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Chapter 18 Cross-Tabulated Counts Part A

Chapter 18 Cross-Tabulated Counts Part A. Chapter 18, Part A:. 18.1 Types of Samples 18.2 Naturalistic and Cohort Samples 18.3 Chi-Square Test of Association. Types of Samples. I. Naturalistic Samples ≡ simple random sample or complete enumeration of the population

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Chapter 18 Cross-Tabulated Counts Part A

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  1. Chapter 18Cross-Tabulated CountsPart A

  2. Chapter 18, Part A: • 18.1 Types of Samples • 18.2 Naturalistic and Cohort Samples • 18.3 Chi-Square Test of Association

  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) relationship via a naturalistic sample? • A population was identified and sampled • Sample classified as CMV+ and CMV− • Disease occurrence (restenosis) was studied and compared in the groups.

  6. Purposive Cohorts (Type II sample) Fixed numbers in exposure groups • How would we 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. • Disease occurrence (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, N = 585 • Cross-classify education level (categorical exposure) and smoking status (categorical disease) • Talley R-by-C table “cross-tab”

  10. Cross-tabulation (cont.) Row margins Total Column margins

  11. Cross-tabulation of counts For uniformity, we will always: put the exposure variable in rows put the disease variable in columns

  12. Exposure / Disease relationship Use conditional proportions to describe relationships between exposure and disease

  13. Conditional ProportionsExposure / Disease Relationship In naturalistic and cohort samples  row percents!

  14. Example Prevalence of smoking by education: Lower education associated with higher prevalence (negative association between education and smoking)

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

  16. Illustration: RRs Note trend

  17. k Levels of Disease Efficacy of Echinacea example. Randomized controlled clinical trial: echinacea vs. placebo in treatment of URI Exposure ≡ Echinacea vs. placebo Disease ≡ severity of illness Source: JAMA 2003, 290(21), 2824-30

  18. Row Percents for Echinacea Example Echinacea group fared slightly worse than placebo group

  19. Chi-Square Test of Association A. H0: no association in population Ha: association in population B. Test statistic

  20. Observed

  21. Expected

  22. Continuity Corrected Chi-Square • Pearson’s (“uncorrected”) chi-square • Yates’ continuity-corrected chi-square:

  23. Chi-Square Hand Calc.

  24. Chi-Square  P-value • X2stat= 13.20 with 4 df • Table E  4 df row bracket chi-square statistic  look up right tail (P-value) regions • Example bracket X2stat between 11.14 (P = .025) and 13.28 (P = .01) • .01 < P < .025

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

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

  27. 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.

  28. Chi-Square, cont. • Supplement chi-squares with descriptive stat. Chi-square statistics do not quantify effects • For 2-by-2 tables, chi-square and z tests produce identical P-values.

  29. Discussion and demo on power and sample size • For estimation • For testing • Power • Sample size

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