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.

Recently I started a discussion about modeling secular trends using flexible models in the context of cluster randomized trials. I’ve been motivated by a trial I am involved with that is using a stepped-wedge study design. The initial post focused on more standard parallel designs; here, I want to extend the discussion explicitly to the stepped-wedge design.
The stepped-wedge design Stepped-wedge designs are a special class of cluster randomized trial where each cluster is observed in both treatment arms (as opposed to the classic parallel design where only some of the clusters receive the treatment).
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## Generating clustered data with marginal correlations

A student is working on a project to derive an analytic solution to the problem of sample size determination in the context of cluster randomized trials and repeated individual-level measurement (something I’ve thought a little bit about before). Though the goal is an analytic solution, we do want confirmation with simulation. So, I was a little disheartened to discover that the routines I’d developed in simstudy for this were not quite up to the task.
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## Modeling the secular trend in a cluster randomized trial using very flexible models

A key challenge - maybe the key challenge - of a stepped wedge clinical trial design is the threat of confounding by time. This is a cross-over design where the unit of randomization is a group or cluster, where each cluster begins in the control state and transitions to the intervention. It is the transition point that is randomized. Since outcomes could be changing over time regardless of the intervention, it is important to model the time trends when conducting the efficacy analysis.
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## Presenting results for multinomial logistic regression: a marginal approach using propensity scores

Multinomial logistic regression modeling can provide an understanding of the factors influencing an unordered, categorical outcome. For example, if we are interested in identifying individual-level characteristics associated with political parties in the United States (Democratic, Republican, Libertarian, Green), a multinomial model would be a reasonable approach to for estimating the strength of the associations. In the case of a randomized trial or epidemiological study, we might be primarily interested in the effect of a specific intervention or exposure while controlling for other covariates.
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## Flexible simulation in simstudy with customized distribution functions

Really, the only problem with the simstudy package (😄) is that there is a hard limit to the possible probability distributions that are available (the current count is 15 - see here for a complete description). However, it turns out that there is more flexibility than first meets the eye, and we can easily accommodate a limitless number as long as you are willing to provide some extra code.
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## Simulating data from a non-linear function by specifying a handful of points

Trying to simulate data with non-linear relationships can be frustrating, since there is not always an obvious mathematical expression that will give you the shape you are looking for. I’ve come up with a relatively simple solution for somewhat complex scenarios that only requires the specification of a few points that lie on or near the desired curve. (Clearly, if the relationships are straightforward, such as relationships that can easily be represented by quadratic or cubic polynomials, there is no need to go through all this trouble.
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## simstudy updated to version 0.5.0

A new version of simstudy is available on CRAN. There are two major enhancements and several new features. In the “major” category, I would include (1) changes to survival data generation that accommodate hazard ratios that can change over time, as well as competing risks, and (2) the addition of functions to allow users to sample from existing data sets with replacement to generate “synthetic” data will real life distribution properties.
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## To impute or not: the case of an RCT with baseline and follow-up measurements

Under normal conditions, conducting a randomized clinical trial is challenging. Throw in a pandemic and things like site selection, patient recruitment and patient follow-up can be particularly vexing. In any study, subjects need to be retained long enough so that outcomes can be measured; during a period when there are so many potential disruptions, this can become quite difficult. This issue of loss to follow-up recently came up during a conversation among a group of researchers who were troubleshooting challenges they are all experiencing in their ongoing trials.
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## Simulating time-to-event outcomes with non-proportional hazards

As I mentioned last time, I am working on an update of simstudy that will make generating survival/time-to-event data a bit more flexible. I previously presented the functionality related to competing risks, and this time I’ll describe generating survival data that has time-dependent hazard ratios. (As I mentioned last time, if you want to try this at home, you will need the development version of simstudy that you can install using devtools::install_github(“kgoldfeld/simstudy”).
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## Adding competing risks in survival data generation

I am working on an update of simstudy that will make generating survival/time-to-event data a bit more flexible. There are two biggish enhancements. The first facilitates generation of competing events, and the second allows for the possibility of generating survival data that has time-dependent hazard ratios. This post focuses on the first enhancement, and a follow up will provide examples of the second. (If you want to try this at home, you will need the development version of simstudy, which you can install using devtools::install_github(“kgoldfeld/simstudy”).
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