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

3. For SOC¼1, SBP¼150, and SMK¼1, X¼(SOC,
   SBP, SMK, SOCSBP, SOCSMK)¼(1, 150, 1, 150, 1)
   and
   Model 1 ;P^ðXÞ¼ 1 =ð 1 þexpf½ 1 : 18  0 : 52 ð 1 Þ
   þ 0 : 04 ð 150 Þ 0 : 56 ð 1 Þ
    0 : 033 ð 1  150 Þ 0 : 175 ð 1  1 ފgÞ:
   ¼ 1 =f 1 þexp½ð 1 : 035 ފg
   ¼ 1 =ð 1 þ 2 : 815 Þ
   ¼ 0 : 262


4. ForModel 2, person 1(SOC¼1, SMK¼1, SBP¼150):
   ^PðXÞ¼ 1 =ð 1 þexpf½ 1 : 19  0 : 50 ð 1 Þ
   þ 0 : 01 ð 150 Þ 0 : 42 ð 1 ފgÞ
   ¼ 1 =f 1 þexp½ð 0 : 61 ފg
   ¼ 1 =ð 1 þ 1 : 84 Þ
   ¼ 0 : 352
   ForModel 2, person2(SOC¼0,SMK¼1, SBP¼150):
   ^PðXÞ¼ 1 =ð 1 þexpf½ 1 : 19  0 : 50 ð 0 Þ
   þ 0 : 01 ð 150 Þ 0 : 42 ð 1 ފgÞ
   ¼ 1 =f 1 þexp½ð 0 : 11 ފg
   ¼ 1 =ð 1 þ 1 : 116 Þ
   ¼ 0 : 473


5. The risk computed forModel 1is 0.262, whereas the
   risk computed forModel 2, person 1is 0.352. Note that
   both risks are computed for the same person (i.e.,
   SOC¼1, SMK¼1, SBP¼150), yet they yield
   different values because the models are different. In
   particular,Model 1contains two product terms that
   are not contained in Model 2, and consequently,
   computed risks for a given person can be expected to
   be somewhat different for different models.


6. UsingModel 2results,

RRð1vs: 2 Þ¼

PðSOC¼ 0 ;SMK¼ 1 ;SBP¼ 150 Þ

PðSOC¼ 1 ;SMK¼ 1 ;SBP¼ 150 Þ

¼ 0 : 352 = 0 : 473 ¼ 1 = 1 : 34 ¼ 0 : 744

This estimated risk ratio is less than 1 because the risk

for high social class persons (SOC¼1) is less than the

risk for low social class persons (SOC¼0) in this data

set. More specifically, the risk for low social class

persons is 1.34 times as large as the risk for high social

class persons.

38 1. Introduction to Logistic Regression