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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. Twentyfour 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. \({ }^{36}\) (a) Create a two-way table presenting the results of this study. (b) State appropriate hypotheses to test for difference in virologic failure rates between treatment groups. (c) Complete the hypothesis test and state an appropriate conclusion.

Step by step solution

01

Organize Data into a Two-Way Table

To create a two-way table, we organize the data by treatment group and virologic failure outcome. The rows will represent the types of treatment (Nevaripine and Lopinavir), while the columns will show the outcomes (virologic failure or no failure). The table: \[ \begin{array}{c|c|c|c} & \text{Virologic Failure} & \text{No Virologic Failure} & \text{Total} \ \hline \text{Nevaripine} & 26 & 94 & 120 \ \hline \text{Lopinavir} & 10 & 110 & 120 \ \hline \text{Total} & 36 & 204 & 240 \ \end{array} \]

02

State the Hypotheses

The null hypothesis \( H_0 \) is that there is no difference in virologic failure rates between the Nevaripine and Lopinavir treatment groups. The alternative hypothesis \( H_a \) is that there is a difference in virologic failure rates between the two groups.

03

Calculate the Test Statistic

We perform a chi-square test for independence using the two-way table. First, calculate the expected frequencies: for Nevaripine with virologic failure: \( \frac{120 \times 36}{240} = 18 \); without failure: \( \frac{120 \times 204}{240} = 102 \); and similarly for Lopinavir. The test statistic \( \chi^2 \) is calculated as follows: \[ \chi^2 = \sum \frac{(O - E)^2}{E} \] where \( O \) is the observed frequency and \( E \) is the expected frequency. Substitute and calculate \( \chi^2 \).

04

Determine the Critical Value

The degrees of freedom \( df \) is \(( ext{number of rows} - 1) \times ( ext{number of columns} - 1) = 1\). At a significance level \( \alpha = 0.05 \), find the critical value for \( \chi^2 \) using a chi-square distribution table (\( \chi_{0.05, 1}^2 \approx 3.84 \)).

05

Conclusion of Hypothesis Test

Compare the test statistic to the critical value. If the \( \chi^2 \) test statistic is greater than the critical value, reject the null hypothesis \( H_0 \). Otherwise, do not reject \( H_0 \). The \( \chi^2 \) calculation yields a value greater than 3.84, indicating a statistically significant difference in virologic failure rates between the two treatments.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Clinical Study

A clinical study is a type of research involving people, aimed at answering specific health-related questions. In this exercise about HIV treatment, a clinical study was conducted to compare the effects of two anti-HIV drugs: Nevaripine and Lopinavir. In this study, 240 HIV-infected women participated, each receiving one of the two treatments. The main goal was to assess virologic failure rates, which helped researchers determine if one treatment was more effective. By conducting such studies, researchers gather critical data to inform medical guidelines and treatment practices.

Chi-Square Test

The chi-square test is a statistical method used to determine if there is a significant difference between expected and observed frequencies in a categorical dataset. In the context of this study, the chi-square test was carried out to evaluate if the difference in virologic failure rates between women treated with Nevaripine and those treated with Lopinavir was statistically significant. This method is useful when you want to compare two or more groups, helping researchers confirm or challenge the assumptions based on data.

Two-Way Table

A two-way table, or contingency table, organizes data into rows and columns and is used to display the frequency distribution of variables. In this exercise, the two-way table was employed to present data related to the two treatment groups and the outcomes of virologic failure or no failure. For example, it showed 26 instances of virologic failure out of 120 women treated with Nevaripine, and 10 instances for the Lopinavir group. This structure makes it easier to visualize differences and similarities between groups, serving as a basis for further statistical calculations, like the chi-square test.

Virologic Failure

Virologic failure occurs when a treatment for a viral infection, like HIV, does not reduce the viral load in a patient's body as expected. This study focused on the rate of virologic failure as a primary outcome measure. After 24 weeks, researchers assessed which of the two treatments led to more cases of virologic failure. Understanding virologic failure helps researchers and clinicians evaluate how effectively a drug inhibits the virus, which is crucial for developing effective treatment strategies and improving patient outcomes.

Null Hypothesis

The null hypothesis is a fundamental concept in hypothesis testing that assumes there is no effect or difference between groups under investigation. In this exercise, the null hypothesis posited that there was no difference between the virologic failure rates of the Nevaripine and Lopinavir treatments. Testing the null hypothesis involves using collected data to determine its validity. If the chi-square test statistic exceeds the critical value, researchers reject the null hypothesis, supporting the idea that a difference does exist. Otherwise, they fail to reject it, implying no significant difference.