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.

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. [Read More]

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. [Read More]

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). [Read More]

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. [Read More]

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. [Read More]

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). [Read More]

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. [Read More]

A example in causal inference designed to frustrate: an estimate pretty much guaranteed to be biased

I am putting together a brief lecture introducing causal inference for graduate students studying biostatistics. As part of this lecture, I thought it would be helpful to spend a little time describing directed acyclic graphs (DAGs), since they are an extremely helpful tool for communicating assumptions about the causal relationships underlying a researcher’s data. The strength of DAGs is that they help us think how these underlying relationships in the data might lead to biases in causal effect estimation, and suggest ways to estimate causal effects that eliminate these biases. [Read More]

Using the uniform sum distribution to introduce probability

I’ve never taught an intro probability/statistics course. If I ever did, I would certainly want to bring the underlying wonder of the subject to life. I’ve always found it almost magical the way mathematical formulation can be mirrored by computer simulation, the way proof can be guided by observed data generation processes, and the way DGPs can confirm analytic solutions. I would like to begin such a course with a somewhat unusual but accessible problem that would evoke these themes from the start. [Read More]

Correlated longitudinal data with varying time intervals

I was recently contacted to see if simstudy can create a data set of correlated outcomes that are measured over time, but at different intervals for each individual. The quick answer is there is no specific function to do this. However, if you are willing to assume an “exchangeable” correlation structure, where measurements far apart in time are just as correlated as measurements taken close together, then you could just generate individual-level random effects (intercepts and/or slopes) and pretty much call it a day. [Read More]