# Best way to compare pre vs post levels in treatment vs control groups?

In a study, drug was given to tt (treatment) group and not to cc (control) group and blood levels of (say) cholesterol were tested before and after in each subject.

I have following data:

  id grp preLevel postLevel diff percentDiff prePostRatio
1  1  tt      140       110   30        0.21         1.27
2  2  tt      150       120   30        0.20         1.25
3  3  cc      135       125   10        0.07         1.08
4  4  cc      155       145   10        0.06         1.07
...


I can perform t.test or wilcox.test and compare the two groups. But what is the best parameter to analyze: absolute difference, percent difference or pre/post ratio? Or it does not matter and they will all produce same result?

Edit:

For above data should I use t.test/ wilcox.test or repeated measures anova as described on this page: http://ww2.coastal.edu/kingw/statistics/R-tutorials/repeated.html using following code with rearranged data:

id  grp  pre_or_post level
1   tt   pre         140
1   tt   post        110
2   tt   pre         150
2   tt   post        120
3   cc   pre         135
3   cc   post        125
...

aov(level ~ grp * pre_or_post + Error(id/pre_or_post), data=mydata)


Also, how will the method of analysis differ if it is a parallel group study with different subjects in treatment and controls groups or it is a cross-over study with same subjects being in treatment and control groups at different times?

• Related thread: Best practice when analysing pre-post treatment-control designs.
– chl
Oct 26 '14 at 16:44
• Thanks for the link. I am surprised to see that experts do not agree on analysis of this very common situation (at least in biomedical area it is very common).
– rnso
Oct 26 '14 at 17:29

It really depends on whether there were pre-treatment differences in the preLevels of the Treatment and Control group. Ideally, especially in a clinical trial, the groups would be randomly chosen and identical before treatment. In that case, absolute differences, percentage differences, and pre-post ratios will correlate very highly and will show much the same thing.

If you were in a situation where you had groups that differed at baseline, it would be a different story. If you imagine that, for some reason, the treatment group started off at an average cholesterol of 200 while the control group started at 100, absolute differences and ratios would give you very different results. If the cholesterol of the treatment group dropped 20 points (absolute) and the control only 10, percentage and pre-post ratio measures would show no difference between groups, while absolute values would pick up on the difference. In that case, absolute values would likely be the right choice of measure.

In general, ratios and percentages can be dangerous because they can hide differences such as the one I just described, so I would tend towards testing absolute differences first, and only using ratios etc when the situation makes them specifically appropriate.

• Please see my edit in the question above regarding query on use of anova with repeated measures here.
– rnso
Oct 26 '14 at 3:21
• With only two groups a t.test is appropriate - anova extends to more than two groups, which you don't need as is. Oct 26 '14 at 10:36
• Any need in view of 'repeated measures' or 'Error correction' by Error(id/pre_or_post). I was concerned since the example given in the link is exactly like my data (pre and post for chicken vs pasta diet).
– rnso
Oct 26 '14 at 11:47
• A paired t-test is designed for repeated measures, see www-users.cs.umn.edu/~ludford/Stat_Guide/Paired_t.htm . Oct 26 '14 at 12:55
• Thanks for the link but we are not doing 'paired' t.test here since we are comparing delta of treatment vs delta of control group, and 2 groups are different and not same subjects.
– rnso
Oct 26 '14 at 13:14