ouR data generation

Way back in 2018, long before the pandemic, I described a soon-to-be implemented simstudy function genMultiFac that facilitates the generation of multi-factorial study data. I followed up that post with a description of how we can use these types of efficient designs to answer multiple questions in the context of a single study.

Fast forward three years, and I am thinking about these designs again for a new grant application that proposes to study simultaneously three interventions aimed at reducing emergency department (ED) use for people living with dementia. The primary interest is to evaluate each intervention on its own terms, but also to assess whether any combinations seem to be particularly effective. While this will be a fairly large cluster randomized trial with about 80 EDs being randomized to one of the 8 possible combinations, I was concerned about our ability to estimate the interaction effects of multiple interventions with sufficient precision to draw useful conclusions, particularly if the combined effects of two or three interventions are less than additive. (That is, two interventions may be better than one, but not twice as good.)

In the previous post, I simulated data from a hypothetical RCT that had heterogeneous treatment effects across subgroups defined by three covariates. I presented two Bayesian models, a strongly pooled model and an unpooled version, that could be used to estimate all the subgroup effects in a single model. I compared the estimates to a set of linear regression models that were estimated for each subgroup separately.

My goal in doing these comparisons is to see how often we might draw the wrong conclusion about subgroup effects when we conduct these types of analyses. In a typical frequentist framework, the probability of making a mistake is usually considerably greater than the 5% error rate that we allow ourselves, because conducting multiple tests gives us more chances to make a mistake. By using Bayesian hierarchical models that share information across subgroups and more reasonably measure uncertainty, I wanted to see if we can reduce the chances of drawing the wrong conclusions.

I’m part of a team that recently submitted the results of a randomized clinical trial for publication in a journal. The overall findings of the study were inconclusive, and we certainly didn’t try to hide that fact in our paper. Of course, the story was a bit more complicated, as the RCT was conducted during various phases of the COVID-19 pandemic; the context in which the therapeutic treatment was provided changed over time. In particular, other new treatments became standard of care along the way, resulting in apparent heterogeneous treatment effects for the therapy we were studying. It appears as if the treatment we were studying might have been effective only in one period when alternative treatments were not available. While we planned to evaluate the treatment effect over time, it was not our primary planned analysis, and the journal objected to the inclusion of the these secondary analyses.

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.

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.

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.

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.)

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. My research associate, Yifan Xu, and I were asked to see what we could do to help out.

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.

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. Whether I am conducting a power analysis using simulation or exploring operating characteristics of different models, I take a pretty similar approach. I refer to this structure when I am starting a new project, so I thought it would be nice to have it easily accessible online - and that way others might be able to refer to it as well.