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

in the subject-specific baseline risk, the population

averaging for a marginal odds ratio attenuates (i.e.,

weakens) the effect of the individual level odds ratio.

12. Subject 1 and Subject 2 have the same distribution of
    exposure: 100 exposed out of 200 observations.Note.
    In a case-control setting we would consider that there
    is a different distribution of exposure whereD¼0.


13. With one observation per subject, an odds ratio is
    estimating a population-averaged (marginal) odds
    ratio since in that setting observations must be pooled
    over subjects.


14. The baseline risk for Subject 1 is 0.25, whereas the
    baseline risk for Subject 2 is 0.10, indicating that there
    is heterogeneity of the baseline risk between subjects.


15. The risk ratio is 2.0 for both Subject 1 and Subject
    2 separately and the risk ratio is also 2.0 for the pooled
    data. In contrast to the odds ratio, if the distribution
    of exposure is the same across subjects, then pooling
    the data does not attenuate the risk ratio in the pres-
    ence of heterogeneity of the baseline risk.

598 16. Other Approaches for Analysis of Correlated Data