Question: “Large Trial Find AIDS Vaccine Fails to Stop Infection”, by Andrew Pollack with Lawrence K. Altman, New York Times, February 24, 2003, p. A 1.

“The first large-scale trial of an AIDS vaccine has ended with disappointing results. The vaccine, Aidsvax, was developed by the biotechnology company VaxGen. The company had hoped to have the vaccine approved for use by some time in 2004. The experiment involved 5400 participants, of whom 5100 were sexually active gay men and 300 were women judged to be at high risk of infection. About 2/3 were assigned to the treatment group, and received seven vaccinations over a three year period. The control group received placebo injections.”

Using the information below, answer the following questions.

All Subjects

Total receiving Placebo: 1,679
Total receiving Vaccine: 3,330
Infected at End of Trial - Placebo: 98
Infected at End of Trial - Vaccine: 191
Percentage Who Became Infected - Placebo: 5.8%
Percentage Who Became Infected - Vaccine: 5.7%

a. Estimate the difference in the proportion of infected subjects between those on the placebo and those on the vaccine with a 95% confidence interval. Note, z* = 1.96 for a 95% confidence interval.

b. Using the confidence interval in part (a), test that there is a difference in the proportion of infected subjects between those who receive placebo and those who receive the vaccine . State the null and alternative hypotheses, decision and conclusion in the context of the problem.

c. Are the assumptions for the confidence interval in part (a) satisfied? Explain.

d. Compute the sample size needed to determine if the vaccine and placebo groups were statistically difference with 80% power (with n₁ = n₂), if the true proportion infected who receive placebo and who receive vaccine were based on this study (0.058 and 0.057). Explain why you need such large sample sizes to determine that the proportion infected on vaccine is statistically different than the proportion infected on placebo.

“A controversy ensued, however, when the VaxGen reported that it had found significant effects in certain subgroups of the 500 minority participants. Among African-Americans and Asians, the treated participants had a 3.7% infection rate compared with 9.9% for the controls.”

e. Using the information below, estimate the difference in the proportion of infected subjects between those on the placebo and those on the vaccine in this subpopulation with a 95% confidence interval. Does the interval indicate that there is a difference in the proportion infected between the two treatment groups?

Black, Asian, other combined
Total receiving Placebo: 171
Total receiving Vaccine: 327
Infected at End of Trial - Placebo: 17
Infected at End of Trial - Vaccine: 12
Percentage Who Became Infected - Placebo: 9.9%
Percentage Who Became Infected - Vaccine: 3.7%

f. This test can also be done within a 2x2 table using a Chi-Square test.

i. Make a table for the data for the Black and Asian subpopulation and compute the chi-square test statistic.

ii. What is the critical value for the test at the 0.05 significant level? (i.e. value of test statistic such that any value falling above the critical value would result in rejecting the null hypothesis). Use the website http://www.stat.sc.edu/~west/applets/chisqdemo.html

iii. What is the conclusion of the test? How does the conclusion compare with the conclusion based on the confidence interval?