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.

This is a relatively brief addendum to last week’s post, where I described how the rvar datatype implemented in the R package posterior makes it quite easy to perform posterior probability checks to assess goodness of fit. In the initial post, I generated data from a linear model and estimated parameters for a linear regression model, and, unsurprisingly, the model fit the data quite well. When I introduced a quadratic term into the data generating process and fit the same linear model (without a quadratic term), equally unsurprising, the model wasn’t a great fit.
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## Fitting your model is only the beginning: Bayesian posterior probability checks with rvars

Say we’ve collected data and estimated parameters of a model that give structure to the data. An important question to ask is whether the model is a reasonable approximation of the true underlying data generating process. If we did a good job, we should be able to turn around and generate data from the model itself that looks similar to the data we started with. And if we didn’t do such a great job, the newly generated data will diverge from the original.
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## Estimating a risk difference (and confidence intervals) using logistic regression

The odds ratio (OR) – the effect size parameter estimated in logistic regression – is notoriously difficult to interpret. It is a ratio of two quantities (odds, under different conditions) that are themselves ratios of probabilities. I think it is pretty clear that a very large or small OR implies a strong treatment effect, but translating that effect into a clinical context can be challenging, particularly since ORs cannot be mapped to unique probabilities.
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## Sample size determination in the context of Bayesian analysis

Given my recent involvement with the design of a somewhat complex trial centered around a Bayesian data analysis, I am appreciating more and more that Bayesian approaches are a very real option for clinical trial design. A key element of any study design is sample size. While some would argue that sample size considerations are not critical to the Bayesian design (since Bayesian inference is agnostic to any pre-specified sample size and is not really affected by how frequently you look at the data along the way), it might be a bit of a challenge to submit a grant without telling the potential funders how many subjects you plan on recruiting (since that could have a rather big effect on the level of resources - financial and time - required.
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## Generating random lists of names with errors to explore fuzzy word matching

Health data systems are not always perfect, a point that was made quite obvious when a study I am involved with required a matched list of nursing home residents taken from one system with set results from PCR tests for COVID-19 drawn from another. Name spellings for the same person from the second list were not always consistent across different PCR tests, nor were they always consistent with the cohort we were interested in studying defined by the first list.
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## 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.
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## 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.
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## 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.
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## 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.
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## 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:
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