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 frequently draw on examples using my R package simstudy. Occasionally, I opine on other topics related to causal inference, evidence, and research more generally.

The case of three MAR mechanisms: when is multiple imputation mandatory?

I thought I’d written about this before, but I searched through my posts and I couldn’t find what I was looking for. If I am repeating myself, my apologies. I explored missing data two years ago, using directed acyclic graphs (DAGs) to help understand the various missing data mechanisms (MAR, MCAR, and MNAR). The DAGs provide insight into when it is appropriate to use observed data to get unbiased estimates of population quantities even though some of the observations are missing information. [Read More]

Framework for power analysis using simulation

The simstudy package started as a collection of functions I developed as I found myself repeating many of the same types of simulations for different projects. It was a way of organizing my work that I decided to share with others in case they wanted a routine way to generate data as well. simstudy has expanded a bit from that, but replicability is still a key motivation. What I have here is another attempt to document and organize a process that I find myself doing quite often - repeated data generation and model fitting. [Read More]

Randomization tests make fewer assumptions and seem pretty intuitive

I’m preparing a lecture on simulation for a statistical modeling class, and I plan on describing a couple of cases where simulation is intrinsic to the analytic method rather than as a tool for exploration and planning. MCMC methods used for Bayesian estimation, bootstrapping, and randomization tests all come to mind. Randomization tests are particularly interesting as an approach to conducting hypothesis tests, because they allow us to avoid making unrealistic assumptions. [Read More]

Visualizing the treatment effect with an ordinal outcome

If it’s true that many readers of a journal article focus on the abstract, figures and tables while skimming the rest, it is particularly important tell your story with a well conceived graphic or two. Along with a group of collaborators, I am trying to figure out the best way to represent an ordered categorical outcome from an RCT. In this case, there are a lot of categories, so the images can get confusing. [Read More]

How useful is it to show uncertainty in a plot comparing proportions?

I recently created a simple plot for a paper describing a pilot study of an intervention targeting depression. This small study was largely conducted to assess the feasibility and acceptability of implementing an existing intervention in a new population. The primary outcome measure that was collected was the proportion of patients in each study arm who remained depressed following the intervention. The plot of the study results that we included in the paper looked something like this: [Read More]

Finding answers faster for COVID-19: an application of Bayesian predictive probabilities

As we evaluate therapies for COVID-19 to help improve outcomes during the pandemic, researchers need to be able to make recommendations as quickly as possible. There really is no time to lose. The Data & Safety Monitoring Board (DSMB) of COMPILE, a prospective individual patient data meta-analysis, recognizes this. They are regularly monitoring the data to determine if there is a sufficiently strong signal to indicate effectiveness of convalescent plasma (CP) for hospitalized patients not on ventilation. [Read More]

Coming soon: effortlessly generate ordinal data without assuming proportional odds

I’m starting off 2021 with my 99th post ever to introduce a new feature that will be incorporated into simstudy soon to make it a bit easier to generate ordinal data without requiring an assumption of proportional odds. I should wait until this feature has been incorporated into the development version, but I want to put it out there in case any one has any further suggestions. In any case, having this out in plain view will motivate me to get back to work on the package. [Read More]

Constrained randomization to evaulate the vaccine rollout in nursing homes

On an incredibly heartening note, two COVID-19 vaccines have been approved for use in the US and other countries around the world. More are possibly on the way. The big challenge, at least here in the United States, is to convince people that these vaccines are safe and effective; we need people to get vaccinated as soon as they are able to slow the spread of this disease. I for one will not hesitate for a moment to get a shot when I have the opportunity, though I don’t think biostatisticians are too high on the priority list. [Read More]

A Bayesian implementation of a latent threshold model

In the previous post, I described a latent threshold model that might be helpful if we want to dichotomize a continuous predictor but we don’t know the appropriate cut-off point. This was motivated by a need to identify a threshold of antibody levels present in convalescent plasma that is currently being tested as a therapy for hospitalized patients with COVID in a number of RCTs, including those that are particpating in the ongoing COMPILE meta-analysis. [Read More]

A latent threshold model to dichotomize a continuous predictor

This is the context. In the convalescent plasma pooled individual patient level meta-analysis we are conducting as part of the COMPILE study, there is great interest in understanding the impact of antibody levels on outcomes. (I’ve described various aspects of the analysis in previous posts, most recently here). In other words, not all convalescent plasma is equal. If we had a clear measure of antibodies, we could model the relationship of these levels with the outcome of interest, such as health status as captured by the WHO 11-point scale or mortality, and call it a day. [Read More]