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

Introduction In this chapter, the standard logistic model is extended to handle outcome variables that have more than two cate- ...

Objectives Upon completing this chapter, the learner should be able to: State or recognize the difference between nominal and o ...

Presentation I. Overview Modeling outcomes with more than two levels FOCUS Examples of multilevel outcomes: Absent, mild, moder ...

Disadvantage of dichotomizing: Loss of detail (e.g., mild vs. none? moderate vs. mild?) Alternate approach: Use model for a poly ...

II. Polytomous Logistic Regression: An Example with Three Categories ? E D When modeling a multilevel outcome variable, the epid ...

Outcome categories: A B C D Reference (arbitrary choice) Then compare: A vs. C, B vs. C, and D vs. C Dichotomous vs. polytomous ...

Odds of disease: a ratio of probabilities Dichotomous outcome: odds¼ PðD¼ 1 Þ 1 PðD¼ 1 Þ ¼ PðD¼ 1 Þ PðD¼ 0 Þ Polytomous outcome ...

Model for three categories, one predictor (X 1 = AGEGP): ln PðD¼ 1 jX 1 Þ PðD¼ 0 jX 1 Þ  ¼a 1 þb 11 X 1 ln PðD¼ 2 jX 1 Þ PðD¼ ...

Two odds ratios: OR 1 (category 1 vs. category 0) (Adenosquamous vs. Adenocarcinoma) OR 2 (category 2 vs. category 0) (Other vs. ...

General case for one predictor ORg¼expbg 1 X** 1 X* 1 hi ;where g¼ 1 ; 2 Computer output for polytomous model: Is output list ...

The equation for the estimated log odds of Other (category 2) vs. Adenocarcinoma (cate- gory 0) is negative 1.4534 plus 0.4256 t ...

Interpretation of alphas Log odds where allXs set to 0. Not informative if sampling done by outcome (i.e., “disease”) status. IV ...

Likelihood ratio test Assess significance ofX 1 2 bs tested at the same time + 2 degrees of freedom The 95% confidence interval ...

Wald test bfor single outcome level tested For two levels: H 0 :b 11 ¼ 0 H 0 :b 21 ¼ 0 Z¼ ^bg 1 s^bg 1 Nð 0 ; 1 Þ In the endome ...

Conclusion: Is AGEGP significant? ) Yes: Adenocarcinoma vs. Adenosquamous ) No: Other vs. Adenosquamous. Decision: Retain or dro ...

Recall that AGEGP is coded as 0 for aged 50–64 or 1 for aged 65–79. Both estrogen use and smoking status are also coded as dicho ...

Suppose we are interested in the effect of AGEGP, controlling for the effects of ESTRO- GEN and SMOKING. The odds ratio for the ...

The 95% confidence intervals are calculated using the standard errors of the parameter esti- mates from the three-variable model ...

Adding interaction terms D¼(0, 1, 2) Two independent variables (X 1 ,X 2 ) log odds¼agþbg 1 X 1 þbg 2 X 2 þbg 3 X 1 X 2 , where ...

Extending model to G outcomes Outcome variable has G levels: (0, 1, 2,...,G1) ln PðD¼gjXÞ PðD¼ 0 jXÞ  ¼agþ~ k i¼ 1 bgiXi; whe ...