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

25. For a 40-year-old male smoker with CHOL¼200 and
    OCC¼1, we have
    X¼ðAGE¼ 40 ;SMK¼ 1 ;SEX¼ 1 ;CHOL
    ¼ 200 ;OCC¼ 1 Þ;

assuming that SMK and SEX are coded as SMK¼1if

smoke, 0 otherwise, and SEX¼1 if male, 0 if female, and

^PðXÞ¼ 1 =ð 1 þexpf½ 4 : 32 þ 0 : 0274 ð 40 Þþ 0 : 5859 ð 1 Þ

þ 1 : 1523 ð 1 Þþ 0 : 0087 ð 200 Þ 0 : 5309 ð 1 ފgÞ

¼ 1 =f 1 þexp½ð 0 : 2767 ފg

¼ 1 =ð 1 þ 1 : 319 Þ

¼ 0 : 431 :

26. For a 40-year-old malenonsmoker with CHOL¼ 200
    and OCC¼1,X¼(AGE¼40, SMK¼0, SEX¼1,
    CHOL¼200, OCC¼1)
    and
    ^PðXÞ¼ 1 =ð 1 þexpf½ 4 : 32 þ 0 : 0274 ð 40 Þþ 0 : 5859 ð 0 Þ
    þ 1 : 1523 ð 1 Þþ 0 : 0087 ð 200 Þ 0 : 5309 ð 1 ފgÞ
    ¼ 1 =f 1 þexp½ð 0 : 8626 ފg
    ¼ 1 =ð 1 þ 2 : 369 Þ
    ¼ 0 : 297


27. The RR is estimated as follows:

P^ðAGE¼ 40 ;SMK¼ 1 ;SEX¼ 1 ;CHOL¼ 200 ;OCC¼ 1 Þ

P^ðAGE¼ 40 ;SMK¼ 0 ;SEX¼ 1 ;CHOL¼ 200 ;OCC¼ 1 Þ

¼ 0 : 431 = 0 : 297

¼ 1 : 45

This estimate can be interpreted to say smokers have

1.45 times as high a risk for getting hypertension as

nonsmokers, controlling for age, sex, cholesterol level,

and occupation.

28. If the study design had been case-control or cross-
    sectional, the risk ratio computation of Question 27
    would be inappropriate because a risk or risk ratio
    cannot be directly estimated by using a logistic model
    unless the study design is follow-up. More specifically,
    the constant termacannot be estimated from case-
    control or cross-sectional studies.


29. OR (SMK controlling for AGE, SEX, CHOL, OCC)d

¼e

^b

whereb^¼ 0 :5859 is the coefficient of SMK in the

fitted model

¼expð 0 : 5859 Þ

¼ 1 : 80

668 Test Answers