WHI Data. 2-by-2 Table. Data conditions. Illustrative Example: WHI Trial. Sample Proportions. Chapter 17 Comparing Two Proportions

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1 Chpter 7 6/7/009 Chpter 7 Comprig Two Proportios Dt coditios Biry respose Biry expltory fctor vi two idepedet groups: Group = exposed Group = oexposed Nottio: Jue 09 3 Smple Proportios Smple proportio (verge risk), group : p ˆ = Smple proportio (verge risk), group : p ˆ = 4 Rdom Assigmet Illustrtive Exmple: WHI Tril Group = Group = 80 Estroge Tretmet Plcebo Compre risks of idex outcome* *Deth, MI, brest ccer, etc. 5 -by- Tble Successes Filures Totl Group b Group b Totl m m N p ˆ = p ˆ = 6 WHI Dt D+ D Totl E E Totl = = = = Bsic Biostt

2 Chpter 7 6/7/ Hypothesis Test A. H 0 : p = p (equivletly H 0 : RR = ) B. Test sttistic (three optios) z (lrge smples) Chi-squre (lrge smples, ext chpter) Fisher s exct (y size smple) C. P-vlue D. Iterpret evidece gist the Fisher s Exct Test A. Hypotheses. H 0 : p = p vs. H : p p [two-sided] OR H : p > p [leftsided] OR H : p < p [right-sided] B. Test sttistic. Noe, per se; reiterte dt C. P-vlue. Use WiPepi > Compre.exe > Progrm A D. Iterprettio: Level of evidece gist clim of H 0 H Exmple: Fisher s Test Coloic ecrosis. The icidece of coloic ecrosis i exposed group is of 7. The icidece i o-exposed group is 0 of 86. Ask: Is this differece sttisticlly sigifict? A.Hypothesis sttemets. Uder the ull hypothesis, there is o differece i risks i the two popultios. Thus: H 0 : p = p H : p > p (oe-sided) or H : p p (two-sided) 0 Fisher s Test, Exmple B. Test sttistic oe per se, other th dt (right) D+ D E+ 5 E 0 86 C. P-vlue. Use WiPepi > Compre.exe > A. D. Iterpret. The P-vlue of.04 strog ( sigifict ) evidece gist H Proportio Rtio (Reltive Risk) Reltive risk is used to refer to the RATIO of y two public helth proportios Sice icidece proportios represet verge risks, the this rtio is lso clled risk rtio: R ˆR = Exmple: RR (WHI Dt) + Totl Estroge Estroge = = ; = = ˆ RR = = = Bsic Biostt

3 Chpter 7 6/7/009 Exmple: RR (WHI Dt) The RR is risk multiplier, e.g., the RR estimte of.5 suggests the risk i the exposed group is.5 times tht of the oexposed group Whe p = p, RR =. Thus, the bselie RR, idictig o ssocitio, is to get the percet chge i risk, subtrct from the RR estimte: RR =.5 = 0.5 = 5% chge i risk ( α)00% CI for the RR e where SE l RR ˆ l RR ˆ z ± α = SE l RR ˆ l turl log, bse e + See pp for full discussio % CI for RR, WHI D+ D Totl E E WiPepi > Compre.exe > Progrm B D+ D Totl E E l RR ˆ = l(.483) = 0.38 SE ˆ = l RR 75 For 90% cofidece, z = ± (.645)(0.0590) 0.38± ,0.36 e = e = e = (.05,.5) = See prior slide for hd clcultios Systemtic Error CIs d P-vlues ddress rdom error oly I observtiol studies, systemtic errors re more importt th rdom error Cosider three types of systemtic errors: Cofoudig Iformtio bis Selectio bis 8 Cofoudig Cofoudig = mixig together of the effects of the expltory vrible with the extreous fctors. Exmple: WHI tril foud 5% icrese i risk i estroge exposed group. Erlier observtiol studies foud 40% lower i estroge exposed groups. Plusible expltio: Cofoudig by extreous lifestyles fctors i observtiol studies 9 Bsic Biostt 3

4 Chpter 7 6/7/009 Iformtio Bis Iformtio bis - mismesuremet (misclssifictio) ledig to overestimtio or uderestimtio i risk Nodifferetil misclssifictio (occurs to the sme extet i the groups) teds to bis results towrd the ull or hve o effect Differetil misclssifictio (oe groups experieces greter degree of misclssifictio th the other) bis c be i either directio. Nodifferetil & Differetil Misclssifictio - Exmples 30 3 Selectio Bis Selectio bis systemtic error relted to mer i which study prticipts re selected Exmple. If we shoot rrow ito the brod side of br d drw bull s-eye where it hd lded, hve we idetified ythig tht is ordom? Smple Size & Power for Comprig Proportios Three pproches:. eeded to estimte give effect with mrgi of error m (ot covered i Ch 7). eeded to test H 0 t give α d power 3. Power of test of H 0 uder give coditios 3 33 Smple Size Requiremets for Comprig Proportios Depeds o: r smple size rtio = / β power (cceptble type II error rte) α sigificce level (type I error rte) p expected proportio, group p expected proportio i group, or expected effect size (e.g., RR) 34 Formuls o pp (quite complex) I prctice use tbles or (better yet) computer progrms WiPEPI > Compre.exe > Smple size Clcultio 35 Bsic Biostt 4

5 Chpter 7 6/7/009 WiPepi > Compre > S 36 Bsic Biostt 5