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 (SES), lifetime number of partners, and the experimental group. Table 4.9 summarizes study results.

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

b. 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.

Table 4.9 Table for Exercise 4.15 on condom use.

Variables Odds Ratio 95% Confidence Interval Group (Education vs. None) 4.04 (1.17, 13.9)

Gender (Males vs. Females) 1.38 (1.23, 12.88)

SES (High vs. Low) 5.82 (1.87, 18.28)

Lifetime no. of Partners 3.22 (1.08, 11.31)

Source: Rickert et al., Clin. Pediatrics, 205–210 (1992).