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IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #27

IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #27. Comparison of Observational Studies. Statistical Analyses - 1 (Cross-Sectional & Case-Control). Prevalence = proportion of cases p a = a/c 1 = exposed to risk factor p b = b/c 2 = not exposed to risk factor.

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IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #27

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  1. IE 552 Mechanics of Musculoskeletal System Dr. Andris Freivalds Class #27 IE 552

  2. Comparison of Observational Studies IE 552

  3. Statistical Analyses - 1 (Cross-Sectional & Case-Control) • Prevalence = proportion of cases • pa = a/c1 = exposed to risk factor • pb = b/c2 = not exposed to risk factor IE 552

  4. Statistical Analyses - 2 • Prevalence difference = pa -pb • Confidence interval = pa –pb + zα/2[pa(1- pa)/c1 + [pb(1- pb)/c2]½ IE 552

  5. Normal Distribution IE 552

  6. Statistical Analyses - Odds Ratio • OR = ratio of prevalence odds for exposed ratio of prevalence odds for unexposed • OR = pa/(1- pa) = ad/bc pb/(1- pb) IE 552

  7. Contingency Table in a Case-Control Study IE 552

  8. IE 552

  9. Statistical Analyses - Odds Ratio • Confidence interval = OR e(+zα/2 SE) • SE = (1/a + 1/b + 1/c + 1/d)½ IE 552

  10. Statistical Analyses – Chi Square • χ2 = ∑(oi-ei)2/ei • o = observed values • e = expected values • ea = c1/n x r1/n x n = c1r1/n IE 552

  11. Statistical Analyses – Chi Square • Compare to χ2α/2 with • degrees of freedom = (r-1)(c-1) • χ2 = n(ad – bc)2 c1c2r1r2 IE 552

  12. Chi-Square Critical Values IE 552

  13. Statistical Analyses (Cohort Studies) • Relative Risk or Risk Ratio (RR) • Relates risk for exposed compared to unexposed groups • Rexp = # exposed incurring injury = a/(a+c) all exposed individuals • Runexp = b/(b+d) • RR = Rexp/Runexp = a(b+d) b(a+c) IE 552

  14. Contingency Table in a Cohort Study IE 552

  15. IE 552

  16. Statistical Analyses - 2 • RR confidence interval = RR e(+zα/2 SE) • SE = │ c + d │½ │ a(a+c) b(b+d)│ • Attributable Risk (AR) = (RR -1)/RR IE 552

  17. RR vs. OR • Case-control studies • RR?? but disease didn’t cause risk • OR better, snapshot in time • Cohort studies • Both measure the association between exposure and risk • OR = ad/bc ≈ a(b+d)/b(a+c) = RR • If a & b are small wrt c & d IE 552

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