Randomized experiment

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Flowchart of four phases (enrollment, intervention allocation, follow-up, and data analysis) of a parallel randomized trial of two groups, modified from the CONSORT 2010 Statement Flowchart of Phases of Parallel Randomized Trial - Modified from CONSORT 2010.png
Flowchart of four phases (enrollment, intervention allocation, follow-up, and data analysis) of a parallel randomized trial of two groups, modified from the CONSORT 2010 Statement

In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in experimental design and in survey sampling.

Contents

Overview

In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization.

Randomized experimentation is not haphazard. Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers). Randomization also produces ignorable designs, which are valuable in model-based statistical inference, especially Bayesian or likelihood-based. In the design of experiments, the simplest design for comparing treatments is the "completely randomized design". Some "restriction on randomization" can occur with blocking and experiments that have hard-to-change factors; additional restrictions on randomization can occur when a full randomization is infeasible or when it is desirable to reduce the variance of estimators of selected effects.

Randomization of treatment in clinical trials pose ethical problems. In some cases, randomization reduces the therapeutic options for both physician and patient, and so randomization requires clinical equipoise regarding the treatments.

Online randomized controlled experiments

Web sites can run randomized controlled experiments [2] to create a feedback loop. [3] Key differences between offline experimentation and online experiments include: [3] [4]

History

A controlled experiment appears to have been suggested in the Old Testament's Book of Daniel. King Nebuchadnezzar proposed that some Israelites eat "a daily amount of food and wine from the king's table." Daniel preferred a vegetarian diet, but the official was concerned that the king would "see you looking worse than the other young men your age? The king would then have my head because of you." Daniel then proposed the following controlled experiment: "Test your servants for ten days. Give us nothing but vegetables to eat and water to drink. Then compare our appearance with that of the young men who eat the royal food, and treat your servants in accordance with what you see". (Daniel 1, 12– 13). [8] [9]

Randomized experiments were institutionalized in psychology and education in the late eighteen-hundreds, following the invention of randomized experiments by C. S. Peirce. [10] [11] [12] [13] Outside of psychology and education, randomized experiments were popularized by R.A. Fisher in his book Statistical Methods for Research Workers , which also introduced additional principles of experimental design.

Statistical interpretation

The Rubin Causal Model provides a common way to describe a randomized experiment. While the Rubin Causal Model provides a framework for defining the causal parameters (i.e., the effects of a randomized treatment on an outcome), the analysis of experiments can take a number of forms. The model assumes that there are two potential outcomes for each unit in the study: the outcome if the unit receives the treatment and the outcome if the unit does not receive the treatment. The difference between these two potential outcomes is known as the treatment effect, which is the causal effect of the treatment on the outcome. Most commonly, randomized experiments are analyzed using ANOVA, student's t-test, regression analysis, or a similar statistical test. The model also accounts for potential confounding factors, which are factors that could affect both the treatment and the outcome. By controlling for these confounding factors, the model helps to ensure that any observed treatment effect is truly causal and not simply the result of other factors that are correlated with both the treatment and the outcome.

The Rubin Causal Model is a useful a framework for understanding how to estimate the causal effect of the treatment, even when there are confounding variables that may affect the outcome. This model specifies that the causal effect of the treatment is the difference in the outcomes that would have been observed for each individual if they had received the treatment and if they had not received the treatment. In practice, it is not possible to observe both potential outcomes for the same individual, so statistical methods are used to estimate the causal effect using data from the experiment.

Empirical evidence that randomization makes a difference

Empirically differences between randomized and non-randomized studies, [14] [ needs update ] and between adequately and inadequately randomized trials have been difficult to detect. [15] [16]

See also

Related Research Articles

<span class="mw-page-title-main">Design of experiments</span> Design of tasks

The design of experiments, also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.

<span class="mw-page-title-main">Experiment</span> Scientific procedure performed to validate a hypothesis

An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experimental studies.

<span class="mw-page-title-main">Randomized controlled trial</span> Form of scientific experiment

A randomized controlled trial is a form of scientific experiment used to control factors not under direct experimental control. Examples of RCTs are clinical trials that compare the effects of drugs, surgical techniques, medical devices, diagnostic procedures or other medical treatments.

<span class="mw-page-title-main">Field experiment</span> Experiment conducted outside the laboratory

Field experiments are experiments carried out outside of laboratory settings.

Internal validity is the extent to which a piece of evidence supports a claim about cause and effect, within the context of a particular study. It is one of the most important properties of scientific studies and is an important concept in reasoning about evidence more generally. Internal validity is determined by how well a study can rule out alternative explanations for its findings. It contrasts with external validity, the extent to which results can justify conclusions about other contexts. Both internal and external validity can be described using qualitative or quantitative forms of causal notation.

External validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can generalize or transport to other situations, people, stimuli, and times. Generalizability refers to the applicability of a predefined sample to a broader population while transportability refers to the applicability of one sample to another target population. In contrast, internal validity is the validity of conclusions drawn within the context of a particular study.

<span class="mw-page-title-main">Confounding</span> Variable or factor in causal inference

In causal inference, a confounder is a variable that influences both the dependent variable and independent variable, causing a spurious association. Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations. The existence of confounders is an important quantitative explanation why correlation does not imply causation. Some notations are explicitly designed to identify the existence, possible existence, or non-existence of confounders in causal relationships between elements of a system.

The Rubin causal model (RCM), also known as the Neyman–Rubin causal model, is an approach to the statistical analysis of cause and effect based on the framework of potential outcomes, named after Donald Rubin. The name "Rubin causal model" was first coined by Paul W. Holland. The potential outcomes framework was first proposed by Jerzy Neyman in his 1923 Master's thesis, though he discussed it only in the context of completely randomized experiments. Rubin extended it into a general framework for thinking about causation in both observational and experimental studies.

<span class="mw-page-title-main">Observational study</span> Study with uncontrolled variable of interest

In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints. One common observational study is about the possible effect of a treatment on subjects, where the assignment of subjects into a treated group versus a control group is outside the control of the investigator. This is in contrast with experiments, such as randomized controlled trials, where each subject is randomly assigned to a treated group or a control group. Observational studies, for lacking an assignment mechanism, naturally present difficulties for inferential analysis.

<span class="mw-page-title-main">A/B testing</span> Experiment methodology

A/B testing is a user experience research methodology. A/B tests consist of a randomized experiment that usually involves two variants, although the concept can be also extended to multiple variants of the same variable. It includes application of statistical hypothesis testing or "two-sample hypothesis testing" as used in the field of statistics. A/B testing is a way to compare multiple versions of a single variable, for example by testing a subject's response to variant A against variant B, and determining which of the variants is more effective.

<span class="mw-page-title-main">Quasi-experiment</span> Empirical interventional study

A quasi-experiment is an empirical interventional study used to estimate the causal impact of an intervention on target population without random assignment. Quasi-experimental research shares similarities with the traditional experimental design or randomized controlled trial, but it specifically lacks the element of random assignment to treatment or control. Instead, quasi-experimental designs typically allow the researcher to control the assignment to the treatment condition, but using some criterion other than random assignment.

The average treatment effect (ATE) is a measure used to compare treatments in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the difference in mean (average) outcomes between units assigned to the treatment and units assigned to the control. In a randomized trial, the average treatment effect can be estimated from a sample using a comparison in mean outcomes for treated and untreated units. However, the ATE is generally understood as a causal parameter that a researcher desires to know, defined without reference to the study design or estimation procedure. Both observational studies and experimental study designs with random assignment may enable one to estimate an ATE in a variety of ways.

In the statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment, policy, or other intervention by accounting for the covariates that predict receiving the treatment. PSM attempts to reduce the bias due to confounding variables that could be found in an estimate of the treatment effect obtained from simply comparing outcomes among units that received the treatment versus those that did not. Paul R. Rosenbaum and Donald Rubin introduced the technique in 1983.

An N of 1 trial (N=1) is a multiple crossover clinical trial, conducted in a single patient. A trial in which random allocation is used to determine the order in which an experimental and a control intervention are given to a single patient is an N of 1 randomized controlled trial. Some N of 1 trials involve randomized assignment and blinding, but the order of experimental and control interventions can also be fixed by the researcher.

Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment. The goal of matching is to reduce bias for the estimated treatment effect in an observational-data study, by finding, for every treated unit, one non-treated unit(s) with similar observable characteristics against which the covariates are balanced out. By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding. Propensity score matching, an early matching technique, was developed as part of the Rubin causal model, but has been shown to increase model dependence, bias, inefficiency, and power and is no longer recommended compared to other matching methods. A simple, easy-to-understand, and statistically powerful method of matching known as Coarsened Exact Matching or CEM.

Causal analysis is the field of experimental design and statistics pertaining to establishing cause and effect. Typically it involves establishing four elements: correlation, sequence in time, a plausible physical or information-theoretical mechanism for an observed effect to follow from a possible cause, and eliminating the possibility of common and alternative ("special") causes. Such analysis usually involves one or more artificial or natural experiments.

Principal stratification is a statistical technique used in causal inference when adjusting results for post-treatment covariates. The idea is to identify underlying strata and then compute causal effects only within strata. It is a generalization of the local average treatment effect (LATE) in the sense of presenting applications besides all-or-none compliance. The LATE method, which was independently developed by Imbens and Angrist (1994) and Baker and Lindeman (1994) also included the key exclusion restriction and monotonicity assumptions for identifiability. For the history of early developments see Baker, Kramer, Lindeman.

Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed. The study of why things occur is called etiology, and can be described using the language of scientific causal notation. Causal inference is said to provide the evidence of causality theorized by causal reasoning.

Causal analysis is the field of experimental design and statistical analysis pertaining to establishing cause and effect. Exploratory causal analysis (ECA), also known as data causality or causal discovery is the use of statistical algorithms to infer associations in observed data sets that are potentially causal under strict assumptions. ECA is a type of causal inference distinct from causal modeling and treatment effects in randomized controlled trials. It is exploratory research usually preceding more formal causal research in the same way exploratory data analysis often precedes statistical hypothesis testing in data analysis

In the design of experiments, a sample ratio mismatch (SRM) is a statistically significant difference between the expected and actual ratios of the sizes of treatment and control groups in an experiment. Sample ratio mismatches also known as unbalanced sampling often occur in online controlled experiments due to failures in randomization and instrumentation.

References

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