A phase 3, randomized controlled trial was conducted to evaluate the effect of Drug X and Drug Y on serum parathyroid hormone (PTH) concentrations in patients receiving hemodialysis with severe secondary hyperparathyroidism. A total of 508 patients were randomly assigned to Drug X or Drug Y after each hemodialysis session for 26 weeks. The primary efficacy endpoint was the percentage of patients achieving 30% reduction in mean PTH from baseline during weeks 20-27. A secondary efficacy endpoint was the percentage of patients achieving mean PTH

Question

A phase 3, randomized controlled trial was conducted to evaluate the effect of Drug X and Drug Y on serum parathyroid hormone (PTH) concentrations in patients receiving hemodialysis with severe secondary hyperparathyroidism.  A total of 508 patients were randomly assigned to Drug X or Drug Y after each hemodialysis session for 26 weeks.  The primary efficacy endpoint was the percentage of patients achieving >30% reduction in mean PTH from baseline during weeks 20-27.  A secondary efficacy endpoint was the percentage of patients achieving mean PTH <300 pg/mL.  An excerpt of the study results is as follows:  Based on these results, which of the following is a possible 95% confidence interval for the difference in the percentage of patients who achieved the primary efficacy endpoint between Drug X and Drug Y?
A)(−13.9% to −8.9%) 
B)(−15.5% to −5.2%) 
C)(−19.3% to −12.7%) 
D)(−10.2% to 9.7%) 
E)(−21.6% to 0.8%)

Quizplus · Accepted Answer

Explanation: A confidence interval (CI) is constructed by taking a sample value (eg, difference in sample percentages) and adding and subtracting a margin of error. Consequently, the interval always contains the sample value, and the sample value is typically at the center of the interval. The CI of a given difference in percentages indicates, with a certain confidence level (eg, 95%), whether the difference in percentages is significantly different from the null value (ie, the null value for a difference = 0). A CI is statistically significant if it excludes the null value. This study evaluated the effect of Drug X and Drug Y on serum parathyroid hormone (PTH) concentrations in patients receiving hemodialysis with severe secondary hyperparathyroidism. The primary endpoint was the percentage of patients achieving >30% reduction from baseline in mean PTH during weeks 20-27. The percentage of patients who achieved the primary endpoint with Drug X was 74.0% and with Drug Y was 85.4% for a difference of −11.4% that was statistically significant (p < 0.001). The p-value corresponds to a test of the difference of percentages equal to 0, so a significant result means that the difference in the primary endpoint between drugs is significantly different from 0. Because the difference in the percentage of patients who achieved the primary endpoint between drugs is significantly different from 0, a 95% CI for the same difference in percentages excludes 0 (Choices D and E). The interval always contains the sample value (ie, difference in sample percentages), so −11.4% must be included in the interval (Choice C) and located at its center (Choice B). Therefore, a possible 95% CI for the difference in the percentage of patients who achieved the primary endpoint between Drug X and Drug Y is (−13.9% to −8.9%). Educational objective: A confidence interval (CI) always contains the sample value at the center of the interval. A CI that excludes a null value (ie, difference in percentages = 0) is statistically significant.

A Phase 3, Randomized Controlled Trial Was Conducted to Evaluate