HIV in sub-Saharan Africa. In July 2008 the US National Institutes of Health ann

Question

HIV in sub-Saharan Africa. In July 2008 the US National Institutes of Health announced
that it was stopping a clinical study early because of unexpected results. The study
population consisted of HIV-infected women in sub-Saharan Africa who had been given single
dose Nevaripine (a treatment for HIV) while giving birth, to prevent transmission of HIV to the
infant. The study was a randomized comparison of continued treatment of a woman (after successful
childbirth) with Nevaripine vs. Lopinavir, a second drug used to treat HIV. 240 women
participated in the study; 120 were randomized to each of the two treatments. Twenty-four weeks
after starting the study treatment, each woman was tested to determine if the HIV infection was
becoming worse (an outcome called virologic failure). Twenty-six of the 120 women treated with
Nevaripine experienced virologic failure, while 10 of the 120 women treated with the other drug
experienced virologic failure.59
(a) Create a two-way table presenting the results of this study.
(b) State appropriate hypotheses to test for independence of treatment and virologic failure.
(c) Complete the hypothesis test and state an appropriate conclusion. (Reminder: Verify any
necessary conditions for the test.)

Explanation / Answer

a)

b)

H0:Assumes that there is no association between the two variables.
HA:Assumes that there is an association between the two variables.

c) Random assignment was used, so the observations in each group are independent. A key assumption of the chi square test of independence is that each subject contributes data to only one cell. Therefore the sum of all cell frequencies in the table must be the same as the number of subjects in the experiment. This is satisfied. Each cell has atleast a count of 5

Degree of freedom, DF = (r - 1) * (c - 1)
where r is the number of levels for one catagorical variable, and c is the number of levels for the other categorical variable.

First we have to calculate the expected value of the two nominal variables.

Expected frequencies. The expected frequency counts are computed separately for each level of one categorical variable at each level of the other categorical variable. Compute r * c expected frequencies, according to the following formula.

Er,c = (nr * nc) / n

where Er,c is the expected frequency count for level r of Variable A and level c of Variable B, nris the total number of sample observations at level r of Variable A, nc is the total number of sample observations at level c of Variable B, and n is the total sample size.

Test statistic. The test statistic is a chi-square random variable (2) defined by the following equation.

2 = [ (Or,c - Er,c)2 / Er,c ]
2 = ((26-18)2/18) + ((94-102)2/102) + ((10-18)2/18) + ((110-102)2/102) = 8.366
p-value = 0.0038

With yates correction

2 = ((26-18-0.5)2/18) + ((abs(94-102)-0.5)2/102) + ((abs(10-18)-0.5)2/18) + ((110-102-0.5)2/102) = 7.3529
p-value = 0.006695

The 2 test statistic is 7.35, with 1 degree of freedom results in a p-value of =0.0067. Since the p-value is low, we reject H0. There is strong evidence of a difference in virologic failure rates between the Nevaripine and Lopinavir groups and they do not appear to be independent.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.