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

Chapter 5 1. Conditional ML estimation is the appropriate method
of estimation because the study involves matching.

2. Age and socioeconomic status are missing from the
   printout because they are matching variables and
   have been accounted for in the model by nuisance
   parameters which are not estimated by the
   conditional estimation method.


3. H 0 :bSMK¼0 in the no interaction model (Model I), or
   alternatively,H 0 :OR¼1, where OR denotes the odds
   ratio for the effect of SMK on cervical cancer status,
   adjusted for the other variables (NS and AS) in model I;
   test statistic: Wald statisticZ¼

^bSMK

S^bSMK, which is

approximately normal (0, 1) underH 0 ,or

alternatively,Z^2 is approximately chi square with one

degree of freedom underH 0 ; test

computation:Z¼^10 ::^43613167 ¼ 4 : 53 ; alternatively,Z^2 ¼20.56;

the one‐tailedP‐value is 0.0000/2¼0.0000, which is

highly significant.

4. The point estimate of the odds ratio for the effect of
   SMK on cervical cancer status adjusted for the other
   variables in model I is given by e1.4361¼4.20.
   The 95% interval estimate for the above odds ratio is
   given by

exp^bSMK 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Vard b^SMK

r 

¼expð 1 : 4361  1 : 96  0 : 3617 Þ¼e^0 :^8154 ;e^2 :^0568



¼ð 2 : 26 ; 7 : 82 Þ:

5. Null hypothesis for the likelihood ratio test for the
   effect of SMKNS:H 0 :bSMKNS¼0, wherebSMKNS
   is the coefficient of SMKNS in model II;
   Likelihood ratio statistic: LR¼ 2 lnL^Ið 2 lnL^IIÞ
   whereL^IandL^IIare the maximized likelihood
   functions for models I and II, respectively. This
   statistic has approximately a chi‐square distribution
   with one degree of freedom under the null hypothesis.
   Test computation: LR¼174.97171.46¼3.51. The
   P‐value is less than 0.10 but greater than 0.05, which
   gives borderline significance because we would reject
   the null hypothesis at the 10% level but not at the 5%
   level. Thus, we conclude that the effect of the interaction
   of NS with SMK is of borderline significance.


6. Null hypothesis for the Wald test for the effect
   of SMKNS is the same as that for the likelihood
   ratio test:H 0 :bSMKNS¼0 wherebSMKNSis the
   coefficient of SMKNS in model II;

672 Test Answers