Exercises Sheet 2

(W) denotes workshop exercises; (A) denotes homework questions; (E) additional exercises for completion in your own time.

Workshop Exercises

1. (W) Treatment $A$ is to be compared to treatment B for treating influenza. Should a cross-over trial be considered? Why or why not?

2. (W) What is carry-over? How may a $AB/BA$ design be modified to address this problem?

3. (W) State two advantages and two dis-advantages of a cross-over design.

4. (W)The table below gives the results from a randomised double-blind cross-over trial comparing Nicardipine (N) and placebo (P) in patients with Raynaud’s phenomenon. The data are the number of attacks in two weeks. There was a one-week wash-out period between the two treatment periods.

   N / P		P / N
   Period 1	Period 2	Period 1	Period 2
   16	12	18	12
   26	19	12	4
   8	20	46	37
   37	44	51	58
   9	25	28	2
   41	36	29	18
   52	36	51	44
   10	11	46	14
   11	20	18	30
   30	27	44	4

   1. Conduct a ‘simple analysis’ (ignoring a possible period effect) to compare the two treatments.

   2. The expected values in an $AB/BA$ cross-over trial with period effect are given in the course notes. Show how can the treatment effect $\tau$ and period effect $\pi$ be estimated using the expected period differences for the sequence groups.

   3. Allow for a period effect in your analysis (i.e estimate the treatment effect allowing for a period effect) and give a corresponding 95% confidence interval.

   4. Estimate the period effect and give a corresponding 95% confidence interval.

   5. Interpret your findings to part b) and c) in context of the study aims.

   6. What is the key difference between estimates of treatment effects and estimates of carry-over effects in $AB/BA$ designs?

   Homework Exercises

5. (H) The following table is from a randomised controlled clinical trial. Sixty five pregnant women at high risk of pregnancy-induced hypertension were randomised to 100mg of Aspirin daily or placebo during the third trimester of pregnancy. Patients in the treatment and control group were classified as to whether or not they developed hypertension during the follow-up period.

   	Hypertension
   	Yes	No	Total
   Aspirin	4	30	34
   Placebo	11	20	31
   Total	15	50	65

   1. Use a Z-test of proportions to investigate whether Aspirin reduces the risk of hypertension.

   2. Calculate estimates of the risk difference, relative risk, and odds ratio of hypertension for those who were administered Aspirin compared to those who were administered a placebo.

   3. Give 95% confidence intervals for the risk difference, relative risk, and odds ratio.

   4. Briefly interpret the results in context of the study aims.

   5. How does the standard error for the difference in proportions in a) (the denominator in the test statistic) differ from the standard error when constructing a confidence interval for the true risk difference in c).

   Group Work: Critical Appraisal

6. In the second part of the workshop we will critically appraise the BMJ paper: Randomised Controlled Trial of Magnetic Bracelets for relieving pain in osteoarthritis of the hip and knee. BMJ 2004, 429; 1450-4. We will use the CASP tool for appraising a clinical trial working in groups. The CASP tool is available here: http://www.casp-uk.net/casp-tools-checklists

   All materials are also on the courses Moodle page.