What is the correct way to test for a difference in mean between groups in a cluster RCT?

[Zoe Hyde]

I have data on about 1,650 people, recruited from 12 health clinics, participating in a cluster randomised controlled trial.

Because of the cluster design, I know that I have to do something like:

regress age i.gender, vce(cluster clinic)

rather than:

ttest age, by(gender)

when I am looking at differences between types of individuals in the study.

But what do I do if I want to test for a difference between the clusters? For example, I want to know if the patients at each clinic are of a similar age. Can I just do one of the following?

oneway age clinic, tabulate

regress age i.clinic

The F statistic is missing for the model if I try this instead:

regress age i.clinic, vce(cluster clinic)

[Maxence Morlet]

Theoretically you should be able to exactly replicate results obtained with ttest and with reg commandsif both are executed without any options after the comma.

You are trying to test whether the randomisation process worked well, right?

I do not know how your variable clinic is structured, but I assume from the

 
 regress age i.clinic, vce(cluster clinic)

Stata will omit one clinic (the base group) and then give you coefficients for all other clinics, which will be the average change in age in a given clinic, relative to the mean age in the base, or comparison clinic. If coefficients (or one coefficient) are (is) significant, this means that age may be systematically different across clinics. Randomisation would then be compromised, and results may not be causal.

A ttest, or simple conditional mean comparison (the OLS regression you showed) are both parametric methods. They make distributional assumptions that may be violated.

I would go further and use non-parametric methods. I would visualise and compare the distributions of relevant covariates by clinic using kernel methods.

You can also use rank tests and other nonparametric tests, which do not make any distributional assumptions (see e.g. Wilcoxon's tests). Using nonparametric tests, you could test whether two samples come from a population with the same median. This is also indicative of whether your randomisation process has worked well or not.

[Maxence Morlet]

Check out section 2.4 of this paper https://www.sciencedirect.com/scienc...04407620302797