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.
Causal inference
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.
Estimating causal effects from observational studies
In this post I’ll continue my notes based on Miguel Hernán and James Robins’ soon to be published book, Causal Inference. In this post I’ll look at some of what is covered in their third chapter, on estimation of causal effects from observational studies.