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I'm very new to the world of statistics, so sorry in advance for my limited knowledge. I hope you don't mind helping me.

We are currently setting up a multicenter RCT of treatment A versus placebo in 8 hospitals. The primary outcome is duration of treatment (time from randomization till stop of treatment = delivery), which is decided by the treating physician (based on protocol and personal opinion) and by patient-related factors (3 variables that tell us how unwell the patient is at inclusion). We believe that a 5 day prolongation of treatment duration is clinically relevant ('the longer the better'). The data we have from previous trials are mainly medians (the median treatment duration in placebo group is 10 days), as treatment duration is highly skewed (most treatments stop after a few days, only few are treated longer).

I came across this article: https://pubmed.ncbi.nlm.nih.gov/29197347/ Their method for sample size calculation seems to fit our stuation. However, I'm having trouble finding the correct way to calculate the sample size and take into account the (large) impact of differences in treatment duration between centers and how to correct for that. I have stratified randomization by center but I understand that an additional correction must be made to account for the correlation introduced in the data by stratifying.

Thank you all very much for your time and efforts in advance, Catherina

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  • $\begingroup$ So each hospital will include both treated and untreated patients? $\endgroup$
    – num_39
    Commented Apr 4 at 11:01
  • $\begingroup$ Yes, each hospital will randomize patients individually between treatment A (a specific medicine) and placebo, aside from usual care (all kinds of other medicines). Treatment is stopped in all cases (placebo/treatment A/inelegible patients with only usual care) if the physician believes the patient has become too ill. $\endgroup$
    – Catherina Muscat
    Commented Apr 4 at 12:12
  • $\begingroup$ 0. Welcome to CV.SE. 1. Good question and good on you to ask upon it, too often people just find some specialised references and follow it without critically thinking why they do certain things (+1). 2. I think a simulation based approach will give you the best mileage. If anything, you will also know how you are going to analyse your results when you get them. Please see my answer below for a more details. $\endgroup$
    – usεr11852
    Commented Apr 5 at 15:05

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Most statisticians ignore centers when doing sample size calculations. That doesn't cause too much of a problem.

The best models for duration of treatment are the Cox proportional hazards model or the proportional odds ordinal logistic model. Both handle the skewness in the outcome variable. They can both handle right censoring (patient still on treatment when planned follow-up ends).

The proportional odds model is a generalization of the Wilcoxon test. Sample size calculations for this approach may be found here. You'll need pilot data with a distribution of treatment durations to use the methods there.

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Given your non-trivial design, I would suggest you turn this task a bit onto its head and use a simulation-based sample size planning approach. A nice intro to this would be: External validation of clinical prediction models: simulation-based sample size calculations were more reliable than rules-of-thumb by Snell et al. Now, particular to what your use case, a mixed effects model seems relevant, as the center would be a random factor. There is the simr package that widely used and allows one to calculate power for generalised linear mixed models, via simulations. The vignettes as simple to follow, but if we want more insights, the CV.SE thread on What would "small", "medium," and "large" effect sizes be for mixed effects model in simr? has some good external references on the matter.

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    $\begingroup$ There is also the simstudy package. (Its author has a blog with simulation examples of various kind.) $\endgroup$
    – dipetkov
    Commented Apr 5 at 17:55
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    $\begingroup$ @dipetkov: Thank you for mentioning. (+1) I had not come across it. $\endgroup$
    – usεr11852
    Commented Apr 5 at 20:02
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Let me see if I understand:

  • Your main outcome here is time until stopping of treatment. While the paper you linked mentions sample size calculations for medians, I think a time-to-event analyses is best. Frank seems to agree (unsurprisingly since my views are largely influenced by his).
  • There appears to be within center correlation for length of treatment (equivalently time to treatment stop). Why is this? Do you have reason to believe the correlation is very strong? Do you have data from these hospitals which may give you a sense of what the difference between hospitals might be?
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