Assignment II for Biostats Course VHM 801 at AVC - Fall Semester 2026

The assignment is worth 10% 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.

The data for the assignment originate from a study on the effect of a treatment against a rheumatic condition in humans. Twenty volunteer patients were selected to participate in the study, and based on patient characteristics such as sex, age and severity of the condition the patients were divided into 10 pairs of similar patients. For example, the two patients in the first pair were selected to be of the same sex and to be of similar age and similar rheumatic condition, and so on for the other pairs. Within each pair, one patient was randomly assigned to treatment and the other patient to placebo. The treatment and placebo were given in form of tablets that were identical except for the active ingredient of treatment tablets.

Measurements of the range of motion of the knee affected by the condition were made for each patient before the tablets were administered (visit 1) and again after a suitable follow-up period (visit 2). Higher values correspond to improved health. The table below shows all the values measured, with the 10 patients (labeled 1-10) in the placebo group shown to the left and the 10 patients (labeled 11-20) in the treatment group to the right. Files containing the full data (except the patient numbers) are available in Minitab format and also in comma-separated format, for import into Stata and other statistical software.

	Placebo group			Treatment group
Patient	visit 1	visit 2	Pair	visit 1	visit 2	Patient
1	9.53	12.03	1	9.47	12.36	11
2	12.86	12.47	2	10.26	12.49	12
3	10.51	8.59	3	6.66	11.04	13
4	10.31	10.61	4	11.70	12.11	14
5	14.00	14.59	5	13.39	17.65	15
6	7.87	8.48	6	7.24	9.51	16
7	4.78	3.82	7	4.79	4.79	17
8	10.63	12.24	8	9.71	12.11	18
9	11.19	12.17	9	10.52	12.88	19
10	9.86	12.39	10	11.92	13.10	20

The home assignment has five questions which should all be answered. Recall that all solutions should be accompanied by text explaining the procedures used and by suitable documentation for the results presented. Because a choice between several valid analyses may exist in these questions, it is also important that you describe the rationale for your chosen approach.

1. Characterize the experimental design and comment briefly on relevant features of the study (such as randomization and blinding).

2. The researchers conducting the study wanted to ensure that the treatment assignment had made the two treatment groups (initially) comparable. Estimate the mean difference in visit 1 measurements between patients of the placebo and treatment groups. Supplement the estimate with a suitable confidence interval and interpret it (briefly). Use that information (and possibly other statistics you want to compute) to conclude about any systematic difference in initial measurements between the two groups. As part of your analysis, make sure to state assumptions for the statistical inference and to comment (briefly) on whether these assumptions seem reasonable. (Hint: To keep the assignment at a reasonable length and because of the rather small sample size, for this and subsequent questions you may limit any descriptive analysis to the essentials for the assessments you make.)

3. It was of interest to assess any placebo effect, that is, whether the patients in the placebo group showed a systematic improvement in the measurement after being administered the inactive tablet. Carry out an analysis for this question, using the same steps as described under Question 2.

4. The main question of interest was whether the treatment showed an improvement in the condition when compared to placebo. Carry out an analysis for this question, using the same steps as above, but make sure to also include a statistical test to support your conclusions.

5. In this final question, you are requested to explore and discuss the impact of the pairs on the results obtained; the broad question we seek to answer is whether the pairing was useful or not. This can be addressed in many ways, and you are by no means expected to provide a complete discussion.

   Specifically, you can choose between considering the impact of the pairing on (a) the initial measurements, or (b) the quantification of the treatment effect. For both situations, you can (i) illustrate the impact of the pairing descriptively, possibly graphically, with a corresponding interpretation of what the descriptive analysis tells you, or (ii) you can assess the impact numerically by comparing the results from statistical analyses that do and do not take the pairing into account.
   Note: You are not expected to use analytical tools/methods beyond what has been covered so far in the course to answer the question. If you nevertheless choose to do so, you will need to explain such methods to demonstrate your understanding of them.

   Describe clearly what is the focus of your discussion, for example among the options listed above, and interpret your findings carefully. It is allowed, even if not required, to include multiple (at most two) different ways of assessing the impact of the pairing, and if you do, separate them clearly in terms of their aims, results and interpretations.