Interpret a confidence interval, 2 sided hypothesis, agree with inference based on interval.

Question

A double-blind randomized clinical trial comparing chelation to placebo used a treadmill test in which the response was the length of time until a subject experienced ischemia

a. After 27 weeks of treatment, the sample mean time for the chelation group was 652 seconds. A 95% confidence interval for the population mean for chelation minus the population mean for placebo was -53 to 36 seconds. Explain how to interpret the confidence interval.

b. A significance test comparing the mean had P-value = 0.69. Specify the hypotheses for this test, which was two-sided.

c. The authors concluded from the test, "There is no evidence to support a beneficial effect of chelation therapy" (M. Knudtson et al. JAMA. vol. 287. p. 481.2002). Explain how this conclusion agrees with inference based on the values in the confidence interval.

Answer 1

When the change in condition in the placebo group is subtracted from the change of condition in the experimental group, what is left is the effect of treatment in the experimental group. The range of -53 to 36 seconds that was found by subtracting the 95% confidence intervals indicates the range about the mean with 95% confidence, or it would be expected that 95% of patients treated would fall into this range of 599 to 688 seconds post treatment. A large portion of those treated would be expected to have the opposite of the intended result from the treatment.

The p value of 0.69 in the hypothesis testing is an evaluation of the null hypothesis, which would be that there is no difference between the treatment and placebo groups. Subtracting that value from 1 gives the level of confidence that the hypothesis is correct, or that the drug had its intended effect. That value is 0.31, or if this experimental design were carried out 100 times, the expected results would show the intended effect in 31 of those trials. This is below the standard of 95% confidence for supporting the hypothesis, so the authors were correct in their conclusion.

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