15.30. In a study of 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 sex, socioeconomic status, lifetime number of partners, and the experimental group. Table 15.26 summarizes results.

(a) Find the parameter estimates for the fitted model, using (1, 0) dummy variables for the first three explanatory variables.

(b) Explain why either the estimate of 1.38 for the odds ratio for sex or the corresponding confidence interval seems incorrect. The confidence interval is based on taking antilogs of endpoints of a confidence interval for the log odds ratio. Show that if the reported confidence interval is correct, then 1.38 is actually the log odds ratio, and the estimated odds ratio equals 3.98.

TABLE 15.26 Variables Group (education versus none) Sex (males versus females) SES (high versus low) Lifetime number of partners Odds Ratio 95% Confidence Interval 4.04 (1.17, 13.9) 1.38 (1.23. 12.88) 5.82 (1.87, 18.28) 3.22 (1.08, 11.31) Source: V. I. Rickert et al., Clinical Pediatrics, Vol. 31 (1992), pp. 205-210.