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

Answers to
Practice
Exercises

1. F: cases are selected first, and controls are matched to
   cases.


2. F: the age distribution for unexposed persons is con-
   strained to be the same as for exposed persons.


3. T


4. T


5. F: matching is not needed to obtain a valid estimate of
   effect.


6. F: when in doubt, matching may not lead to increased
   precision; it is safe to match only if the potential
   matching factors are strong risk factors expected to
   be confounders in the data.


7. T


8. F: the Mantel–Haenszel chi-square statistic is equal to
   McNemar’s test statistic.


9. F: the number of strata equals the number of matched
   sets.


10. F: the computed value of McNemar’s test statistic is
    6.67; the MOR is 2.


11. logit PðXÞ¼aþbEþ~

209

i¼ 1

g 1 iV 1 i,

where theV 1 idenote dummy variables indicating the

different matched pairs (strata).

12. Using the output, the estimated odds ratio is exp
    (0.693), which equals 1.9997. TheMOR is computedd
    asX/Yequals 40/20¼2. Thus, the estimate obtained
    using conditional logistic regression is equal to the
    MOR.d


13. The Wald statistic, which is aZstatistic, is computed
    as 0.693/0.274, which equals 2.5292. This is significant
    at the 0.01 level of significance, i.e.,Pis less than 0.01.
    The squared Wald statistic, which has a chi-square
    distribution with one degree of freedom under the
    null hypothesis of no effect, is computed to be 6.40.
    The McNemar chi-square statistic is 6.67, which is
    quite similar to the Wald result, though not exactly
    the same.


14. The 95% confidence interval for the odds ratio is given
    by the formula exp



^b 1 : 96

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

vard ^b

r 

,

which is computed to be

exp (0.6931.960.274)¼exp (0.6930.53704),

which equals (e0.15596,e1.23004)¼(1.17, 3.42).

This confidence interval around the point estimate of

2 indicates that the point estimate is somewhat unsta-

ble. In particular, the lower limit is close to the null

value of 1, whereas the upper limit is close to 4. Note

also that the confidence interval does not include the

426 11. Analysis of Matched Data Using Logistic Regression