This site is a compendium of R code meant to highlight the various uses of simulation to aid in the understanding of probability, statistics, and study design. I will frequently draw on examples using my R package `simstudy`

. Occasionally, I will opine on other topics related to causal inference, evidence, and research more generally.

In the last two posts, I introduced the notion of time-varying intra-cluster correlations in the context of stepped-wedge study designs. (See here and here). Though I generated lots of data for those posts, I didn’t fit any models to see if I could recover the estimates and any underlying assumptions. That’s what I am doing now.
My focus here is on the simplest case, where the ICC’s are constant over time and between time.
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## More on those stepped-wedge design assumptions: varying intra-cluster correlations over time

In my last post, I wrote about within- and between-period intra-cluster correlations in the context of stepped-wedge cluster randomized study designs. These are quite important to understand when figuring out sample size requirements (and models for analysis, which I’ll be writing about soon.) Here, I’m extending the constant ICC assumption I presented last time around by introducing some complexity into the correlation structure. Much of the code I am using can be found in last week’s post, so if anything seems a little unclear, hop over here.
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## Planning a stepped-wedge trial? Make sure you know what you're assuming about intra-cluster correlations ...

A few weeks ago, I was at the annual meeting of the NIH Collaboratory, which is an innovative collection of collaboratory cores, demonstration projects, and NIH Institutes and Centers that is developing new models for implementing and supporting large-scale health services research. A study I am involved with - Primary Palliative Care for Emergency Medicine - is one of the demonstration projects in this collaboratory.
The second day of this meeting included four panels devoted to the design and analysis of embedded pragmatic clinical trials, and focused on the challenges of conducting rigorous research in the real-world context of a health delivery system.
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## Don't get too excited - it might just be regression to the mean

It is always exciting to find an interesting pattern in the data that seems to point to some important difference or relationship. A while ago, one of my colleagues shared a figure with me that looked something like this:
It looks like something is going on. On average low scorers in the first period increased a bit in the second period, and high scorers decreased a bit. Something is going on, but nothing specific to the data in question; it is just probability working its magic.
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## simstudy update - stepped-wedge design treatment assignment

simstudy has just been updated (version 0.1.13 on CRAN), and includes one interesting addition (and a couple of bug fixes). I am working on a post (or two) about intra-cluster correlations (ICCs) and stepped-wedge study designs (which I’ve written about before), and I was getting tired of going through the convoluted process of generating data from a time-dependent treatment assignment process. So, I wrote a new function, trtStepWedge, that should simplify things.
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## Generating and modeling over-dispersed binomial data

A couple of weeks ago, I was inspired by a study to write about a classic design issue that arises in cluster randomized trials: should we focus on the number of clusters or the size of those clusters? This trial, which is concerned with preventing opioid use disorder for at-risk patients in primary care clinics, has also motivated this second post, which concerns another important issue - over-dispersion.
A count outcome In this study, one of the primary outcomes is the number of days of opioid use over a six-month follow-up period (to be recorded monthly by patient-report and aggregated for the six-month measure).
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## What matters more in a cluster randomized trial: number or size?

I am involved with a trial of an intervention designed to prevent full-blown opioid use disorder for patients who may have an incipient opioid use problem. Given the nature of the intervention, it was clear the only feasible way to conduct this particular study is to randomize at the physician rather than the patient level.
There was a concern that the number of patients eligible for the study might be limited, so that each physician might only have a handful of patients able to participate, if that many.
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## Even with randomization, mediation analysis can still be confounded

Randomization is super useful because it usually eliminates the risk that confounding will lead to a biased estimate of a treatment effect. However, this only goes so far. If you are conducting a meditation analysis in the hopes of understanding the underlying causal mechanism of a treatment, it is important to remember that the mediator has not been randomized, only the treatment. This means that the estimated mediation effect is still at risk of being confounded.
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## Musings on missing data

I’ve been meaning to share an analysis I recently did to estimate the strength of the relationship between a young child’s ability to recognize emotions in others (e.g. teachers and fellow students) and her longer term academic success. The study itself is quite interesting (hopefully it will be published sometime soon), but I really wanted to write about it here as it involved the challenging problem of missing data in the context of heterogeneous effects (different across sub-groups) and clustering (by schools).
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## A case where prospective matching may limit bias in a randomized trial

Analysis is important, but study design is paramount. I am involved with the Diabetes Research, Education, and Action for Minorities (DREAM) Initiative, which is, among other things, estimating the effect of a group-based therapy program on weight loss for patients who have been identified as pre-diabetic (which means they have elevated HbA1c levels). The original plan was to randomize patients at a clinic to treatment or control, and then follow up with those assigned to the treatment group to see if they wanted to participate.
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