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

null value, which supports the statistical significance

found in Exercise 13.

15. 
    

    If unconditional ML estimation had been used, the
    odds ratio estimate would be higher (i.e., an overesti-
    mate) than the estimate obtained using conditional
    ML estimation. In particular, because the study
    involved pair-matching, the unconditional odds ratio
    is the square of the conditional odds ratio estimate.
    Thus, for this dataset, the conditional estimate is
    given byMOR equal to 2, whereas the unconditionald
    estimate is given by the square of 2 or 4. The correct
    estimate is 2, not 4.

    
    


16. 
    

logit PðXÞ¼aþbCONþ~

99

i¼ 1

g 1 iV 1 iþg 21 NPþg 22 ASCM

þg 23 PARþdCONPAR;

where theV 1 iare 99 dummy variables indicating the

100 matching strata, with each stratum containing

three observations.

17. RORd ¼exp ^bþ^dPAR



.

18. A recommended strategy for model building involves
    first testing for the significance of the interaction term
    in the starting model given in Exercise 16. If this test is
    significant, then the final model must contain the
    interaction term, the main effect of PAR (from the
    Hierarchy Principle), and the 99 dummy variables
    for matching. The other two variables NP and ASCM
    may be dropped as nonconfounders if the odds ratio
    given by Exercise 17 does not meaningfully change
    when either or both variables are removed from the
    model. If the interaction test is not significant, then
    the reduced (no interaction) model is given by the
    expression

logit PðXÞ¼aþbCONþ~

99

i¼ 1

g 1 iV 1 iþg 21 NP

þg 22 ASCMþg 23 PAR:

Using this reduced model, the odds ratio formula is

given by exp(b), wherebis the coefficient of the CON

variable. The final model must contain the 99 dummy

variables which incorporate the matching into the

model. However, NP, ASCM, and/or PAR may be

dropped as nonconfounders if the odds ratio exp(b)

does not change when one or more of these three

variables are dropped from the model. Finally, preci-

sion of the estimate needs to be considered by

Answers to Practice Exercises 427