# Estimand

An estimand is a quantity that is to be estimated in a statistical analysis.[1] The term is used to more clearly distinguish the target of inference from the method used to obtain an approximation of this target (i.e., the estimator) and the specific value obtained from a given method and dataset (i.e., the estimate).[2] For instance, a normally distributed random variable $\displaystyle{ X }$ has two defining parameters, its mean $\displaystyle{ \mu }$ and variance $\displaystyle{ \sigma^{2} }$. A variance estimator: $\displaystyle{ s^{2} = \sum_{i=1}^{n} \left. \left( x_{i} - \bar{x} \right)^{2} \right/ (n-1) }$,

yields an estimate of 7 for a data set $\displaystyle{ x = \left\{ 2, 3, 7 \right\} }$; then $\displaystyle{ s^{2} }$ is called an estimator of $\displaystyle{ \sigma^{2} }$, and $\displaystyle{ \sigma^{2} }$ is called the estimand.

## Definition

In relation to an Estimator, an estimand is the outcome of different treatments of interest. It can formally be thought of as any quantity that is to be estimated in any type of experiment.[3]

## Overview

An estimand is closely linked to the purpose or objective of an analysis. It describes what is to be estimated based on the question of interest.[4] This is in contrast to an estimator, which defines the specific rule according to which the estimand is to be estimated. While the estimand will often be free of the specific assumptions e.g. regarding missing data, such assumption will typically have to be made when defining the specific estimator. For this reason, it is logical to conduct sensitivity analyses using different estimators for the same estimand, in order to test the robustness of inference to different assumptions.[5]

According to Ian Lundberg,  Rebecca Johnson, and Brandon M. Stewart, quantitative studies frequently fail to define their estimand.[1] This is problematic because it becomes impossible for the reader to know whether the statistical procedures in a study are appropriate unless they know the estimand.[1]

## Examples

If our question of interest is whether instituting an intervention such as a vaccination campaign in a defined population in a country would reduce the number of deaths in that population in that country, then our estimand will be some measure of risk reduction (e.g. it could be a hazard ratio, or a risk ratio over one year) that would describe the effect of starting a vaccination campaign. We may have data from a clinical trial available to estimate the estimand. In judging the effect on the population level, we will have to reflect that some people may refuse to be vaccinated so that excluding those in the clinical trial from the analysis, who refused to be vaccinated may be inappropriate. Furthermore, we may not know the survival status of all those who were vaccinated, so that assumptions will have to be made in this regard in order to define an estimator.

One possible estimator for obtaining a specific estimate might be a hazard ratio based on a survival analysis that assumes a particular survival distribution conducted on all subjects to whom the intervention was offered, treating those who were lost to follow-up to be right-censored under random censorship. It might be that the trial population differs from the population, on which the vaccination campaign would be conducted, in which case this might also have to be taken into account. An alternative estimator used in a sensitivity analysis might assume that people, who were not followed for their vital status to the end of the trial, may be more likely to have died by a certain amount.

### Epidemiological

In establishing clinical trials, often practitioners want to focus on measuring the effects of their treatments on a population of individuals. These aforementioned clinical settings are built with ideal scenarios, far removed from any intercurrent events. However, as this will often not be the case in reality, variability needs to taken into account during the planning and execution of these trials.[6] By building foundational objectives around the idea of the estimand framework in clinical medicine, it allows practitioners to align the clinical study objective with the study design, endpoint, and analysis to improve study planning and the interpretation of analysis..[7] Essentially meaning that the estimand provides a way to explicitly state how these intercurrent events will be dealt with in achieving the objective of the treatment in question.

## ICH

On October 22, 2014, the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH) produced a final concept paper titled Choosing Appropriate Estimands and Defining Sensitivity Analyses in Clinical Trials as an addendum to their E9 guidance.[8] On 16 October 2017 ICH announced that it had published the draft addendum on defining appropriate estimands for a clinical trial/sensitivity analyses for consultation.[9][10] The final addendum to the ICH E9 guidance was released on November 20, 2019.[11]

By providing a structured framework for translating the objectives of a clinical trial to a matching trial design, conduct and analysis ICH aims to improve discussions between pharmaceutical companies and regulators authorities on drug development programs. The ultimate goal is to make sure that clinical trials provide clearly defined information on the effects of the studied medicines.[10]

## References

1. Lundberg, Ian; Johnson, Rebecca; Stewart, Brandon M. (2021). "What Is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory" (in en). American Sociological Review 86 (3): 532–565. doi:10.1177/00031224211004187. ISSN 0003-1224.
2. Mosteller, F.; Tukey, J. W. (1987). "Data Analysis, including Statistics". The Collected Works of John W. Tukey: Philosophy and Principles of Data Analysis 1965–1986. 4. CRC Press. pp. 601–720 [p. 633]. ISBN 0-534-05101-4.
3. Lawrance, Rachael; Degtyarev, Evgeny; Griffiths, Philip; Trask, Peter; Lau, Helen; D’Alessio, Denise; Griebsch, Ingolf; Wallenstein, Gudrun et al. (24 August 2020). "What is an estimand & how does it relate to quantifying the effect of treatment on patient-reported quality of life outcomes in clinical trials?". Springer. pp. 68. doi:10.1186/s41687-020-00218-5.
4. National Research Council (2010). The Prevention and Treatment of Missing Data in Clinical Trials. Panel on Handling Missing Data in Clinical Trials. Committee on National Statistics, Division of Behavioral and Social Sciences and Education.. Washington, DC: The National Academies Press.
5. International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use (2014). Draft (final) concept paper on choosing appropriate estimands and definining sensitivity analyses in confirmatory clinical trials.
6. Team, Statistical Consultancy. "Estimands – What you need to know" (in en-us).
7. International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (2019). "ICH E9 Addendum on Estimands".