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.

Causal mediation estimation measures the unobservable

Posted on November 6, 2018

I put together a series of demos for a group of epidemiology students who are studying causal mediation analysis. Since mediation analysis is not always so clear or intuitive, I thought, of course, that going through some examples of simulating data for this process could clarify things a bit. Quite often we are interested in understanding the relationship between an exposure or intervention on an outcome. Does exposure AA (could be randomized or not) have an effect on outcome YY? [Read More]
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Cross-over study design with a major constraint

Posted on October 23, 2018

Every new study presents its own challenges. (I would have to say that one of the great things about being a biostatistician is the immense variety of research questions that I get to wrestle with.) Recently, I was approached by a group of researchers who wanted to evaluate an intervention. Actually, they had two, but the second one was a minor tweak added to the first. They were trying to figure out how to design the study to answer two questions: (1) is intervention AA better than doing nothing and (2) is A+A^+, the slightly augmented version of AA, better than just AA? [Read More]
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In regression, we assume noise is independent of all measured predictors. What happens if it isn't?

Posted on October 9, 2018

A number of key assumptions underlie the linear regression model - among them linearity and normally distributed noise (error) terms with constant variance In this post, I consider an additional assumption: the unobserved noise is uncorrelated with any covariates or predictors in the model. In this simple model: Yi=β0+β1Xi+ei,Y_i = \beta_0 + \beta_1X_i + e_i, YiY_i has both a structural and stochastic (random) component. The structural component is the linear relationship of YY with XX. [Read More]
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simstudy update: improved correlated binary outcomes

Posted on September 25, 2018

An updated version of the simstudy package (0.1.10) is now available on CRAN. The impetus for this release was a series of requests about generating correlated binary outcomes. In the last post, I described a beta-binomial data generating process that uses the recently added beta distribution. In addition to that update, I’ve added functionality to genCorGen and addCorGen, functions which generate correlated data from non-Gaussian or normally distributed data such as Poisson, Gamma, and binary data. [Read More]
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Binary, beta, beta-binomial

Posted on September 11, 2018

I’ve been working on updates for the simstudy package. In the past few weeks, a couple of folks independently reached out to me about generating correlated binary data. One user was not impressed by the copula algorithm that is already implemented. I’ve added an option to use an algorithm developed by Emrich and Piedmonte in 1991, and will be incorporating that option soon in the functions genCorGen and addCorGen. [Read More]
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The power of stepped-wedge designs

Posted on August 28, 2018

Just before heading out on vacation last month, I put up a post that purported to compare stepped-wedge study designs with more traditional cluster randomized trials. Either because I rushed or was just lazy, I didn’t exactly do what I set out to do. I did confirm that a multi-site randomized clinical trial can be more efficient than a cluster randomized trial when there is variability across clusters. (I compared randomizing within a cluster with randomization by cluster. [Read More]
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Multivariate ordinal categorical data generation

Posted on August 15, 2018

An economist contacted me about the ability of simstudy to generate correlated ordinal categorical outcomes. He is trying to generate data as an aide to teaching cost-effectiveness analysis, and is hoping to simulate responses to a quality-of-life survey instrument, the EQ-5D. The particular instrument has five questions related to mobility, self-care, activities, pain, and anxiety. Each item has three possible responses: (1) no problems, (2) some problems, and (3) a lot of problems. [Read More]
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Randomize by, or within, cluster?

Posted on July 19, 2018

I am involved with a stepped-wedge designed study that is exploring whether we can improve care for patients with end-stage disease who show up in the emergency room. The plan is to train nurses and physicians in palliative care. (A while ago, I described what the stepped wedge design is.) Under this design, 33 sites around the country will receive the training at some point, which is no small task (and fortunately as the statistician, this is a part of the study I have little involvement). [Read More]
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How the odds ratio confounds: a brief study in a few colorful figures

Posted on July 10, 2018

The odds ratio always confounds: while it may be constant across different groups or clusters, the risk ratios or risk differences across those groups may vary quite substantially. This makes it really hard to interpret an effect. And then there is inconsistency between marginal and conditional odds ratios, a topic I seem to be visiting frequently, most recently last month. My aim here is to generate a few figures that might highlight some of these issues. [Read More]
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Re-referencing factor levels to estimate standard errors when there is interaction turns out to be a really simple solution

Posted on June 26, 2018

Maybe this should be filed under topics that are so obvious that it is not worth writing about. But, I hate to let a good simulation just sit on my computer. I was recently working on a paper investigating the relationship of emotion knowledge (EK) in very young kids with academic performance a year or two later. The idea is that kids who are more emotionally intelligent might be better prepared to learn. [Read More]
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