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.

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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.

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Randomisation as the basis for inference in trials

Today I was lucky enough to listen Prof William Rosenberger present the 15th Armitage lecture in Cambridge. Prof Rosenberger has worked extensively on randomisation in trials in various respects (see his book), and he delivered a really interesting talk. The talk can now be viewed online here.

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Live stream seminar 26th October 2017: Covariate adjustment and prediction of mean response in randomised trials

Next Thursday (14:00 UK time, 26th October 2017) I'll be giving a seminar at the University of Southampton in the UK on my recent work on covariate adjustment and prediction of mean response in randomised trials. The seminar will be live streamed here, which after the talk will be accessible as a recording.

The talk abstract can be found here.

Testing equality of two survival distributions: log-rank/Cox versus RMST

Cox's proportional hazards model is by far the most common approach used to model survival or time to event data. For a simple two group comparison, such as in a randomised controlled trial, the model says that the hazard of failure in one group is a constant ratio (over time) of the hazard of failure in the other group. A test that this hazard ratio equals 1 is a test of the null hypothesis of equality of the survival functions of the two groups. The log rank test is essentially equivalent to the score test that the HR=1 in the Cox model, and is commonly used as the primary analysis hypothesis test in randomised trials.

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