Combining bootstrapping and multiple imputation under uncongeniality

Tomorrow I'm giving a talk (slides here) at the Joint Statistical Meeting in Vancouver on some work I've been doing on combining bootstrapping with multiple imputation (MI), something I've written about here before. That post looked at a recent paper by Schomaker and Heumann (2018) on various ways of combining bootstrapping and MI. A more recent post discussed an arXiv paper by von Hippel (2018) on maximum likelihood multiple imputation, which also contains a nice proposal for combining bootstrap and MI. My talk this week is about how these perform when the imputation and analysis models are not congenial.

Read moreCombining bootstrapping and multiple imputation under uncongeniality

Missing not at random sensitivity analysis with FCS multiple imputation

Daniel Tompsett and colleagues have recently published a paper (open access here) on performing missing not at random (MNAR) sensitivity analyses within the fully conditional specification (FCS) framework for multiple imputation (MI). A number of previous papers had explored versions of the approach, and Tompsett et al bring these together to formalise the basis for the approach (which they term NARFCS) and importantly how to choose values of the sensitivity parameters involved.

Read moreMissing not at random sensitivity analysis with FCS multiple imputation

Multiple imputation when estimating relative risks

Sullivan and colleagues have recently published a nice paper exploring multiple imputation for missing covariates or outcome when one is interested in estimating relative risks. They performed simulations where missing covariates or outcomes were imputed either using multivariate normal imputation or using fully conditional specification imputation (FCS), and where the true outcome model is a log link binomial model. They concluded that multivariate normal imputation performed poorly, producing estimated coefficients which were biased towards the null. Fully conditional specification performed better, although estimates were still biased in certain situations.

Read moreMultiple imputation when estimating relative risks

Causal interpretation of the hazard ratio from RCTs when proportional hazards holds

In 2015 I wrote a post about the causal interpretation of hazard ratios estimated in randomised trials, following a paper by Aalen and colleagues. One of the arguments made in that paper was that the hazard ratio does not have a valid interpretation as a causal effect in this setting, even when the proportional hazards assumption holds:

This makes it unclear what the hazard ratio computed for a randomized survival study really means. Note, that this has nothing to do with the fit of the Cox model. The model may fit perfectly in the marginal case with X as the only covariate, but the present problem remains.

With recent discussions on estimands in light of the estimand addendum to ICH E9, I have been thinking more on the argument/claim by Aalen et al.

Read moreCausal interpretation of the hazard ratio from RCTs when proportional hazards holds

Maximum likelihood multiple imputation

I just came across a very interesting draft paper on arXiv by Paul von Hippel on 'maximum likelihood multiple imputation'. von Hippel has made many important contributions to the multiple imputation (MI) literature, including the paper which advocated that one 'transform then impute' when one has interaction or non-linear terms in the substantive model of interest. The present paper on maximum likelihood multiple imputation is in its seventh draft on arXiv, the first being released back in 2012. I haven't read every detail of the paper, but it looks to me to be another thought provoking and potentially practice changing paper. This post will not attempt by any means to cover all of the important points made in the paper, but will just highlight a few.

Read moreMaximum likelihood multiple imputation