Measures of Association & rate standardization

1. Measures of Association & rate standardization 白其卉 中研院生醫所 For lecture 2002/12/02

2. Association Index: measures of association -- Index of measured relationship of risk factor (RF) and disease (Dx) 表示危險因子與疾病間的相關程度之指標

3. Introduction • Analytic epidemiology (epi) • Cohort study (prospective) • Fixed cohort • Dynamic cohort • Case-control study (retrospective) • Major aims in analytic epi • verify the relationship of RF & Dx

4. How do we describe risk & its association on risk?

5. Measures of Association • Absolute risk • Attribute risk • Relative risk • Risk ratios (RR) • Odds ratios (OR) • Risk Difference

6. Absolute risk • Magnitude of risk of a disease in a population • Descriptive unit of magnitude of risk: • Rate: incldence, prevalence, morbidity, mortality… • Limitation: • Absolute risk is not comparative. • Absolute risk does not allow one to establish association between exposure and disease

7. Status 或 event 的測量指標 * Odds

8. 常見的流行病學測量指標

9. Incidence / incidence density • Definition: • 某段觀察時間內，單位時間中所有可能發生某特定事件的人發生該事件的率。 I：新病例數 P：觀察人數（有可能發生者才算） T：觀察期間 2 / ( 7 + 2 + 4.5 + 3 + 6 ) = 2 / 22.5 = 0.089 / 年

10. Cumulative incidence rate • Definition: • 某世代族群或某固定族群的人，經過某段觀察時間後，發生某事件﹙疾病﹚的人口佔該世代族群人口總數的百分比。 • 該事件﹙疾病﹚的發生情形，用以推估在族群中的任一人發生該事件或得該疾病的機率，也稱危險度﹙risk﹚。 • 當疾病或事件的發生機率很小時，累積發生率幾乎可等於發生率乘以年齡層距之總和。 • 2/（5-2/2）= 0.5

11. No Disease Disease A B A + B =N1 Exposed Unexposed C D C + D =N0 A + C =M1 B + D =M0 N • 相差危險性 • P1 - P0 • 相對危險性 • P1/P0 • 相對差異量(危險變化量) • (P1 - P0) / P1 • 對比值 • P1 (1- P0) / P0 (1- P1) • 發病機率 • P1 = A/N1 • P0 = C/N0

12. Disease risk in exposed Risk exposure Disease risk in nonexposed Risk nonexposure Relative Risk • Definition: • The ratio of the risk of disease in persons exposed compared to the risk of disease in persons unexposed • Common formula of relative risk (RR) RR= = • Diseased risk: cumulate rate(incidence), rate(incidence) density • relative risk; rate ratio; risk ratio…

13. Incidenceexposed No Disease Relative Risk = Disease Incidenceunexposed A B a + b =N1 Exposed Unexposed C D C + D =N0 Incidence Densityexposed A + C B + D N Rate Ratio = Cumulative Incidenceexposed Incidence Densityunexposed A/N1 Risk Ratio = Risk Ratio = Cumulative Incidenceunexposed C/N0 Ex Dx Ex.

14. Interpretation of Relative Risk • RR > 1 - the risk of disease in the exposed group is greater than the risk in the unexposed group • RR = 1 - the risk of disease is the same in the exposed and unexposed • RR < 1 - the risk of disease in the exposed group is less than the risk in the unexposed

15. No Disease Disease A B N1 Exposed Unexposed C D N0 A + C B + D N For Fixed Cohort Equal follow-up time: 不考慮time • Cumulate incidence • 研究對象發病的機率(risk) • CI1 = A/N1 • CI0 = C/N0 • RRCI = CI1/CI0 • = (A/N1)/(C/N0) • RDCI = CI1- CI0 • = (A/N1) - (C/N0) ORCI = CI1(1-CI1) / CI0 (1-CI0) = AD/BC

16. Point estimation & 95% confidence interval

17. Hypothetical testing

18. In a prospective study, 8000 persons, including 3000 hypertensive and 5000 normtensive patients, were followed for 10 years. There were 84 and 87 CHD cases in hypertensive and normtensive persons, respectively. • RR=? Ex-1

19. Answer: CI in exposed (HT) patients = 84/3000 = 28.0 CI in non-exposed (non-HT) patients = 87/5000 = 17.4 Relative risk = 28.0/17.4 = 1.61 Ex-1

20. Observed Person-years Disease A L1 N1 Exposed Unexposed C L0 N0 A + C = m1 L1 + L0 = L N For Dynamic Cohort Unequal follow-up time: 考慮 time • Incidence density • 單位人時的發病狀況(rate) • ID1 = A/L1 • ID0 = C/L0 • RRID = ID1/ID0 • = (A/L1)/(C/L0) • RDID = ID1- ID0 • = (A/L1) - (C/L0) No odds

21. Point estimation & 95% confidence interval Hypothetical testing P0=L1/L q0=1-p0

22. B肝帶原之追蹤研究共追蹤帶原者450人年及非帶原者380人年, 在追蹤期間有35名對象發生肝細胞癌,其中15名為帶原者,20名為非帶原者歐. • RR=? Ex-2

23. Person- Years HCC 450 15 HBsAg(+) 20 380 HBsAg(-) 35 830 Overall rate = 35/830 = 0.042 cases/PY = 4.2 cases/100 PY IDexposed= 15/450 = 3.3 cases/100 PY IDunexposed = 20/380 = 5.3 cases/100 PY Rate Ratio = 3.3 cases/100 PYO/5.3 cases/100 PYO = 0.62 Ex-2

24. Dx/non-Dx in exposured Exposure/unexposure in Dx Dx ratioexposed Ex ratiodisease Dx/non-Dx in unexposured Dx ratiounexposed Exposure/unexposure in nonDx Ex rationon-Dx Odds Ratio • Definition: • The ratio of the ratio of exposure in diseased persons compared to the ratio of exposure in non-diseased persons • Common formula of odds ratio (OR) OR.cohort = = = OR.cs-cn=

25. Random sample; case-control study No Disease No Disease Disease Disease A a b B A + B a + b Exposed Exposed C c d D C + D c + d Unexposed Unexposed a+c A + C b + d B + D N a+b+c+d Population; Cohort study Odds(Ex)=(A/N1)/(1-A/N1) Odds(nonEx)=(C/N0)/(1-C/N0) Odds Ratio = odds(Ex)/odds(nonEx) = A*D/B*C Odds(Dx)=(a/a+c)/(c/a+c) Odds(nonEx)=(b/b+d)/(d/b+d) Odds Ratio = odds(Dx)/odds(nonDx) = a*d/b*c ~ A*D/B*C Dx Ex

26. Interpretation of Odds Ratio • OR > 1 - the odds of exposure in the diseased group is greater than the risk in the non-diseased group • OR = 1 - the odds of exposure is the same in the diseased and non-diseased • OR < 1 - the odds of exposure in the diseased group is less than the risk in the non-diseased group

27. Point estimation & 95% confidence interval Hypothetical testing

28. In case-control study of 74 Endometrial Cancer patients & their 664 controls, 56 cases and 274 controls received estrogen therapy ever. • OR=? EX-3

29. No Cancer Cancer 56 330 274 Estrogens No Estrogens 18 390 408 664 74 738 Odds ratio = 56*390/18*274 = 4.42 Estrogens and Endometrial Cancer EX-3

30. Relative Risks and Odds RatiosWhen are They Similar? Why does Odds Ratio represent Relative Risk ?

31. If case & control from fixed cohort • Assumption: • Case and control are random sample from diseased & non-diseased population (representative) • Probability (ex CI) is very small (rare disease)

32. Persons- Years Disease A L1=N1*t1 Exposed C L0 = N0*t0 Unexposed A + C L1 + L0 = L If case & control from dynamic cohort • Assumption: • Case and control are random sample from diseased & non-diseased population (representative) • Density sampling (time-matching) If t0=t1, Odds(Ex)=(A/N1) Odds(nonEx)=(C/N0) Odds Ratio = (A/N1)/ (C/N0) = (A/L1)/ (C/L0) = RRID

33. Statistical applicationlinear regression • Try to determine the relationship between two random variablesX and Y • Y ~ continuous variables ~ N(u,var) • X ~ continuous variables usually ~ N(u,var) • Y= a+bXi+e • Interpretation of intercept & slope (coefficient). • Obtain RDCI in cohort study

35. Statistical applicationlogistic regression • Try to determine the relationship between risk factors Xi and disease probability(Y) • Y ~ binary variables ~ B(p) • Y = logit P =log (P/1-P) • P/(1-P) ~ disease odds (log odds) • Odds ratios = P1q0 / p0q1 • Log (odds) = logit P1– logit P0 = beta • Logit P0 = alpha

36. Logistic regression • Y = logit P = Exp (a+bXi+e) • Log transform of disease probability in each risk category is expressed as a linear function of regression • P1 =exp(a+b)/1+exp(a+b) • P0 =exp(a)/1+exp(a)

37. Logistic regression • The exposure risk(X) to disease risk(Y) fit the multiplicative hypothesis. • Logit P(x1,x2) = a+b1x1+b2x2+rx1x2 • b1 = log (r10) • b2 = log (r01) • r = log (r11/r10r01) = logit p11-logit p10- logit p01+logit p00 • Obtain ORCI in cohort study, and OR in case-control study

38. Statistical ApplicationCox proportion hazard model • Try to determine the relationship of between risk factors Xi and disease probability(Y) under considering time to event • Y~binary (dead/alive) ~ B(p) • All risk factors are assumed to be constant over time • hi(t) = Exp (a+bXi+e) h0 (t) • h0 (t): baseline hazard function; ID0 • hi (t): hazard function in exposed group; IDi • Obtain RRID in cohort study (hazard ratio)

39. Appendix II: Analysis of cohort studies (Clive Osmond) Cohort studies may be classified according to both the type of data that are collected at baseline and the nature of the eventual outcome measure. The combination determines the appropriate strategy for analysis. Below we consider four common combinations, mention the usual method of analysis, and give an example of each. (Table 14.2)

40. Back

41. Adjusted rate -Standardization 透過調整人口結構的不同,用以比較人口組成不同的團體比率

42. Status 或 event 的測量指標

43. The problems when we compare rates in 2 populations

44. Standardization • 當將兩個族群的率拿來加以比較時，常因其各自的加權量不同而有所差異，造成解釋上的困難 • 標準化比率是為了比較兩個以上團體的比率所推算出來的假想總合比率。 • 用途: • 比較人口組成不同的團體比率。 • 進行國際比較 方法: Direct method Indirect method

45. Direct standardization • SIR（Standardized incidence ratio) • 標準化發生率比 SIR = ai：指標族群發生個案﹙事件﹚數 bi：對照組發生個案﹙事件﹚數 N1i：指標族群分層觀察人年（人）數 N0i：對照族群分層觀察人年（人）數 ：標準族群各年齡層人數 ：標準族群各年齡層總人數

46. Exposed (N1) Non-Exposed (N0) PY death MR PY death MR Young 3000 30 0.01 1000 5 0.005 Aged 1000 30 0.03 9000 225 0.025 Total 4,000 60 0.015 10,000 230 0.023 SIR： Wi = N0i + N1i4000+10000 指標組群發生率：(4000×0.01＋10000×0.03)/14000＝0.024重新計算死亡率 對照族群發生率NE：(4000×0.005＋10000×0.025)/14000＝0.019 率比：0.024/0.019＝1.26已暴露和未暴露的比值

47. Indirect standardization • SMR（Standardized mortality ratio) • 標準化死亡比 在族群之間作比值 SMR= ~ Observed/Expected ai：指標族群分層死亡（罹病）人數 bi：對照族群分層死亡（罹病）人數 N0i：對照族群分層觀察人年（人）數 ：指標族群各年齡層人數

48. Exposed (N1) Non-Exposed (N0) PY death MR PY death MR Young 3000 30 0.01 1000 5 0.005 Aged 1000 30 0.03 9000 225 0.025 Total 4,000 60 0.015 10,000 230 0.023 SMR：觀察值/期望值