Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Objectives Upon completion of this chapter, the learner should be able to: State or recognize the logistic model for a simple a ...

e. assuming no interaction, state or recognize the null hypothesis for testing the significance of this odds ratio in terms of a ...

Presentation I. Overview Special Cases:  Simple analysis ( ) a b c d  Multiplicative interaction  Controlling several confoun ...

II. Special Case – Simple Analysis X 1 ¼E¼exposure (0, 1) D¼disease (0, 1) E¼ 1 E¼ 0 D¼ 1 ab D¼ 0 cd PðXÞ¼ 1 1 þeðÞaþb^1 E , wh ...

RORE¼ 1 vs:E¼ 0 ¼ R 1 1 R 1 R 0 1 R 0 Substitute PðÞ¼X 1 1 þeðÞaþ~biXi into ROR formula: E¼ 1 :R 1 ¼ 1 1 þeðÞaþ½b^1 ^1 Š ¼ ...

General: RORX 1 ,X 0 ¼e ~ k biðÞX 1 iX 0 i i¼ 1 Simple analysis: k¼1,X¼(X 1 ),bi¼b 1 group 1: X 1 ¼E¼ 1 group 0: X 0 ¼E¼ 0 X 1 ...

E¼ 1 E¼ 0 D¼ 1 ab D¼ (^0) cd RORd ¼e^b¼ad=bc Simple analysis: does not need computer Other special cases: require computer III. ...

Note: above table not for simple analysis. B¼ 1 B¼ 0 A¼ (^1) R 11 R 10 A¼ 0 R 01 R 00 B= 1 A= 1 A= (^0) referent cell B= 0 OR 11 ...

DEFINITION OR 11 = OR 10 × OR 01 no interaction on a multiplicative scale multiplication No interaction: effect of AandB acting ...

As an example of no interaction on a multipli- cative scale, suppose the risksRABin the four- fold table are given byR 11 equal ...

REFERENCE multiplicative interaction vs. additive interaction Epidemiologic Research, Chap. 19 Logistic model variables: X 1 ¼Að ...

H 0 no interaction on a multiplica- tive scale ,H 0 :OR 11 ¼OR 10 OR 01 ,H 0 : OR 11 OR 10 OR 01 ¼ 1 ,H 0 :lne OR 11 OR 10 OR ...

IV. TheE, V, WModel – A General Model Containing a (0, 1) Exposure and Potential Confounders and Effect Modifiers The variables: ...

The generalE, V, WModel single exposure, controlling forC 1 , C 2 ,...,Cp We will assume here that both AGE and CHL are treated ...

E, V, WModel k¼p 1 þp 2 þ 1 ¼no. of variables in model p 1 ¼no. of potential confounders p 2 ¼no. of potential interactions 1 ¼e ...

REFERENCES FOR CHOICE OF Vs AND Ws FROM Cs  Chap. 6: Modeling Strategy Guidelines  Epidemiologic Research, Chap. 21 Assume:Vs ...

Adjusted odds ratio forE¼1 vs. E¼0 givenC 1 ,C 2 ,...,Cpfixed ROR¼exp bþ~ p 2 j¼ 1 djWj !  giterms not in formula  Formula ass ...

 Vs not in OR formula butVsin model, so OR formula controls confounding: logit P(X) = a + bE + Σ gi Vi + E Σ dj Wj No interacti ...

In using this formula, note that to obtain a numerical value for this odds ratio, not only do we need estimates of the coefficie ...

Choice of W values depends on investigator Thisexpressionforthe oddsratio tells usthatwe obtain a different value for the estima ...