Estimands and the treatment policy strategy in the presence of truncating events

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I’ve posted a couple of times now (here and here) about our estimands article that recently appeared in the BMJ¹. In this post I discuss an interesting rapid response we received about truncating events².

A truncating event is sometimes described as an event that precludes observation of the outcome of interest. Supposing the outcome of interest is not death, but a some participants may die (when planning the study) or do die (actually occurs in the study), we cannot measure the outcome of interest for those participants.

Response and subsequent exchange

Kim Blond’s rapid response took us to task on a statement we had made:

Because the treatment policy strategy requires outcome data after the intercurrent event, it cannot be used for truncating events.

Blond saw this statement as at-odds with something written in another paper³, which says,

a competing event generally acts as a mediator of the treatment effect on the event of interest, leading to uncertain interpretation of the total effect.

Hmm… the term ‘mediator’ seems odd here, but I’ll try and stay on-topic. We replied that we do not see any contradiction. Blond responded again, saying that Janvin et al. connect the treatment policy strategy to what the causal mediation literature terms the total effect⁴. Agreed! Janvin et al. say,

it is important to understand that (1) also coincides with an example of a total effect as historically defined in the causal mediation literature.

Yes, and the important thing to realise is that that literature was not considering truncating intercurrent events (our second response picked up on what the papers had been considering).

With truncating events, is the treatment policy strategy even non-identifiable or just nonsense?

I said above that people sometimes describe a truncating event as one that precludes observation of the outcome of interest. This does not seem strong enough.

Truncating events create a sort of structural non-positivity⁵: it’s not just that we don’t observe the outcome of interest after a truncating event; it’s that it doesn’t conceptually exist! I usually think of structural non-positivity as something that affects identification, but that doesn’t get to it.

If we’re interested in the total effect / treatment-policy estimand, we cannot even conceive of the potential outcome – by definition there is none – so treatment policy is an impossible target and we cannot even think about identification! I don’t know what the right word for this is… ‘undefined’?

For treatment-policy estimands, I’m sure what we wrote is correct.

For other intercurrent event strategies, people are sometimes interested in a hypothetical strategy, i.e., if the truncating event never occurred in this population, which is I think what the mediation literature terms a direct effect⁶. This seems to require consideration of the effect of the truncating event on outcome of interest and I don’t really understand how identification works here – something something cross-world counterfactuals?

1. BC Kahan, J Hindley, M Edwards, S Cro, TP Morris. The estimands framework: a primer on the ICH E9(R1) addendum BMJ 2024; 384:e076316 doi:10.1136/bmj-2023-076316

2. www.bmj.com/content/384/bmj-2023-076316/rr

3. JG Young, MJ Stensrud, EJ Tchetgen Tchetgen, MA Hernán. A causal framework for classical statistical estimands in failure-time settings with competing events. Stat Med. 2020; 39(8):1199–1236. doi:10.1002/sim.8471

4. M Janvin M, JG Young, PC Ryalen, MJ Stensrud. Causal inference with recurrent and competing events. Lifetime Data Analysis. 2024; 30(1):59–118. doi:10.1007/s10985-023-09594-8

5. Hey there was a nice pre-print a couple of years back from Paul Zivich revisiting positivity. I should read it again:

PN Zivich, SR Cole, D Westreich. Positivity: Identifiability and estimability. arXiv. 2022; 2207.05010. doi:10.48550/arXiv.2207.05010

6. Please correct me if wrong! I know there are different types of indirect and direct effects and spent ages trying to get to grips with them a few years ago, but alas, that part of my brain seems to have died.