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When observations are independent, formulae and software are readily available to plan and design studies of appropriate size and power to detect important associations. When observations are correlated or clustered, results obtained from…

Applications · Statistics 2021-03-15 David M. Thompson

There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying…

Methodology · Statistics 2023-07-20 Samuel I. Watson , Alan Girling , Karla Hemming

Marginal structural models fit via inverse probability of treatment weighting are commonly used to control for confounding when estimating causal effects from observational data. When planning a study that will be analyzed with marginal…

Applications · Statistics 2020-03-16 Bonnie E. Shook-Sa , Michael G. Hudgens

Multivariate outcomes are common in pragmatic cluster randomized trials. While sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. In this…

Methodology · Statistics 2022-12-05 Kendra Davis-Plourde , Monica Taljaard , Fan Li

We describe how to calculate standard errors for A/B tests that include clustered data, ratio metrics, and/or covariate adjustment. We may do this for power analysis/sample size calculations prior to running an experiment using historical…

Methodology · Statistics 2024-06-12 Tim Hesterberg , Ben Knight

Mixtures of linear mixed models are widely used for modelling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients…

Methodology · Statistics 2025-11-25 Lucas Kock , Nadja Klein , David J. Nott

Composite endpoints are increasingly used in clinical trials to capture treatment effects across multiple or hierarchically ordered outcomes. Although inference procedures based on win statistics, such as the win ratio, win odds, and net…

Methodology · Statistics 2025-10-28 Xi Fang , Zhiqiang Cao , Fan Li

In randomized trials, appropriately adjusting for baseline variables and short-term outcomes can lead to increased precision and reduced sample size. We examine the impact of such adjustment in group sequential designs, i.e., designs with…

Methodology · Statistics 2019-10-28 Tianchen Qian , Michael Rosenblum , Huitong Qiu

Paired cluster-randomized experiments (pCRTs) are common across many disciplines because there is often natural clustering of individuals, and paired randomization can help balance baseline covariates to improve experimental precision.…

Methodology · Statistics 2024-07-03 Charlotte Z. Mann , Adam C. Sales , Johann A. Gagnon-Bartsch

The Regression Discontinuity Design (RDD) is a quasi-experimental design that estimates the causal effect of a treatment when its assignment is defined by a threshold value for a continuous assignment variable. The RDD assumes that subjects…

Applications · Statistics 2020-03-27 Federico Ricciardi , Silvia Liverani , Gianluca Baio

Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they…

Methodology · Statistics 2017-10-20 Abby Flynt , Nema Dean

A stepped wedge cluster randomized trial is a type of longitudinal cluster design that sequentially switches clusters to intervention over time until all clusters are treated. While the traditional posttest-only parallel design requires…

Applications · Statistics 2021-01-05 Fan Li

Adaptive sample size re-estimation, early stopping, and trial re-design at interim analyses can reduce expected sample sizes in randomised trials. Cluster randomised trials, in which groups of participants are randomly allocated to…

Methodology · Statistics 2026-03-09 Samuel I. Watson , James Martin

Adaptive approaches, allowing for more flexible trial design, have been proposed for individually randomized trials to save time or reduce sample size. However, adaptive designs for cluster-randomized trials in which groups of participants…

Methodology · Statistics 2022-01-10 Junwei Shen , Shirin Golchi , Erica E. M. Moodie , David Benrimoh

When designing experimental studies with human participants, experimenters must decide how many trials each participant will complete, as well as how many participants to test. Most discussion of statistical power (the ability of a study…

Neurons and Cognition · Quantitative Biology 2021-08-30 Daniel H. Baker , Greta Vilidaite , Freya A. Lygo , Anika K. Smith , Tessa R. Flack , Andre D. Gouws , Timothy J. Andrews

Hybrid studies allow investigators to simultaneously study an intervention effectiveness outcome and an implementation research outcome. In particular, type 2 hybrid studies support research that places equal importance on both outcomes…

Variance reduction for causal inference in the presence of network interference is often achieved through either outcome modeling, typically analyzed under unit-randomized Bernoulli designs, or clustered experimental designs, typically…

Methodology · Statistics 2026-01-19 Matthew Eichhorn , Samir Khan , Johan Ugander , Christina Lee Yu

This paper studies inference in cluster randomized trials where treatment status is determined according to a "matched pairs" design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the…

Econometrics · Economics 2025-08-14 Yuehao Bai , Jizhou Liu , Azeem M. Shaikh , Max Tabord-Meehan

Educational research often studies subjects that are in naturally clustered groups of classrooms or schools. When designing a randomized experiment to evaluate an intervention directed at teachers, but with effects on teachers and their…

Applications · Statistics 2009-08-17 Brenda Jenney , Sharon Lohr

In repeated measures factorial designs involving clustered units, parametric methods such as linear mixed effects models are used to handle within subject correlations. However, assumptions of these parametric models such as continuity and…

Methodology · Statistics 2021-04-13 Solomon W. Harrar , Yue Cui
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