## 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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## Why you shouldn't use propensity score matching

I've just watched a highly thought provoking presentation by Gary King of Harvard, available here https://youtu.be/rBv39pK1iEs, on why propensity score matching should not be used to adjust for confounding in observational studies. The presentation makes great use of graphs to explain the concepts and arguments for some of the issues with propensity score matching.

Read moreWhy you shouldn't use propensity score matching

## Estimating effects when outcomes are truncated by death

A common situation arises when one wants to estimate the effect of a treatment or exposure at some time point t in an observational cohort or randomised trial. For example, what is the mean difference in some outcome Y at time t between the two groups of interest. To make things a bit simpler, let's suppose that subjects were allocated to the two groups (e.g. two treatments A and B) randomly, as in a randomised trial. Now suppose that some of the subjects die before time t, such that their outcome Y is not observed. Then we can no longer compare Y between the two groups in all subjects, because some values of Y are missing, or truncated by death.

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## 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.

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## Conditional randomization, standardization, and inverse probability weighting

In a previous post, I began following the developments in Miguel Hernán and James Robins' soon to be published book, Causal Inference. There I gave an overview of the first topics they cover, namely potential outcomes, causal effects, and randomization. In this post I'll continue, with some personal notes on the remaining parts of Chapter 2 of their book, on conditional randomization, standardization, and inverse probability weighting.

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