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Chapter 10: Problem 45

In a 2018 article published in The Lancet, Sprigg et al. studied the effect of tranexamic acid in treating patients with intracerebral hemorrhages using a randomized, placebo-controlled trial. Of the 1161 subjects treated with tranexamic acid, 383 suffered an adverse outcome after 2 days. Of the 1164 subjects given a placebo, 419 suffered an adverse outcome after 2 days. a. Find the percentage in each group that suffered an adverse outcome. Round off to one decimal place as needed. b. Create a two-way table with the treatment labels (drug/placebo) across the top. c. Test the hypothesis that treatment and adverse outcome are associated using a significance level of \(0.05\).

Short Answer

Expert verified
33.0% of the tranexamic acid group and 36.0% of the placebo group suffered an adverse outcome. Whether there's a statistically significant association between treatment and outcome would be determined by a Chi-square test of independence. If the p-value from the test is less than 0.05, we reject the null in favor of the alternative hypothesis meaning there's significant evidence that treatment and outcome are related.

Step by step solution

01

Calculate Percentage

To calculate the percentage of patients who suffered an adverse outcome in each group, we divide the number of individuals who suffered an adverse outcome by the total number in that group, then multiply by 100. For the group treated with tranexamic acid, this percentage is \( \frac{383}{1161} \times 100 \approx 33.0\% \). For the placebo group, this percentage is \( \frac{419}{1164} \times 100 \approx 36.0\% \).
02

Create a Two-Way Table

We are going to create a two-way table with the treatment labels across the top and the outcomes on the side. The table will look like this:| | Tranexamic Acid | Placebo ||-------------|-----------------|---------|| Adverse | 383 | 419 || Non-Adverse | 778 | 745 |Here, the numbers for non-adverse outcomes are calculated by subtracting the number of adverse outcomes from the total number of subjects in each group.
03

Test the Hypothesis

Here we'll be testing the hypothesis that treatment and adverse outcome are associated using a significance level of 0.05. This is a Chi-square test of independence. Here, the null hypothesis (\(H_0\)) is that treatment and adverse outcome are independent, and the alternative hypothesis (\(H_a\)) is that they are associated. Using software or a statistical table, we calculate the Chi-square statistic and the corresponding p-value. If the p-value is less than 0.05, we will reject the null hypothesis, implying that there is a significant association between treatment and adverse outcome.

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