# Layman’s abstract for Pharmaceutical Statistics article: Identifying treatment effects using trimmed means when data are missing not at random

Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

The article featured today is from Pharmaceutical Statistics, with the abstract now available to read here.

Identifying treatment effects using trimmed means when data are missing not at randomPharmaceutical Statistics20211– 13https://doi.org/10.1002/pst.2147

There exist few statistical methods that can identify treatment effects in clinical trials with outcomes that are missing not at random (MNAR). This is unfortunate as the MNAR scenario is commonplace – e.g. when patients discontinue from a clinical trial because their health condition is not improving.

Popular approaches for MNAR dropouts in clinical trials assume the missing endpoints are distributed as the observed outcomes in the reference arm or as the baseline measurements. Not only is it overconfident to claim to know the exact distribution of these missing endpoints, furthermore, this assumption generally leads to a more conservative estimate of the treatment effect, in spite of the fact that MNAR dropouts could create bias in either direction.

In this paper, we demonstrate how a novel approach using trimmed means[1] can overcome these limitations in the MNAR setting. We mathematically prove that if your treatment effect is additive and the missing outcomes come from the poor end of the distribution, then the causal effect of treatment can be identified by the approach and unbiasedly estimated. The following animation illustrates this:

Without missing data, we would simply calculate the means in each arm of the study and subtract them to estimate the treatment effect. However, some observations go missing (10% in the experimental arm and 20% in the control arm). Nevertheless, we can leverage the fact that these outcomes, had they been observed, would have fallen below a common quantile from both distributions. Therefore, when we remove all data below the chosen quantile, the difference in trimmed means is equivalent to the difference we would have observed notwithstanding the missing data.

Having patients with poor outcomes leave a clinical trial early has historically been seen as a nuisance. This work shows how one can actually exploit this problem to identify the treatment effect.

References

[1] Permutt T, Li F. Trimmed means for symptom trials with dropoutsPharm Stat. 2017;16(1):20–28.