Camila Olarte Parra, Rhian Daniel and myself have just released a pre-print on arXiv (now published in Statistics in Biopharmaceutical Research) in detailing recent work looking at statistical methods targeting so called hypothetical estimands in clinical trials. The ICH E9 addendum on estimands is having a widespread impact on the way clinical trials are planned and analysed. One of the *strategies *described by the addendum for handling so called intercurrent events is the hypothetical strategy. This is where one hypothesizes of a way in which the trial could be modified such that the intercurrent event in question would not take place. For example, in trials where patients may receive a rescue medication, we could conceive of a trial where such medication were not made available. The goal of inference is then what treatment effect we would have seen in such a modified trial.

In the paper, building on work by others (e.g. Lipkovich et al 2020), we show how causal inference concepts and methods can be used to define and estimate hypothetical estimands. Currently estimation of estimands which use the hypothetical strategy is predominantly carried out using missing data methods such as mixed models and multiple imputation. To do so, any outcome measurements available after the intercurrent event being dealt with using the hypothetical strategy are deleted/ignored, and an analysis using these methods is performed, assuming the resulting missing data are missing at random (MAR). We set out to see how estimation of hypothetical estimands would proceed using the language and machinery from causal inference.

In this post I’ll highlight a few of the things the paper covers.

**Equivalence between missing data methods and causal inference methods**

In the paper we show that that application of missing data methods, such as mixed models or multiple imputation, are identical to certain implementations of the G-formula/G-computation approach from the causal inference literature. Similarly, and more obviously, inverse probability of treatment weighted estimators from causal inference are identical to certain inverse probability of missing weighted estimators from the missing data literature. The equivalence of certain implementations of the methods from these two literatures may be helpful for those more familiar with one set or the other. It certainly was for me personally, having been more familiar with missing data methods than causal inference methods. Understanding the equivalences between them I think is also helpful because it enables one to think about the assumptions being used for estimation defined either using causal inference concepts (e.g. potential outcomes and directed acyclic graphs (DAGs)) or in terms of missing data assumptions (like MAR).

**Using data after intercurrent events handled by the hypothetical strategy in the analysis**

For estimating hypothetical estimands currently the standard advice is that you only use outcome data in the analysis from before intercurrent events occur (if the intercurrent event is handled using the hypothetical strategy). We show that in fact data after the intercurrent event can be used in the analysis when using the G-formula approach, provided the modelling accounts for past occurrence of the intercurrent event appropriately. Using outcome data after the occurrence of intercurrent events being handled by the hypothetical strategy offers the potential for more precise estimates, but requires stronger modelling assumptions.

**Understanding MAR using causal diagrams**

We make use of DAGs and single-world intervention graphs to show that if data after the intercurrent event handled using the hypothetical strategy are not measured or are measured but not used in the analysis, the resulting missing hypothetical outcomes are MAR if all common causes of the intercurrent event and final outcome are adjusted for. Crucially, commonly adopted approaches which fit mixed models only to repeated measures of the outcome do not do this. As such, the MAR assumption being assumed in these analyses will not hold if there exist, as typically there does, additional time-varying variables which affect the occurrence of the intercurrent event and also the final outcome.

**Deterministic intercurrent events and extrapolation**

Sometimes the occurrence of the intercurrent event is determined based on clinical criteria. An example is the case of rescue medication, which might be initiated for a patient with diabetes if their diabetes control worsens according to a biomarker such as fasting plasma glucose reaching some specified threshold. If patients in the trial receive rescue strictly if and only if they reach such a threshold, this leads to a violation of the so called positivity assumption. The impact of this is that estimation of the hypothetical estimand is not possible using inverse probability weighted approaches. Approaches such as G-formula, mixed models, or multiple imputation are still feasible, but the validity of their estimates relies on extrapolation beyond the data, since they must predict what would have happened to the patients who received rescue had they not received rescue. Information about these outcomes can only come from patients who did not get rescued, but by definition these patients are different to those who did get rescued, in terms of their fasting plasma glucose levels. Estimation using these methods in such cases is thus more heavily reliant on (untestable) modelling assumptions in a way which is perhaps not fully appreciated.

This work was supported by a UK Medical Research Council grant (MR/T023953/1).