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

The printout given below comes from a matched case-

control study of 313 women in Sydney, Australia (Brock

et al., 1988), to assess the etiologic role of sexual behaviors

and dietary factors on the development of cervical cancer.

Matching was done on age and socioeconomic status.

The outcome variable is cervical cancer status (yes/no),

and the independent variables considered here (all coded

as 1, 0) are vitamin C intake (VITC, high/low), the number

of lifetimesexual partners (NSEX, high/low), age at first

intercourse (SEXAGE, old/young), oral contraceptive pill

use (PILLM ever/never), and smoking status (CSMOK,

ever/never).

Variable Coefficient S.E. eCoeff P 95% Conf.Int.foreCoeff

VITC 0.24411 0.14254 0.7834 .086 0.5924 1.0359

NSEX 0.71902 0.16848 2.0524 .000 1.4752 2.8555

SEXAGE 0.19914 0.25203 0.8194 .426 0.5017 1.3383

PILLM 0.39447 0.19004 1.4836 .037 1.0222 2.1532

CSMOK 1.59663 0.36180 4.9364 .000 2.4290 10.0318

MAX LOG LIKELIHOOD¼73.5088

Using the above printout, answer the following questions:

13. What method of estimation should have been used to
    fit the logistic model for this data set? Explain.


14. Why don’t the variables age and socioeconomic status
    appear in the printout?


15. Describe how to compute the odds ratio for the effect
    of pill use in terms of an estimated regression coeffi-
    cient in the model. Interpret the meaning of this odds
    ratio.


16. What odds ratio is described by the value
    eto0.24411? Interpret this odds ratio.


17. State two alternative ways to describe the null hypoth-
    esis appropriate for testing whether the odds ratio
    described in Question 16 is significant.


18. What is the 95% confidence interval for the odds ratio
    described in Question 16, and what parameter is being
    estimated by this interval?


19. TheP-values given in the table correspond to Wald
    test statistics for each variable adjusted for the others
    in the model. The appropriateZstatistic is computed
    by dividing the estimated coefficient by its standard
    error. What is theZstatistic corresponding to the
    P-value of .086 for the variable VITC?


20. For what purpose is the quantity denoted as MAX
    LOG LIKELIHOOD used?

126 4. Maximum Likelihood Techniques: An Overview