A collaborative group of investigators conducted a randomized trial of the efficacy of an human papillomavirus (HPV) vaccine against the development of anal intraepithelial neoplasia (AIN, a precursor of anal cancer) in gay men.45 Participants were assigned to receive three doses of a quadrivalent vaccine (directed against HPV types 6, 11, 16, and 18) or a placebo, and were examined for the presence of AIN approximately three years following receipt of vaccine or placebo.

Among men in the treatment arm of the trial, there were 74 cases of AIN in 569.0 man-years of follow-up. The corresponding numbers in the placebo group were 103 cases in 588.4 man-years.

a. What was the efficacy of the vaccine against the presence of AIN?

b. The tumors of about 60% of the cases of AIN among participants in the trial contained DNA from HPV 6, 11, 16, or 18, whereas the other cases had DNA of other HPV types present. Had the study outcome been restricted to AIN in which HPV 6, 11, 16, or 18 had been present, would you expect the estimate of efficacy to have been the same, higher, or lower than that calculated in (a)?

Explain. (Assume that the vaccine used had no impact on the occurrence of AIN from HPV types other than 6, 11, 16, and 18.)