Comparison of Proportions Part II

1. Comparison of Proportions Part II Instructor: 李奕慧 yihwei@mail.tcu.edu.tw

2. Lecture Overview • Study designs in epidemiology • Measures of study effect for 2 categorical variables 1. Risk difference 2. Relative risk 3. Odds ratio • McNemar’s test for Matched-pair study

3. Epidemiologic Study Design • Analytical studies • Intervention studies • Clinical trials • Observational studies • Cross-sectional studies • Cohort studies • Case-control studies

4. Measures of Study Effect

5. Risk difference (RD, p1-p2)

6. 建構 p1-p2的信賴區間(confidence interval, CI) 沒戴安全帽頭部受傷的機率，較有戴安全帽者高出39%~61%，戴安全帽的機車騎士，在車禍發生時，可以減少39%~61%的頭部受傷的機會。

7. 檢定 H0:p1-p2=0 versus Ha:p1-p20

8. 2 sample proportion test.xls

9. Example for Clinical trial and Risk Difference BMJ 2006;333;1193-

10. 比較Intervention group與Control group病人住院3天後的死亡率(death after day 3) • 每一個病人皆觀察其死亡(=1)或存活(=0)情形 • Intervention group：5/132 (5%)的人住院3天後死亡 • Control group: 8/133 (8%)的人住院3天後死亡 • 兩組住院3天後死亡率的差異(control-intervention)為 2% (point estimate), 95%CI:(-3% to 8%)，表示兩組母體死亡率差異的範圍介於-3%~8%，Intervention不會影響病人的死亡率。

11. Disease + Exposed Disease - Study population Disease + Non-exposed Disease - Cohort study / Clinical trial (Intervention) (Control)

12. ill not ill a b Exposed c d Unexposed Cohort Data 2 x 2 table Incidence in exposed (p1) = a/(a+b) Incidence in non-exposed(p2) = c/(c+d)

13. Effect measures in cohort studies • Hypothesis • Is the incidence among exposed higher than among unexposed • Absolute measures • Risk difference (RD) • Relative measures • Relative risk/Risk Ratio (RR)

14. Foodborne Outbreak in a Wedding, Dublin not ill Incidence ill 49 49 98 50% Ate ham Did not eat ham 4 6 10 40% 53 55 108 Risk difference 0.5 - 0.4 = 0.1 (10%) Relative risk 0.5 / 0.4 = 1.25

15. RR與OR的意義 RR=1 ln(RR)=0 沒有相關 RR>1 ln(RR)>0 危險因子 RR<1 ln(RR)<0 保護因子

16. Relative risk • RR = 1.25 25 % increase in risk • RR = 1.13 13 % increase in risk • RR = 13 13 fold increase • RR= 0.820% of risk reduction

17. Example for Relative Risk A Randomized Trial of Aspirin on the Risk of Embolic Events in Patients With Infective Endocarditis JACC, 2003;42(5):775–80

18. Aspirin.sav

19. OR = (17/42)/(8/47) = 2.38 RR = (17/59)/(8/55) =1.98 Aspirin.sav

20. Case-control (Retrospective) Exposed Cases Non-exposed Study Population Exposed Controls Non-exposed

21. 有子宮頸癌 CASE 無子宮頸癌 Control Total Smoker 150 50 200 Nonsmoker 150 250 400 Total 300 300 600 Odds ratio in Case-control and Cohort study OR for smoking =(150/150)/(50/250) = 5 OR for cervical cancer = (150/50)/(150/250) = 5 不管是針對暴露因子，或疾病的odds ratio都相等，odds ratio不會因為研究設計而有所改變。

22. Relative Risk and Odds ratio 當疾病發生的機率很低時，OR  RR

23. Cervical cancer2.sav

24. Matched Pair Study Design Journal of Stroke and Cerebrovascular Diseases, 2005: pp 174-178

25. SBP control (<=140 mmHg) status before and after stroke admission H0: Pbefore=Pafter (中風前SBP控制的比例＝中風後SBP控制的比例） Ha: PbeforePafter Stroke.sav

26. Paired categorical data, McNemar test

27. 應該使用McNemar檢定的結果， 而非一般的Chi-square檢定結果。

28. Thank you!