## Monday, April 25, 2022

### Estimands, Estimator, Estimate, and Estimation

With the adoption of ICH E9(R1) "ADDENDUM ON ESTIMANDS AND SENSITIVITY ANALYSIS IN CLINICAL TRIALS TO THE GUIDELINE ON STATISTICAL PRINCIPLES FOR CLINICAL TRIALS",  the word 'Estimand' or 'Estimands' is appearing more and more in the clinical trial protocols, statistical analysis plans, regulatory documents, and publications. Just like the 'intention-to-treat' or 'ITT', the term 'Estimand' starts initially as a bizarre and confusing word, but will eventually be understood by clinical researchers who are working on clinical trials. Along with the word 'estimand', the words 'estimate', 'estimator', and 'estimation' should all be distinguished.

Estimand: A precise description of the treatment effect reflecting the clinical question posed by the trial objective. It summarises at a population-level what the outcomes would be in the same patients under different treatment conditions being compared.
Estimator: A method of analysis to compute an estimate of the estimand using clinical trial data.
Estimate: A numerical value computed by an estimator.

Estimation is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable.

For a clinical trial,
• estimand (trial objective) is the target of estimation (for example, the treatment difference in change from baseline to Week 26 in FEV1)
• estimator is the method of estimation (such as ANCOVA, Logistic regression, Cox regression)
• estimate is the numerical result (such as LS mean difference, odds ratio, hazard ratio and their 95% confidence interval).
Estimate is a rough calculation or guess while estimand is (statistics) that which is being estimated. p-value is from the statistical test is not an estimate (debatable) and naked p-values without the associated estimates should be explained with caution.

The primary estimand (a precise description of the treatment effect reflecting the objective of the clinical trial) assessed effects regardless of treatment discontinuation or rescue interventions.

Using a cake as an example, estimand is the cake we want to make (what you seek), estimator is the recipe for making the cake (how you will get there), and estimate is the final result (what you get) - the cake we actually make - the estimate (final cake) should be close to the estimated (the cake we want to make). We turn our estimand into our estimate by applying an estimator.

In a paper by Little and Lewis (JAMA, 2021) Estimands, Estimators, and Estimates, the estimated and the estimator were compared:
• The estimand compares outcomes that capture the main benefits and risks of treatments
• Estimators should summarize the causal effects of treatments in the sample of individuals in the study
• Estimands should summarize the causal effects of treatments in the target population
• The estimator should provide a valid and unbiased estimate of the study estimand
The paper was in response to the PIONEER 3 study: "Effect of Additional Oral Semaglutide vs Sitagliptin on Glycated Hemoglobin in Adults With Type 2 Diabetes Uncontrolled With Metformin Alone or With Sulfonylurea - The PIONEER 3 Randomized Clinical Trial". In PIONEER 3 trial, the primary estimand is the treatment policy estimand evaluating the treatment effect in change in glycated hemoglobin (HbA1c) from baseline to week 26 for all randomized patients regardless of trial product discontinuation or use of rescue medication. The estimator is to use analysis of covariance with a pattern mixture model using multiple imputation to handle missing data assuming the missing data mechanism is missing at random (MAR). The estimate is the actual value of the treatment differences as expressed as the estimated treatment differences and their 95% confidence intervals: "The 7- and 14-mg/d semaglutide dosages were superior to sitagliptin in reducing HbA1c from baseline at week 26 (estimated treatment differences of –0.3% [95% CI, –0.4% to –0.1%; P < .001] and –0.5% [95% CI, –0.6% to –0.4%; P < .001], respectively)"

In a Sanofi's trial "A randomized, double-blind, placebo-controlled study to evaluate the efficacy and safety of dupilumab in patients with severe steroid-dependent asthma", the primary estimand and the estimator (how the primary efficacy endpoint is analyzed) were discussed:
The primary estimand is the intent-to-treat estimand, the treatment difference between dupilumab and control in the mean percentage reduction of OCS dose at Week 24 while maintaining asthma control of all patients in the ITT population no matter whether the patients discontinue treatment before Week 24 or not. To estimate the estimand, data of patients who permanently discontinue treatment will be incorporated in the primary analysis, and missing data due to patients dropping out from study will be handled by approaches specified in the missing data handling section below.
The primary efficacy endpoint will be analyzed using an analysis of covariance (ANCOVA) model. The model will include the percentage reduction of OCS dose at Week 24 as the response variable, and the treatment groups, optimized OCS dose at baseline, regions (pooled countries), and baseline eosinophil level subgroups (less than 0.15 Giga/L, greater than or equal to 0.15 Giga/L) as covariates. The treatment difference will be tested at the 2-sided significance level of alpha=0.05. Descriptive statistics for the primary efficacy endpoint will be provided, including the number of patients, means, standard errors, and least squares (LS) means by the treatment groups, as well as the difference in LS means and the corresponding 95% confidence interval (CI). The missing data (missing measures at Week 24) will be imputed using pattern mixture model by multiple imputation.

In a paper by Harvard researchers,  "An Applied Researcher’s Guide to Estimating Effects From Multisite Individually Randomized Trials: Estimands, Estimators, and Estimates", the following conclusions are given:

"Defining an estimand is critical to the design, analysis, and interpretation of a multisite RCT. Even when one is interested in estimating an average treatment effect, careful consideration must be given to defining the target of inference. For example, the choice of estimand influences what formula is appropriate when conducting power calculations - yet many write-ups of power calculation are ambiguous or silent with regards to the estimand chosen. relatedly, registering studies and creating analysis plans are becoming the norm when conducting RCTs, yet even newly created registries do not require an estimand be defined. Consequently, readers of an analysis plan are left to assume an implied estimand based on the power calculation formula used and/or estimator selected. Similarly, many scholarly articles and reports do not state a target of inference, making it difficult to assess whether the chosen estimator is appropriate and obscuring the goal of the research. We recommend defining the estimand(s) early in the research process and clearly stating them in important products."