • Prevalence ratio • Odds ratio • Cohort study • Risk ratio (cumulative incidence) • Rate ratio (incidence rate) • 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

  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

  5. 2 x 2 table for association of disease and exposure Disease Yes No Yes a + b b a 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 and unexposed Disease Yes No a a Yes b a + b PR = Exposure c c d c + d No

  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. Sample data with prevalence ratio calculated

  9. Describing a PR < 1 In words: Those who are exposed are 0.74 times as likely to have the disease compared with those who are not exposed. OR There is a 0.74 fold lower prevalence of disease among exposed compared to unexposed.

  10. Describing a PR > 1 In words: Those who are exposed are 1.5 times as likely to have the disease compared with those who are not exposed. OR There is a 1.5 fold higher prevalence of disease among exposed compared to unexposed.

  11. 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, disease on the side.

  12. 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

  13. 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

  14. 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

  15. Probability and Odds • Odds another way to express probability of an event • Odds = # events # non-events • Probability = # events # events + # non-events = # events # subjects

  16. 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]

  17. 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

  18. Understanding Odds • To express odds in words, think of it as the 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

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

  20. Odds (continued) • Used in epidemiology because the measure of association available in case-control design is the odds ratio (more on this next week) • Also important because the log odds of the outcome is given by the coefficient of a predictor in a logistic regression. Can use models to obtain multivariable adjustment in cross-sectional design. Less important now that adjusted models for prevalence ratio are possible.

  21. 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

  22. 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

  23. Probability and odds ratios 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

  24. 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 of p / 1-p in exposed / p / 1-p in unexposed

  25. 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 the cross-product.However, calculating as odds of disease in exposed/ odds of disease in unexposed helps to keep track of what you are comparing.

  26. Odds Ratio in Cross-Sectional Study • The study design affects not just the measure of disease occurrence but also the measure of disease 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

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

  28. 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

  29. 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

  30. 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

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

  32. 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

  33. Prevalence ratio and Odds ratio If prevalence of disease is high in either or both exposed and unexposed, Prevalence Ratio 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 Prevalence Ratio only if prevalence islow in both exposed and unexposed group

  34. “Bias” in OR as estimate of PR • Text refers to “bias” in OR as estimate of Prevalence Ratio (or Risk Ratio in a cohort study) • Not “bias” in usual sense because both OR and PR are mathematically valid and use the same numbers • Simply that OR cannot be thought of as a surrogate (“close approximation”) for the PR unless incidence is low

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

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

  37. Relative Measures and Strength of Association with a Risk Factor • 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 • Underscores importance of interpretation of prevalence Odds Ratio in context of disease and exposure prevalences

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

  39. 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

  40. Example: Prevalence ratio not symmetrcial

  41. Example: OR is symmetrical

  42. Important property of odds ratio #3 • Coefficient of a predictor variable in logistic regression is the log odds of the outcome • ecoefficient = OR • Logistic regression. Method of multivariable analysis used most often in cross-sectional studies. Now possible to obtain adjusted models for prevalence ratio.

  43. 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

  44. 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) Melamed et. al. Arterioscler Throm Basc Biol 2010

  45. Example: Adjusted prevalence ratio

  46. 3 Useful Properties of Odds Ratios • Odds ratio of non-event is the reciprocal of the odds ratio of the event (symmetrical) • Regression coefficient in logistic regression equals the log of the odds ratio • Odds ratio of disease equals odds ratio of exposure • Important in case-control studies (Discussed next week)

  47. Measures of Association in a Cohort Study • With cross-sectional data we can calculate a ratio of the probability or of the odds of prevalent disease in two groups, but we cannot measure incidence • A cohort study allows us to calculate the incidence of disease in two or more groups

  48. Measuring Association in a Cohort Following two groups by exposure status within a cohort: Equivalent to following two cohorts defined by exposure

  49. Analysis of Disease Incidence in a Cohort • Measure occurrence of new disease separately in a sub-cohort of exposed and a sub-cohort of unexposed individuals • Compare incidence in each sub-cohort • How?

  50. Two Measures • Recall from previous lectures the 2 measures of incidence: cumulative incidence and incidence rate • Corresponding measures of disease association are risk ratio for comparing cumulative incidences and rate ratio for comparing incidence rates

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