Question

In: Statistics and Probability

The increasing prevalence of uropathogens resistant to antimicrobial agents has stimulated interest in cranberries to prevent...

  1. The increasing prevalence of uropathogens resistant to antimicrobial agents has stimulated interest in cranberries to prevent recurrent urinary tract infections (UTIs). A meta-analysis of the results of 12 well-conducted randomized controlled trials showed that, in women with recurrent UTIs, cranberry products reduced the incidence of recurrences at 12 months by 39% (relative risk, 0.61; 95% confidence interval, 0.40-0.91) as compared with placebo or control interventions. In these trials, cranberries were compared with placebo or no intervention and not with the standard of care prophylaxis, namely, low-dose antibiotics. The objective of the current study is test if cranberries are as good as the standard of care prophylaxis for treating UTIs.

  1. The study is example of a

  1. Superiority (“Difference”) study
  2. Equivalence study
  3. Non-inferiority study

  1. What are the null and alternative hypotheses? (It is okay to describe the hypotheses in words.)

Solutions

Expert Solution

I. When the aim of the randomized controlled trial is to show that one treatment is superior to another, a statistical test is employed and the trial is called a superiority trial. Often a nonsignificant superiority test is wrongly interpreted as proof of no difference between the two treatments. Proving that two treatments are equal in performance is impossible with statistical tools; at most, one can show that they are equivalent. In an equivalence trial, the statistical test aims at showing that two treatments are not too different in characteristics, where "not too different" is defined in a clinical manner. Finally, in a non-inferiority trial, the aim is to show that an experimental treatment is not much worse than a standard treatment.

So this study is example of a Superiority (“Difference”) study.

II. The Null and Alternative Hypothesis are given below:-

Null Hypothesis (H0): incident rate after using cranberry products equals to incident rate after using placebo or control interventions.

Alternative Hypothesis (H1): incident rate after using cranberry products is lesser than incident rate after using placebo or control interventions.


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