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

10. Use the model in Question 9 to obtain the odds ratio
    for the mild, severe, or critical stage of disease (i.e.,
    D  1)] comparing hypertensive smokers vs. nonhy-
    pertensive nonsmokers, controlling for AGE and
    GENDER.


11. Use the model in Question 9 to obtain the odds ratio
    for critical disease only (D 3) comparing hyperten-
    sive smokers vs. nonhypertensive nonsmokers,
    controlling for AGE and GENDER. Compare this
    odds ratio to that obtained for Question 10.


12. Use the model in Question 9 to obtain the odds ratio for
    mild or no disease (D < 2) comparing hypertensive
    smokers vs. nonhypertensive nonsmokers, controlling
    for AGE and GENDER.

Answers to
Practice
Exercises

1. Ordinal model

ln

PðDgjXÞ

PðD<gjXÞ



¼agþb 1 VIRUSþb 2 AIDS

þb 3 COMPLIANCEþb 4 AGE

þb 5 GENDERþb 6 AIDSCOMP;

whereg¼1, 2

2. Ordinal fitted model

ln^ PðD^2 jXÞ

PðD< 2 jXÞ



¼ 2 : 98 þ 1 : 13 VIRUSþ 0 : 82 AIDS

þ 0 : 38 COMPLIANCEþ 0 : 04 AGE

þ 0 : 35 GENDERþ 0 : 31 AIDSCOMP;

ln^ PðD^1 jXÞ

PðD< 1 jXÞ



¼ 1 : 65 þ 1 : 13 VIRUSþ 0 : 82 AIDS

þ 0 : 38 COMPLIANCEþ 0 : 04 AGE

þ 0 : 35 GENDERþ 0 : 31 AIDSCOMP:

3. dOR¼expð 0 : 35 Þ¼ 1 : 42


4. dOR¼expð 0 : 35 Þ¼ 1 : 42


5. Estimated odds¼exp[2.98þ20(0.04)]¼0.11


6. Estimated odds¼exp[1.65þ20(0.04)]¼0.43


7. Estimated odds¼exp[1.65þ20(0.04)þ0.35]¼0.61


8. Estimated odds ratios for noncompliant (COMPLI-
   ANCE¼1) vs. compliant (COMPLIANCE¼0) subjects:
   For AIDS¼0: exp(0.38)¼1.46
   For AIDS¼1: exp(0.38þ0.31)¼1.99

488 13. Ordinal Logistic Regression