Sample size and power replication for CRT

[Galenda Nagudi]

Hello all,

I was added to a cluster randomised trial where they used the parameters explained below for the power calculation. I would like to replicate the calculation. Any insight on how to go about this would be much appreciated.

The outcome is treatment resistance assumed to be 5%, measured up to 12 months after the end of treatment. Calculations are based on comparing this outcome in low/high adherence groups (ratio effect estimate ranging from 3.2-4), assuming a total 1000 participants, 70 clusters, and a design effect of 1.69 and 2.38.

Power for treatment resistance outcome, assuming 70 clusters and Design effects of 1.69 and 2.38
Design Effect	Effective size sample size	Effect estimate (ratio)	Power
1.69	592	3.2	83%
2.38	420	3.2	69%
1.69	592	3.5	88%
2.38	420	3.5	75%
1.69	592	4	91%
2.38	420	4	81%

Additional information is that the trial whose power calculation Iam trying to replicate is a substudy of another trial that made the following assumptions: ICC=0.024, alpha=0.05 (two-sided) & average cluster size of 42. Though its not clear if these estimates were used for the substudy power calculation.

[Tiago Pereira]

Galenda, what is the treatment effect? Is it represented by the 'ratio effect estimate'?

[Galenda Nagudi]

Hello Tiago, thank you for the response. Yes, I believe it is the 'ratio effect estimate'.

And another little edit is the average cluster size for the main trial for its primary outcome is 64. The 42 is an assumption made for the secondary outcome. I hope this is helpful.

[Leonardo Guizzetti]

I think there's quite a bit of information missing here, and some contradictory information. I am assuming that the calculation is based on a simple test of differences in proportions adjusting for clustering, but ratios are also possible. It is not stated whether there are any assumptions of assurance on the power, or if this is a test of non-inferiority or superiority.

Here are some contradictions. The description states an assumption of 1000 people divided amongst 70 clusters, and assuming equally sized clusters, is 14 people per cluster. The design effect is quoted as being 1.69 or 2.38, with an ICC=0.024. The design effect is commonly calculated as 1 + (m-1)*rho, where m is the mean cluster size and rho is the ICC. With a design effect of 1.69, that makes average group size ~30. Both of these are very difference from the average cluster sizes of 42 and 64, also stated in your posts. However, if you assume 1000 patients equally divided in 70 clusters, then a design effect f 1.69 implies an ICC of ~0.048.

The effective sample size column is calculated as the assumed sample size divided by the design effect (e.g., 1000/1.69 ≈ 592).

In any case, I can't reproduce the results you have shown us. I was assuming a really severe design with 1000 people, 35 clusters per arm all of the same size, and an ICC of 0.05, then a two-sided test of a difference of proportions adjusting for clustering to compare 5% vs 16% (a ratio of 3.2), the power is still ~97% or greater with an alpha level of 1%.

There are relatively simple formulas available from standard texts. I referred to the book by Donner and Klar, though I think this book is no longer in print. Moulton has a great book on cluster randomized trails which is still in print.

Source:

Donner and Klar (2000). Design and Analysis of Cluster Randomized Trials in Health Research.

[Galenda Nagudi]

Hello Leonardo, thank you for your response. Apologies for the information that is not clear. Let me try to provide some clarity.

The primamry trial is a non-inferiority design that is comparing nurse-led care to doctor-led care. To determine the number of clusters required to achieve at least 80% power with one-sided alpha of 0.025, an intraclass correlation (ICC) of 0.024 was used. A sample size of 46 clusters (23 physician-led control clusters and 23 nurse-led intervention clusters) with 2,944 total participants, or 1,472 per arm (i.e., 64 participants per cluster on average). The preliminary data suggested nurse-led care short course outcomes comparable to doctors, the nurse-led group proportion is assumed to be 90% under the null hypothesis and not less than 85% under the alternative hypothesis, (i.e., non-inferiority margin of 5%).

I was able to replicate the sample size obtained for the primary study using the following stata command:


[power twoproportions 0.9 0.85, k1(23) k2(23) m1(64) m2(64) rho(0.024)]

I hope this provides better clarity. I will also go ahead to look at the resource you have recommended.

[Tiago Pereira]

Clearly those are not sample size calculations for a non-inferiority trial. Assuming that experimental is inferior in the sample size consideration of a non-inferiority trial is logically inconsistent.