Estimands, Estimators, and Estimates

INTRODUCTION

This JAMA Guide to Statistics and Methods takes a look at estimands, estimators, and estimates in the context of randomized clinical trials and suggests several qualities that make for good estimands, including their scope, ability to summarize treatment effects, external validity, and ability to provide good estimates.

The primary goal of most randomized clinical trials (RCTs) is to draw conclusions about the effect of a treatment in a specific population of patients. The true effect of the intervention, termed the estimand, is estimated with the data acquired in the trial, subject to limitations associated with variations in adherence to treatment, patients being lost to follow-up, and data quality.

The choice of estimand and associated target population should reflect the goals of the trial and can vary according to who designed or sponsored the study, who will use the results of the study, and the motivating scientific question. In the PIONEER 3 trial,¹ investigators compared 3 doses of oral semaglutide with sitagliptin, added to background therapy, in adults with type 2 diabetes. The primary end point was the change in glycated hemoglobin (HbA_1c). The trial design considered 2 estimands for summarizing treatment effect, termed the treatment policy estimand and the trial product estimand.

EXPLANATION OF THE CONCEPT

What Is an Estimand?

The true effect of the intervention is the estimand. The estimand is a target quantity (ie, what the study aspires to measure). It is a summary of patient outcomes, such as a difference in mean outcomes or a difference in mortality rates in the population, comparing patients who receive the investigational treatment with those who do not. Estimands can describe both therapeutic benefits and adverse effects; thus, more than 1 estimand may be needed to capture fully the results of a study.

Trial data provide only estimates of trial estimands because trial participants are sampled from the population and outcomes are not always observed for all randomized participants, and because there are practical limitations in clinical trial execution, such as participants not following the prescribed protocol or not completing the study. An estimator, in contrast to an estimand, is a formula or algorithm used to estimate the target quantity from the clinical trial data, such as the difference in sample means between 2 treatment groups, or the Kaplan-Meier estimator of a survival curve. Statistical inference for an estimand requires a choice of the estimator and a measure of its precision. Typical methods of statistical inference are hypothesis tests, confidence intervals, and posterior credibility intervals in a bayesian analysis. The estimate is the numeric value obtained when the estimator is applied to the actual data from the trial.

Why Is the Choice of Estimand Important?

The optimal choices of estimands and associated target populations are determined by ...