Sample size for visual analog scale outcome in three-level treatment trial with repeated measures

[kivester]

I need to perform a sample size calculation for a proposed study that the outcome of interest is a visual analog score on a scale 0 to 100. The score will be recorded at the start of the study (week 0) and weekly for 6 weeks. There will be three treatment groups. A time*treatment interaction is of interest, but we specifically would like to know the estimated sample size necessary to detect a difference between the 3 groups at week 6. To add to the complexity, the study will be conducted at 6 different centers.

I have fairly good pilot data and expect the scores to look like this:

	Week0	Week1	Week2	Week3	Week4	Week5	Week6
Treatment1	42.2222222	65	75	78.75	85	85.625	87.5
Treatment2	31.4285714	46.4285714	51.4285714	61.4285714	67	67.1428571	70.7142857
Treatment3	36.8253968	50.9	55.9	57.775	60.9	61.2125	62.15

I know I can estimate sample size in proc GLMPOWER, but with the outcome on an ordinal scale I am not sure that is the best thing to do.

Thanks for any help!

[SteveDenham]

To get what you want, you will also need some estimate of the time point variances and the covariance between time points.  At that level, you may be happier using simulation to determine sample size, or using the method outlined by Stroup in this paper 

 https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=1DD150BA59B7EB27C5B890D4154BC3FE?doi=10.1.... 

The other thing I would offer is that your pilot data has most of the VAS scores near the middle of the range.  At that point, you can consider the residuals to be approximately normal rather than using a very difficult to estimate ordinal multinomial (missing values will almost certainly be an issue - I doubt that any of the timepoints has values at all 101 points from 0 to 100.

SteveDenham

[kivester]

Thank you for your help! You are correct, I do not expect that any timepoint will have values from 0 to 100. I will be happy to avoid the ordinal multinomial approach.

Thank you for the Stroup reference!

Katy