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Chapter 17 Comparing Two Proportions

Chapter 17 Comparing Two Proportions. In Chapter 17:. 17.1 Data [17.2 Risk Difference] [17.3 Hypothesis Test] 17.4 Risk Ratio [17.5 Systematic Sources of Error] [17.6 Power and Sample Size]. Data conditions. Binary response variables (“success/failure”) Binary explanatory variable

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Chapter 17 Comparing Two Proportions

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  1. Chapter 17Comparing Two Proportions

  2. In Chapter 17: 17.1 Data [17.2 Risk Difference] [17.3 Hypothesis Test] 17.4 Risk Ratio [17.5 Systematic Sources of Error] [17.6 Power and Sample Size]

  3. Data conditions • Binary response variables (“success/failure”) • Binary explanatory variable • Notation:

  4. Sample Proportions Incidence proportion, exposed group: Incidence proportion, non-exposed group: Incidence proportion ≡ average risk

  5. Example: WHI Estrogen Trial Group 1 n1 = 8506 Estrogen Treatment Compare risks of index disease Random Assignment Group 2 n2 = 8102 Placebo

  6. 2-by-2 Table Risk, non-exposed Risk, exposed

  7. WHI Data Compare these risks

  8. §17.4 Proportion Ratio (Relative Risk) • Compare incidences from the two groups in form of a RATIO • Quantifies effect of the exposure in relative terms Relative Risk Estimator (“RR hat”) Relative Risk Parameter

  9. Example: RR (WHI Data)

  10. Interpretation • When p1 = p2, RR = 1  indicating “no association” • RR > 1  positive association • RR < 1  negative association • The RR indicates how much the exposure multiplies the risk over the baseline risk of the non-exposed group • RR of 1.15 suggests risk in exposed group is “1.15 times” that of non-exposed group • Baseline RR is 1! • Thus, an RR of 1.15 is 0.15 (15%) above the baseline

  11. Confidence Interval for the RR To derive information about the precision of the estimate, calculate a (1– α)100% CI for the RR with this formula: ln ≡ natural log, base e

  12. 90% CI for RR, WHI

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