Repeated measures trial sample size

[Gianfranco Di Gennaro]

Dear all,

I am writing regarding a sample size calculation in STATA.

I have a randomized trial lasting one month with two arms (experimental vs. control). The study outcome is the VAS score (0-100).

There is a baseline measurement, followed by four drug infusions starting on day 1, each spaced four days apart until day 12, with a final measurement on day 30.

My hypothesis is that on day 30, there will be a -20 point difference in VAS in favor of the experimental group. Assuming a homogeneous standard deviation of 25, I would perform an ANCOVA, calculating the sample size considering only the baseline and post-treatment measurements, using a pre-post correlation of 0.8:

sampsi 20 0, sd(25) r01(0.8) pre(1) post(1) alpha(0.05)

I am wondering how I should calculate the sample size while also accounting for all four intermediate measurements after the baseline but before the final measurement.

I have attempted several approaches in STATA, but the correct method is unclear to me.

I appreciate any guidance in advance.

Gianfranco

[Joseph Coveney]

I am wondering how I should calculate the sample size while also accounting for all four intermediate measurements after the baseline but before the final measurement.

The sample size is governed by your hypothesis, which relates solely to the thirty-day observation time point (adjusted for baseline) and does not involve any of the intermediate time points. So, what need is there to account for them?

I have attempted several approaches in STATA, but the correct method is unclear to me.

I gather that the approaches that you tried included power repeated, and that the problem is that you want to adjust for baseline at each of the interim observation intervals? I think that there's literature on the advisability of adding a time-invariant covariate to a repeated-measures analysis of variance, but I guess you've already looked into that.

If all else comes up dry, you can always use simulation (FAQ here and The Stata Journal article here). A couple of things that you might want to consider are (i) the correlation coefficient of 0.8 for a visual analog scale (VAS) separated by a month strikes me as a little high unless everyone's marking left end or right end both times, which would call into question its dynamic range (sensitivity to treatment effect), and (ii) the correlation between the VAS scores closer in to the baseline (and temporally closer to each other) would likely be higher than that between baseline and end-of-study observation time point. I'm not sure how well the sphericity assumption behind repeated-measures ANOVA will hold up with that kind of observation schedule.

[Tiago Pereira]

I would approach the sample size calculation using Monte Carlo approach, as Joseph wisely recommended. The issue is whether to use a multivariate beta or multivariate normal distribution. The former is a bit tricky to simulate, but the correct correlations after the inverse beta function can be achieve with a bit of trial-and-error.

[Gianfranco Di Gennaro]

Thanks Tiago Pereira and Joseph Coveney !
In the end, I think I'll keep the sample size as I calculated it. Indeed, the experimenter didn't provide me with any hypotheses except for the one at day 30, so I'll stick with what Joseph suggested. However, I'll try to calculate the sample size via simulation, if only to learn.

P.S.: Regarding the baseline-day 30 correlation, I referred to a paper that estimated it at 0.83 over a shorter follow-up (2 weeks).
Thanks again.