Odd Aalen and colleagues have recently published an interesting paper on the use of Cox models for estimating treatment effects in randomised controlled trials. In a randomised trial we have the treatment assignment variable X, and an often used primary analysis is to fit a simple Cox model with X as the only covariate. This gives an estimated hazard ratio comparing the hazard in the treatment group compared to the control, and this is assumed constant over time. In any trial, there will almost certainly exist other variables Z, some of which might be measured, and some of which will always be unmeasured, and which influence the outcome. At baseline, X and Z are statistically independent as a result of randomisation, which of course is the reason randomisation in general allows us to make a causal statement about the treatment effect – we need not worry about confounding.
Jonathan Bartlett
On “The fallacy of placing confidence in confidence intervals”
Note: if you read this post, make sure to read the comments/discussion below it with Richard Morey, author of the paper in question, who put me straight on a number of points.
Thanks to Twitter I came across the latest draft of a very nicely written and thought provoking paper “The fallacy of placing confidence in confidence intervals”, by Morey, Rouder, Hoekstra, Lee and Wagenmakers. The paper aims to show why frequentist confidence intervals do not posses a number of properties that researchers often believe that they do. In contrast, they show that Bayesian credible intervals posses these desired properties, and advocate the replacement of confidence intervals with Bayesian credible intervals.
Automatic convergence checking in Bayesian inference with runjags
I’ve been performing some simulation studies comparing a Bayesian to a more traditional frequentist estimation approach in a particular problem. To do this I’ve been using the excellent JAGS package, calling it from R. One of the issues I’ve faced is the question of how long to run the MCMC sampler in the Bayesian approach. Use too few iterations, and the chains will not have converged to their stationary distribution, such that the samples will not be from the posterior distribution of the model parameters. In regular data analysis situations, one can make use of the extensive diagnostic toolkit which has been developed over the years. The most popular of these is I believe to examine trace plots from multiple chains, started with dispersed initial values, and also Gelman and Rubin’s Rhat measure.