1. Chapter 18Cross-Tabulated Counts

2. In Chapter 18: • 18.1 Types of Samples • 18.2 Naturalistic and Cohort Samples • 18.3 Chi-Square Test of Association • 18.4 Test for Trend • 18.5 Case-Control • 18.6 Matched Pairs

3. Types of Samples I. Naturalistic Samples ≡simple random sample or complete enumeration of the population II. Purposive Cohorts ≡ select fixed number of individuals in each exposure group III. Case-Control ≡ select fixed number of diseased and non-diseased individuals

4. Naturalistic (Type I) Sample Random sample of study base

5. Naturalistic (Type I) Sample Random sample of study base • How did we study CMV (the exposure) and restenosis (the disease) with a naturalistic sample? • A population was identified and sampled • The sample was classified as CMV+ and CMV− • The outcome (restenosis) was studied and compared in the groups.

6. Purposive Cohorts (Type II sample) Fixed numbers in exposure groups • How would I do study CMV and restenosis with a purposive cohort design? • A population of CMV+ individuals would be identified. • From this population, select, say 38, individuals. • A population of CMV− individuals would be identified. • From this population, select, say, 38 individuals. • The outcome (restenosis) would be studied and compared among the groups.

7. Case-control (Type III sample) Set number of cases and non-cases • How would I do study CMV and restenosis with a case-control design? • A population of patents who experienced restenosis (cases) would be identified. • From this population, select, say 38, individuals. • A population of patients who did not restenose (controls) would be identified. • From this population, select, say, 38 individuals. • The exposure (CMV) would be studied and compared among the groups.

8. Case-Control (Type III sample) Set number of cases and non-cases

9. Naturalistic Sample Illustrative Example • SRS of 585 • Cross-classify education level (categorical exposure) and smoking status (categorical disease) • Talley R rows by C columns “cross-tab”

10. Table Margins Row margins Total Column margins

11. Naturalistic & Cohort Samples

12. Example Prevalence of smoking by education: Example, prevalence group 1:

13. Relative Risks Let group 1 represent the least exposed group

14. Illustration: RRs Note trend

15. k Levels of Response Efficacy of Echinacea. Randomized controlled clinical trial: echinacea vs. placebo in treatment of URI in children. Response variable ≡ severity of illness Source: JAMA 2003, 290(21), 2824-30

16. Echinacea Example • Purposive cohorts  row percents • % severe, echinacea = 48 / 329 = .146 = 14.6% • % severe, placebo = 40 / 367 = .109 = 10.9% • Echinacea group fared worse than placebo

17. §18.3 Chi-Square Test of Association A. Hypotheses. H0: no association in population Ha: association in population B. Test statistic – by hand or computer C. P-value. Via Table E or software

18. Chi-Square Example H0: no association in the population Ha: association in the population Data

19. Expected Frequencies(under H0)

20. Chi-Square Hand Calc.

21. Chi-Square  P-value • X2stat= 13.20 with 4 df • Table E  4 df row bracket chi-square statistic  look up tail regions (approx P-value) • Example (below) shows bracketing values for example are 11.14 (P = .025) and 13.28 (P = .01)  thus .01 < P < .025

22. Illustration: X2stat= 13.20 with 4 df The P-value = AUC in the tail beyond X2stat

23. WinPEPI > Compare2 > F1 Input screen row 5 not visible Output

24. Continuity Corrected Chi-Square • Two different chi-square statistics • Both used in practice • Pearson’s (“uncorrected”) chi-square • Yates’ continuity-corrected chi-square:

25. Chi-Square, cont. • How the chi-square works. When observed values = expected values, the chi-square statistic is 0. When the observed minus expected values gets large  evidence against H0 mounts • Avoid chi-square tests in small samples. Do not use a chi-square test when more than 20% of the cells have expected values that are less than 5.

26. Chi-Square, cont. 3. Supplement chi-squares with measures of association. Chi-square statistics do not quantify effects (need RR, RD, or OR) 4. Chi-square and z tests (Ch 17) produce identical P-values. The relationship between the statistics is:

27. 18.4 Test for Trend See pp. 431 – 436

28. §18.5 Case-Control Sampling • Identify all cases in source population • Randomly select non-cases (controls) from source population • Ascertain exposure status of subjects • Cross-tabulate Efficient way to study rare outcomes

29. Case-Control Sampling Select non-case at random when case occurs Miettinen. Am J Epidemiol 1976; 103, 226-235.

30. Odds Ratio Cross-tabulate exposure (E) & disease (D) Calculate cross-product ratio OR stochastically = RR

31. BD1 Data • Cases: esophageal cancer • Controls: noncases selected at random from electoral lists • Exposure: alcohol consumption dichotomized at 80 gms/day Relative risk associated with exposure

32. (1– α)100% CI for the OR

33. 90% CI for OR – Example

34. WinPEPI’s Mid-P interval similar to ours WinPEPI > Compare2 > A. Data entry Output

35. Ordinal Exposure Break data up into multiple tables, using the least exposed level as baseline each time

36. Dose-response Ordinal Exposure

37. 18.6 Matched Pairs • Cohort matched pairs: each exposed individual uniquely matched to non-exposed individual • Case-control matched pairs: each case uniquely matched to a control • Controls for matching (confounding) factor • Requires special matched-pair analysis

38. Matched-Pairs, Cohort

39. Matched-Pairs, Case-Control

40. Matched-PairsCase-Cntl Example Cases = colon polyps; Controls = no polyps Exposure = low fruit & veg consumption 88% higher risk w/ low fruit/veg consumption

41. Matched-Pairs - Example

42. WinPEPI > PairEtc > A. Input Output

43. Hypothesis TestMatched Pairs A. H0: OR = 1 B. McNemar’s test (z or chi-square) C. P-value from z stat Avoid if fewer than 5 discordancies expected

44. Twins Mortality Example