Estimand

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An estimand is a quantity that is to be estimated in a statistical analysis. [1] The term is used to 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 has two defining parameters, its mean and variance . A variance estimator:

Contents

,

yields an estimate of 7 for a data set ; then is called an estimator of , and is called the estimand.

Definition

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

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 is not possible 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 from the analysis those in the clinical trial who refuse 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 be 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]

Related Research Articles

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule, the quantity of interest and its result are distinguished. For example, the sample mean is a commonly used estimator of the population mean.

<span class="mw-page-title-main">Meta-analysis</span> Statistical method that summarizes data from multiple sources

A meta-analysis is a statistical analysis that combines the results of multiple scientific studies. Meta-analyses can be performed when there are multiple scientific studies addressing the same question, with each individual study reporting measurements that are expected to have some degree of error. The aim then is to use approaches from statistics to derive a pooled estimate closest to the unknown common truth based on how this error is perceived. It is thus a basic methodology of Metascience. Meta-analytic results are considered the most trustworthy source of evidence by the evidence-based medicine literature.

Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their work. Understanding the source of statistical bias can help to assess whether the observed results are close to actuality. Issues of statistical bias has been argued to be closely linked to issues of statistical validity.

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk, as an estimate of the true MSE.

In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis when a specific alternative hypothesis is true. It is commonly denoted by , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability of making a type II error by wrongly failing to reject the null hypothesis decreases.

In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event happening. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses. The cluster of data-analysis methods concerning effect sizes is referred to as estimation statistics.

In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. In addition, if the random variable has a normal distribution, the sample covariance matrix has a Wishart distribution and a slightly differently scaled version of it is the maximum likelihood estimate. Cases involving missing data, heteroscedasticity, or autocorrelated residuals require deeper considerations. Another issue is the robustness to outliers, to which sample covariance matrices are highly sensitive.

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements. In estimation theory, two approaches are generally considered:

In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable in the input dataset and the output of the (linear) function of the independent variable.

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly.

In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in the regression model. Least squares and weighted least squares may need to be more statistically efficient and prevent misleading inferences. GLS was first described by Alexander Aitken in 1935.

Bootstrapping is any test or metric that uses random sampling with replacement, and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods.

In statistics, the bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more.

The Heckman correction is a statistical technique to correct bias from non-randomly selected samples or otherwise incidentally truncated dependent variables, a pervasive issue in quantitative social sciences when using observational data. Conceptually, this is achieved by explicitly modelling the individual sampling probability of each observation together with the conditional expectation of the dependent variable. The resulting likelihood function is mathematically similar to the tobit model for censored dependent variables, a connection first drawn by James Heckman in 1974. Heckman also developed a two-step control function approach to estimate this model, which avoids the computational burden of having to estimate both equations jointly, albeit at the cost of inefficiency. Heckman received the Nobel Memorial Prize in Economic Sciences in 2000 for his work in this field.

Clinical trials are medical research studies conducted on human subjects. The human subjects are assigned to one or more interventions, and the investigators evaluate the effects of those interventions. The progress and results of clinical trials are analyzed statistically.

A glossary of terms used in clinical research.

A confirmatory trial is an adequately controlled trial where hypotheses are stated in advance and evaluated according to a protocol. This type of trial may be implemented when it is necessary to provide additional or firm evidence of efficacy or safety.

In statistics and econometrics, the first-difference (FD) estimator is an estimator used to address the problem of omitted variables with panel data. It is consistent under the assumptions of the fixed effects model. In certain situations it can be more efficient than the standard fixed effects estimator.

Guidances for statistics in regulatory affairs refers to specific documents or guidelines that provide instructions, recommendations, and standards pertaining to the application of statistical methodologies and practices within the regulatory framework of industries such as pharmaceuticals and medical devices. These guidances serve as a reference for statisticians, researchers, and professionals involved in designing, conducting, analyzing, and reporting studies and trials in compliance with regulatory requirements. These documents embody the prevailing perspectives of regulatory agencies on specific subjects. It is worth noting that in the United States, the term "Guidances" is used, while in Europe, the term "Guidelines" is employed.

In experiments, a spillover is an indirect effect on a subject not directly treated by the experiment. These effects are useful for policy analysis but complicate the statistical analysis of experiments.

References

  1. 1 2 3 Lundberg, Ian; Johnson, Rebecca; Stewart, Brandon M. (2021). "What Is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory". American Sociological Review. 86 (3): 532–565. doi:10.1177/00031224211004187. ISSN   0003-1224. S2CID   235405612.
  2. ↑ Mosteller, F.; Tukey, J. W. (1987) [1968]. "Data Analysis, including Statistics". The Collected Works of John W. Tukey: Philosophy and Principles of Data Analysis 1965–1986. Vol. 4. CRC Press. pp. 601–720 [p. 633]. ISBN   0-534-05101-4 – via Google Books.
  3. ↑ Lawrance, Rachael; Degtyarev, Evgeny; Griffiths, Philip; Trask, Peter; Lau, Helen; D’Alessio, Denise; Griebsch, Ingolf; Wallenstein, Gudrun; Cocks, Kim; Rufibach, Kaspar (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?". Journal of Patient-Reported Outcomes. Springer. 4 (1): 68. doi:10.1186/s41687-020-00218-5. PMC   7445213 . PMID   32833083.
  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". www.quanticate.com. Retrieved 23 January 2021.
  7. ↑ "Estimand Framework: What is it and Why You Need it in Your Clinical Trial". ERT. 4 March 2020. Retrieved 23 January 2021.
  8. ↑ "Choosing Appropriate Estimands and Defining Sensitivity Analyses in Clinical Trials" (PDF). Oct 23, 2015. Retrieved July 1, 2015.
  9. ↑ "ICH releases finalised, draft Guidelines and publishes working party membership for first time". Oct 16, 2017. Retrieved July 6, 2018.
  10. 1 2 "Estimands and Sensitivity Analysis in Clinical Trials E9(R1) Current Step 2 version" (PDF). Jun 16, 2017. Retrieved July 6, 2018.
  11. ↑ International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (2019). "ICH E9 Addendum on Estimands" (PDF). ICH official website. Retrieved December 12, 2019.
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