In a 2018 study reported in The Lancet, Molina et al....

In a 2018 study reported in The Lancet, Molina et al. reported on a study for treatment of patients with HIV-1. The study was a randomized, controlled, double-blind study that compared the effectiveness of ritonavir-boosted darunavir (rbd), the drug currently used to treat HIV-1, with dorovirine, a newly developed drug. Of the 382 subjects taking ritonavir-boosted darunavir, 306 achieved a positive result. Of the 382 subjects taking dorovirine, 321 achieved a positive outcome. See page 430 for guidance. a. Find the sample percentage of subjects who achieved a positive outcome in each group. b. Perform a hypothesis test to test whether the proportion of patients who achieve a positive outcome with the current treatment (ritonavir-boosted darunavir) is different from the proportion of patients who achieve a positive outcome with the new treatment (dorovirine). Use a significance level of $0.01$. Based on this study, do you think dorovirine might be a more effective treatment option for HIV-1 than ritonavir-boosted darunavir? Why or why not?

In a 2018 study reported in The Lancet, Molina et al. reported on a study for treatment of patients with HIV-1. The study was a randomized, controlled, double-blind study that compared the effectiveness of ritonavir-boosted darunavir (rbd), the drug currently used to treat HIV-1, with dorovirine, a newly developed drug. Of the 382 subjects taking ritonavir-boosted darunavir, 306 achieved a positive result. Of the 382 subjects taking dorovirine, 321 achieved a positive outcome. See page 430 for guidance.
a. Find the sample percentage of subjects who achieved a positive outcome in each group.
b. Perform a hypothesis test to test whether the proportion of patients who achieve a positive outcome with the current treatment (ritonavir-boosted darunavir) is different from the proportion of patients who achieve a positive outcome with the new treatment (dorovirine). Use a significance level of $0.01$. Based on this study, do you think dorovirine might be a more effective treatment option for HIV-1 than ritonavir-boosted darunavir? Why or why not?

Key Concepts

Z-Test Statistic

The Z-test statistic is utilized in hypothesis testing when comparing two proportions, particularly when sample sizes are large. It quantifies the difference between the observed sample proportions relative to the expected variation under the null hypothesis, allowing for the determination of the corresponding p-value.

Randomized Controlled Trial

This is an experimental design used to evaluate the effectiveness of interventions by randomly assigning participants to different treatment groups. The randomization helps minimize bias, and the controlled aspects, such as blinding, ensure that the observed effects can be more confidently attributed to the treatments being tested rather than external factors.

Significance Level

The significance level, often denoted by alpha (?), is a threshold used in hypothesis testing to decide whether to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is actually true, effectively setting the standard for how strong the evidence must be to conclude a significant difference exists.

Null and Alternative Hypotheses

In the context of hypothesis testing, the null hypothesis typically states that there is no difference between the groups being compared, while the alternative hypothesis suggests that there is a difference. These hypotheses provide a framework for testing the validity of a presumed effect or difference between treatments or groups.

Two-Sample Proportion Test

This statistical test is used to compare the proportions from two independent groups to determine if there is a significant difference between them. It involves calculating the difference between the sample proportions and assessing how likely that difference could have occurred by random chance if there were no true difference in the populations.

Sample Proportion

This concept refers to the ratio of individuals within a sample that exhibit a certain outcome. It is calculated by dividing the number of subjects who show the outcome of interest by the total number of subjects in the group. This measure is fundamental in statistics for estimating the proportion of an event in a population based on sample data.

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