Introduction to Categorical Data Analysis

130 LOGISTIC REGRESSION
Table 4.16. Clinical Trial Data for Problem 4.20
Response
Sample
Center Treatment Success Failure Odds Ratio
1 Drug 11 25 1.19
Control 10 27
2 Drug 16 4 1.82
Control 22 10
3 Drug 14 5 4.80
Control 7 12
4 Drug 2 14 2.29
Control 1 16
5 Drug 6 11 ∞
Control 0 12
6 Drug 1 10 ∞
Control 0 10
7 Drug 1 4 2.0
Control 1 8
8 Drug 4 2 0.33
Control 6 1
Source: P. J. Beitler and J. R. Landis, Biometrics, 41: 991–1000, 1985.
b. Conduct the Cochran–Mantel–Haenszel test. Specify the hypotheses, report
the P -value, and interpret.
4.21 In a study designed to evaluate whether an educational program makes sexually
active adolescents more likely to obtain condoms, adolescents were randomly
assigned to two experimental groups. The educational program, involving a
lecture and videotape about transmission of the HIV virus, was provided to one
group but not the other. In logistic regression models, factors observed to influence
a teenager to obtain condoms were gender, socioeconomic status, lifetime
number of partners, and the experimental group. Table 4.17 summarizes study
results.
a. Interpret the odds ratio and the related confidence interval for the effect of
group.
b. Find the parameter estimates for the fitted model, using (1, 0) indicator
variables for the first three predictors. Based on the corresponding confidence
interval for the log odds ratio, determine the standard error for the
group effect.
c. Explain why either the estimate of 1.38 for the odds ratio for gender or the
corresponding confidence interval is incorrect. Show that, if the reported
interval is correct, then 1.38 is actually the log odds ratio, and the estimated
odds ratio equals 3.98.