A Bayesian analysis of a factorial design focusing on effect size estimates

Factorial study designs present a number of analytic challenges, not least of which is how to best understand whether simultaneously applying multiple interventions is beneficial. Last time I presented a possible approach that focuses on estimating the variance of effect size estimates using a Bayesian model. The scenario I used there focused on a hypothetical study evaluating two interventions with four different levels each. This time around, I am considering a proposed study to reduce emergency department (ED) use for patients living with dementia that I am actually involved with. [Read More]

Analyzing a factorial design by focusing on the variance of effect sizes

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. [Read More]

Drawing the wrong conclusion about subgroups: a comparison of Bayes and frequentist methods

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. [Read More]

Subgroup analysis using a Bayesian hierarchical model

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. [Read More]

Posterior probability checking with rvars: a quick follow-up

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. [Read More]

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. [Read More]

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. [Read More]

Finding answers faster for COVID-19: an application of Bayesian predictive probabilities

As we evaluate therapies for COVID-19 to help improve outcomes during the pandemic, researchers need to be able to make recommendations as quickly as possible. There really is no time to lose. The Data & Safety Monitoring Board (DSMB) of COMPILE, a prospective individual patient data meta-analysis, recognizes this. They are regularly monitoring the data to determine if there is a sufficiently strong signal to indicate effectiveness of convalescent plasma (CP) for hospitalized patients not on ventilation. [Read More]

A Bayesian implementation of a latent threshold model

In the previous post, I described a latent threshold model that might be helpful if we want to dichotomize a continuous predictor but we don’t know the appropriate cut-off point. This was motivated by a need to identify a threshold of antibody levels present in convalescent plasma that is currently being tested as a therapy for hospitalized patients with COVID in a number of RCTs, including those that are particpating in the ongoing COMPILE meta-analysis. [Read More]

Exploring the properties of a Bayesian model using high performance computing

An obvious downside to estimating Bayesian models is that it can take a considerable amount of time merely to fit a model. And if you need to estimate the same model repeatedly, that considerable amount becomes a prohibitive amount. In this post, which is part of a series (last one here) where I’ve been describing various aspects of the Bayesian analyses we plan to conduct for the COMPILE meta-analysis of convalescent plasma RCTs, I’ll present a somewhat elaborate model to illustrate how we have addressed these computing challenges to explore the properties of these models. [Read More]