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

Alternative form (w/o summation signs): Logit P(X) = a^ +^ b 1 E 1 +^ b 2 E 2 + ... +^ bqEq + g 1 V 1 + g 2 V 2 + ... + gp 1 Vp ...

Option A: Overall (chunk) LR test for interaction; then “subchunk” LR tests for EWs and EEs; then Vs; finally Es EXAMPLE MRSA ex ...

EXAMPLE Model A Output: 2 2ln L¼279.317 Analysis of maximum likelihood estimates Es Vs LR = –2 1n LR(A) – (–2 1n LF) ⇒ No–intera ...

EXAMPLE (continued) Options A and B(continued) Confounding: DoesOR meaningfully change^ when AGE and/or GENDER are dropped? GS m ...

EXAMPLE (continued) Options A and B(continued) However:^b 1 and^b 2 likely differ for each model Estimate Regression Coefficient ...

EXAMPLE (continued) Options A and B(continued) Cannot drop PREVHOSP or PAMU Using Options A or B: No -Interaction Model A is bes ...

EXAMPLE (continued) Option A: Overall (chunk) interaction, then, in order.EWs,EEs, Vs, andEs Option B: AssessEWs first, then, in ...

EXAMPLE (continued) Option C(continued) Must specifyX*andX: X*¼ðE 1 *¼ 1 ; yes E 2 *¼yes 1 Þ vs:X¼ðE 1 ¼ 0 ; no E 2 ¼ 0 no Þ ORG ...

EXAMPLE (continued) Option C(continued) Estimated Regression Coefficients and ORs Model: I(GS) II III IV Vsin model AGE, GEN AGE ...

EXAMPLE (continued) Option C(continued) ⇓ Suppose decide only GS(B) control confounding Model at this point contains E 1 , E 2 , ...

EXAMPLE (continued) Option C(continued) OR formula for Models I and III: OR¼exp½b 1 ðE 1 *E 1 Þþb 2 ðE 2 *E 2 Þ þd*ðE 1 *E 2 * ...

EXAMPLE (continued) Option C(continued) Model III* Output Analysis of maximum likelihood estimates Param DF Estimate Std Err Chi ...

EXAMPLE (continued) Best Model Summary: Options A, B, C Options A and B (same result): ModelA: contains PREVHOSP, PAMU, AGE, and ...

Modeling Strategy Summary: Several Es Step 1: Define initial model (above formula) Step 2: Assess interaction Option A: Overall ...

General Model: OnlyEs andEEs Logit PðXÞ¼aþ~ q i¼ 1 biEiþ~ q i¼ 1 ~ i^0 ¼ 1 i 6 ¼i^0 q d*ii 0 EiEi 0 Modeling Strategy: All Es, n ...

EXAMPLE (continued) Diagram 2)PREVHOSP and PAMU independent risk factors; AGE and GENDER confounders Diagram 2 appropriate)initi ...

III. Screening Variables Scenario: Logistic Model E(0,1) vs.D(0,1) C 1 ,C 2 ,...,Cp “large”p Desired initial model: Logit PðXÞ¼a ...

Backward forCs, then forward forECj:  Start withEand allCj, j¼1,...,p  Sequentially drop nonsignif.Cj  Sequentially addECj ...

Drawbacks of screening: No simultaneous assessment of allEs andCs. No guarantee final model contains all “relevant” variables ...

Answers: Q1. Yes:  Statistical testing only (questionable)  Does not consider confounding or interaction Assess confounding wi ...