In 2007, Paul von Hippel published a nice paper proposing a variant of the conventional multiple imputation (MI) approach to handling missing data. The paper advocated a multiple imputation followed by deletion (MID) approach. The context considered was where we are interested in fitting a regression model for an outcome Y with covariates X, and some Y and X values are missing. The approach advocated consists of running imputation as usual, imputing missing values in Y and X, but then discarding those records where the outcome Y had been imputed. Instead, the reduced datasets, with missing X values imputed but only observed Y values, are analysed as usual, with results combined using Rubin’s rules.
Using hazard ratios to estimate causal effects in RCTs
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.
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.