Assignment II for Biostats Course VHM 801 at AVC - Fall semester 2020

The assignment is worth 15% of the final course mark. Please be aware that by handing in the home assignment you implicitly acknowledge to have read and accepted the instructions for home assignments as described on the VHM 801 homepage.

We consider data from a clinical trial to test a (new) medicine for a particular rheumatic disease. The trial involved 20 patients selected from a suitable patient group. These 20 patients were grouped in 10 pairs so that the two patients in each pair were as similar with respect to age and disease duration as possible. Each patient had the locomotion power in the knee measured twice, once before and once some time after the intake of a pill of either medicine or placebo. In each patient pair, one patient received the medicine and the other patient the placebo. An increase in locomotion power from the first to the second measurement represented an improvement of the patient's condition. The measurements obtained are listed in the table below and are also available in Minitab format and as a comma-separated file, for import into Stata and other statistical software.

Patient	Medicine		Placebo
pair	1st measure	2nd measure	1st measure	2nd measure
1	9.53	12.03	9.47	12.36
2	12.86	12.47	10.26	12.49
3	8.59	10.51	6.66	11.04
4	10.31	10.61	11.70	12.11
5	14.00	14.59	13.39	17.65
6	7.87	8.48	7.24	9.51
7	4.78	3.82	4.79	4.79
8	10.63	12.24	9.71	12.11
9	11.19	12.17	10.52	12.88
10	9.86	12.39	11.92	13.10

Answer to all of the following six questions. Make sure to include explanations and justifications for all procedures and calculations used, including assessments of the assumptions made.

1. Characterize the statistical design, explain the rationale for the pairing of patients, and discuss whether (and if so, how) blinding could be part of the study. Outline also briefly how randomization should be carried out for such a design.

2. For use in future studies, the researchers were interested in establishing a baseline level (prior to any treatment) of the locomotion power of the knee for this patient group. Describe the baseline distribution, and give both a 90% range for locomotion power values and a 90% confidence interval for the mean locomotion power. (Hint: For this question and the next, you are free to either use the methods for inference without knowing the standard deviation or to assume the population standard deviation to be known at a value of 2.5.)

3. In order to ensure a fair comparison between the medicine and placebo group, it is of interest to check that the two groups were similar before the treatment was administered. Carry out a statistical analysis to compare the two groups prior to treatment, and draw conclusions. Discuss specifically whether - considering the experimental design - the result was expected or surprising.

4. One of the key outcomes of the study was a quantification of the improvement (if any) in locomotion power between measurements before and after use of the medicine. Carry out a statistical analysis to estimate and give a suitable interval for the mean improvement in locomotion power among the patients who received the medicine. Interpret your results carefully. (Note: The analysis requested here should not include results for patients in the placebo group.)

5. The use of a control group is one of the key components of a properly executed clinical trial. Expand or revise your analysis from 4.) to incorporate the results for patients in the placebo group. Your analysis should include a statistical test for the treatment effect. Draw conclusions from your analyses in 4.) and 5.), and write a brief summary on the evidence provided by the data for a beneficial treatment effect.

6. Finally, explore and discuss any impact of the pairing of patients in the resulting data. Because no formal method of assessing a question of this type has been demonstrated in the course up till now, you should try to use any relevant information that you can extract from the data. It may help to think about how an effect of the pairing would be expected to show itself in the data. Additionally, in continuation of your exploration and discussion, do you think the pairing was useful, in the sense of helping to obtain stronger results of the trial?