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.

## When there's a fork in the road, take it. Or, taking a look at marginal structural models.

I am going to cut right to the chase, since this is the third of three posts related to confounding and weighting, and it’s kind of a long one. (If you want to catch up, the first two are here and here.) My aim with these three posts is to provide a basic explanation of the marginal structural model (MSM) and how we should interpret the estimates. This is obviously a very rich topic with a vast literature, so if you remain interested in the topic, I recommend checking out this (as of yet unpublished) text book by Hernán & Robins for starters. [Read More]

## When you use inverse probability weighting for estimation, what are the weights actually doing?

Towards the end of Part 1 of this short series on confounding, IPW, and (hopefully) marginal structural models, I talked a little bit about the fact that inverse probability weighting (IPW) can provide unbiased estimates of marginal causal effects in the context of confounding just as more traditional regression models like OLS can. I used an example based on a normally distributed outcome. Now, that example wasn’t super interesting, because in the case of a linear model with homogeneous treatment effects (i. [Read More]

## Characterizing the variance for clustered data that are Gamma distributed

Way back when I was studying algebra and wrestling with one word problem after another (I think now they call them story problems), I complained to my father. He laughed and told me to get used to it. “Life is one big word problem,” is how he put it. Well, maybe one could say any statistical analysis is really just some form of multilevel data analysis, whether we treat it that way or not. [Read More]

## Visualizing how confounding biases estimates of population-wide (or marginal) average causal effects

When we are trying to assess the effect of an exposure or intervention on an outcome, confounding is an ever-present threat to our ability to draw the proper conclusions. My goal (starting here and continuing in upcoming posts) is to think a bit about how to characterize confounding in a way that makes it possible to literally see why improperly estimating intervention effects might lead to bias. Confounding, potential outcomes, and causal effects Typically, we think of a confounder as a factor that influences both exposure and outcome. [Read More]

## A simstudy update provides an excuse to generate and display Likert-type data

I just updated simstudy to version 0.1.7. It is available on CRAN. To mark the occasion, I wanted to highlight a new function, genOrdCat, which puts into practice some code that I presented a little while back as part of a discussion of ordinal logistic regression. The new function was motivated by a reader/researcher who came across my blog while wrestling with a simulation study. After a little back and forth about how to generate ordinal categorical data, I ended up with a function that might be useful. [Read More]

## Thinking about different ways to analyze sub-groups in an RCT

Here’s the scenario: we have an intervention that we think will improve outcomes for a particular population. Furthermore, there are two sub-groups (let’s say defined by which of two medical conditions each person in the population has) and we are interested in knowing if the intervention effect is different for each sub-group. And here’s the question: what is the ideal way to set up a study so that we can assess (1) the intervention effects on the group as a whole, but also (2) the sub-group specific intervention effects? [Read More]

## Who knew likelihood functions could be so pretty?

I just released a new iteration of simstudy (version 0.1.6), which fixes a bug or two and adds several spline related routines (available on CRAN). The previous post focused on using spline curves to generate data, so I won’t repeat myself here. And, apropos of nothing really - I thought I’d take the opportunity to do a simple simulation to briefly explore the likelihood function. It turns out if we generate lots of them, it can be pretty, and maybe provide a little insight. [Read More]

## Can we use B-splines to generate non-linear data?

I’m exploring the idea of adding a function or set of functions to the simstudy package that would make it possible to easily generate non-linear data. One way to do this would be using B-splines. Typically, one uses splines to fit a curve to data, but I thought it might be useful to switch things around a bit to use the underlying splines to generate data. This would facilitate exploring models where we know the assumption of linearity is violated. [Read More]

## A minor update to simstudy provides an excuse to talk a bit about the negative binomial and Poisson distributions

I just updated simstudy to version 0.1.5 (available on CRAN) so that it now includes several new distributions - exponential, discrete uniform, and negative binomial. As part of the release, I thought I’d explore the negative binomial just a bit, particularly as it relates to the Poisson distribution. The Poisson distribution is a discrete (integer) distribution of outcomes of non-negative values that is often used to describe count outcomes. It is characterized by a mean (or rate) and its variance equals its mean. [Read More]

## CACE closed: EM opens up exclusion restriction (among other things)

This is the third, and probably last, of a series of posts touching on the estimation of complier average causal effects (CACE) and latent variable modeling techniques using an expectation-maximization (EM) algorithm . What follows is a simplistic way to implement an EM algorithm in R to do principal strata estimation of CACE. The EM algorithm In this approach, we assume that individuals fall into one of three possible groups - never-takers, always-takers, and compliers - but we cannot see who is who (except in a couple of cases). [Read More]