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

Introduction This introduction to logistic regression describes the rea- sons for the popularity of the logistic model, the mode ...

Objectives Upon completing this chapter, the learner should be able to: Recognize the multivariable problem addressed by logist ...

Presentation FOCUS Form Characteristics Applicability I. The Multivariable Problem E? D E, C 1 , C 2 , C 3? D independent depend ...

Independent variables: X 1 ,X 2 ,...,Xk Xs may beEs,Cs, or combinations The Multivariable Problem X 1 , X 2 ,... , Xk D The anal ...

1 f(z) – ∞ 0 + ∞ 1/2 z f(–∞) = (^1) + e^1 –(–∞) = 1 + e^1 ∞ = 0 f(+∞) = 1 + e–(+∞) 1 = 1 + e^1 – ∞ = 1 Range: 0f(z) 1 0 proba ...

z¼index of combined risk factors 1 threshold – ∞ 0 + ∞ 1/2 S-shape z III. The Logistic Model z¼aþb 1 X 1 þb 2 X 2 þ...þbkXk z = ...

Epidemiologic framework X 1 ,X 2 ,...,Xkmeasured atT 0 Time: T 0 T 1 X 1 , X 2 ,... , Xk D(0,1) P(D¼1|X 1 ,X 2 ,...,Xk) DEFINITI ...

IV. Applying the Logistic Model Formula DEFINITION fit:use data to estimate a,b 1 ,b 2 ,b 3 NOTATION hat¼ˆ parameter() estimator ...

Our fitted model thus becomes P^ðÞX equals 1 over 1 plus e to minus the linear sum3.911 plus 0.652 times CAT plus 0.029 times A ...

 RR (direct method) Conditions for RR (direct method): üFollow-up study üSpecify allXs  RR (indirect method): üOR üAssumptions ...

üCase-control üCross-sectional Breslow and Day (1981) Prentice and Pike (1979) Robust conditions Case-control studies Robust con ...

Simple Analysis E¼ 1 E¼ 0 D¼ 1 ab D¼ 0 cd Risk: only in follow-up OR: case-control or cross-sectional ORc¼ad=bc Case-control and ...

Case-control or cross-sectional studies: P(D E) üP(E|D) 6 ¼risk P(ˆ X)= 1+e 1 estimates –(aˆ+ bˆiXi) Case control: aˆ ⇒ P (ˆ X) ...

VI. Risk Ratios vs. Odds Ratios OR vs. ? follow-up study RR However, according to mathematical theory, the value provided for th ...

Control variables unspecified: ORcdirectly RRcindirectly providedORcRRc Rare disease OR RR (or PR) Yes pp No p Other Other p Lo ...

Logit logit PðXÞ¼lne PðÞX 1 PðXÞ  ; where PðXÞ¼ 1 1 þeðaþ~biXiÞ (1) P(X) (2) 1P(X) (3) PðXÞ 1 PðXÞ (4) lne PðXÞ 1 PðXÞ  ...

1 PðXÞ¼ 1  1 1 þeðÞaþ~biXi ¼ eðÞaþ~biXi 1 þeðÞaþ~biXi P(X) 1 – P(X) 1 1+e–(a+^ biXi) 1+e–(a+^ biXi) e–(a+^ biXi) = ¼e
aþ~ ...

odds : P(X) P 1 – P(X)^1 – P vs. describes risk in logistic model for individual X logit PðXÞ¼lne PðXÞ 1 PðXÞ  ¼log odds for ...

aü bi? X 1 ;X 2 fixed ;...;Xi; varies ...;Xk fixed A second interpretation is thatagives thelogof thebackground,orbaseline, odds ...

logit P(X)¼aþ~biXi i¼L: bL¼¶ln (odds) when¶XL¼1, otherXs fixed The first expression below this model shows that when CAT¼1, AGE¼ ...