Supplementary Exercise 3.10 of IPS7e
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A clinical trial on the preventive effects of vitamin use on colon cancer.
A total of 864 people at risk for colon cancer participated and were randomly
allocated to four vitamin supplementation groups: beta-carotene, vitamins C and E,
all 3 supplements, and placebo. 


(a) The vitamin supplementation is the explanatory variable, and the occurrence
of colon cancer in a 4-year period is the response variable (i.e., a dichotomous, 
or binary, response variable).


(b) It is most natural and efficient (for estimating all treatment comparisons well) 
to use the same number of subjects in all treatment groups, i.e. 864/4=216 subjects 
per group. We can illustrate a completely randomized design with 4 treatment groups 
by the type of diagrams shown in the PSLS and IPS textbooks, as follows:

Random assignment  -> Group 1 (216 persons)  -> beta-carotene supplementation
                   -> Group 2 (216 persons)  -> vitamin C and E supplementation
                   -> Group 3 (216 persons)  -> all three supplements
                   -> Group 4 (216 persons)  -> placebo

In my view, the display is not crucial for the understanding of the design. 


(c) The labels will simply be the numbers 1-864, hence three-digit numbers need
to read from the table of random digits. Starting at line 118 of Table A (PSLS) or B (IPS), 
the first few 3-digit numbers are:
  731 (903) 253 304 470 296 698 ...
The second number exceeds the desired range 1-864, but all the other
numbers could correspond to subjects selected for the beta-carotene
group.


(d) Double-blinding means that neither the study subjects nor the
researchers and staff involved in the study know the true identity of
the treatment groups. The groups are typically labelled by nondescript
names, and only persons not involved in the daily contact with the study
subjects know the real meaning of the labels. 

A further extension of this idea is to not reveal the meaning of the labels to
the people analyzing or monitoring the data -- sometimes termed a triple-blind
design. Although triple-blinding occurs, it is less common than double-blinding
because it is useful to have someone monitoring the study before it has been 
completed. This could for example be important for ethical reasons.


(e) It means that the observed difference between the four treatment
groups could easily have happened by chance alone.


(f) People's diets are closely linked to lifestyles, involving such
potentially important parameters as occupation, social status, amount 
of exercise, and consumption of alcohol. All of these variables can have
confounding effects by being related to both the diet (specifically the
consumption of fruit and vegetables) and the disease risk.