In health services research, experiments are often conducted at the provider or site level rather than the patient level. However, we might still be interested in the outcome at the patient level. For example, we could be interested in understanding the effect of a training program for physicians on their patients. It would be very difficult to randomize patients to be exposed or not to the training if a group of patients all see the same doctor. So the experiment is set up so that only some doctors get the training and others serve as the control; we still compare the outcome at the patient level.
Typically, when conducting an experiment we assume that individual outcomes are not related to each other (other than the common effect of the exposure). With site-level randomization, we can’t make that assumption - groups of patients are all being treated by the same doctor. In general, even before the intervention, there might be variation across physicians. At the same time, patients within a practice will vary. So, we have two sources of variation: between practice and within practice variation that explain overall variation.
I touched on this when I discussed issues related to Gamma distributed clustered data. A key concept is the intra-class coefficient or ICC, which is a measure of how between variation relates to overall variation. The ICC ranges from 0 (where there is no between variation - all site averages are the same) to 1 (where there is no variation within a site - all patients within the site have the same outcomes). Take a look at the earlier post for a bit more detail.
My goal here is to highlight a little function recently added to simstudy (v0.1.9, now available on CRAN). In the course of exploring study designs for cluster randomized trials, it is often useful to understand what happens (to sample size requirements, for example) when the ICC changes. When generating the data, it is difficult to control the ICC directly - we do this by controlling the variation. With normally distributed data, the ICC is an obvious function of the variances used to generate the data, so the connection is pretty clear. But, when the outcomes have binary, Poisson, or Gamma distributions (or anything else really), the connection between variation and the ICC is not always so obvious. Figuring out how to specify the data to generate a particular ICC might require quite a bit of trial and error.
The new function, iccRE (short for ICC random effects), allows users to specify target ICCs for a desired distribution (along with relevant parameters). The function returns the corresponding random effect variances that would be specified at the cluster level to generate the desired ICC(s).
Here’s an example for three possible ICCs in the context of the normal distribution:
library(simstudy)
targetICC