Power Analysis of Trials with Multilevel Data: 1st Edition (Hardback) book cover

Power Analysis of Trials with Multilevel Data

1st Edition

By Mirjam Moerbeek, Steven Teerenstra

Chapman and Hall/CRC

288 pages | 48 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781498729895
pub: 2015-07-07
SAVE ~$19.59
eBook (VitalSource) : 9780429154300
pub: 2015-07-01
from $46.98

FREE Standard Shipping!


Power Analysis of Trials with Multilevel Data covers using power and sample size calculations to design trials that involve nested data structures. The book gives a thorough overview of power analysis that details terminology and notation, outlines key concepts of statistical power and power analysis, and explains why they are necessary in trial design. It guides you in performing power calculations with hierarchical data, which enables more effective trial design.

The authors are leading experts in the field who recognize that power analysis has attracted attention from applied statisticians in social, behavioral, medical, and health science. Their book supplies formulae that allow statisticians and researchers in these fields to perform calculations that enable them to plan cost-efficient trials. The formulae can also be applied to other sciences.

Using power analysis in trial design is increasingly important in a scientific community where experimentation is often expensive, competition for funding among researchers is intense, and agencies that finance research require proposals to give thorough justification for funding. This handbook shows how power analysis shapes trial designs that have high statistical power and low cost, using real-life examples.

The book covers multiple types of trials, including cluster randomized trials, multisite trials, individually randomized group treatment trials, and longitudinal intervention studies. It also offers insight on choosing which trial is best suited to a given project. Power Analysis of Trials with Multilevel Data helps you craft an optimal research design and anticipate the necessary sample size of data to collect to give your research maximum effectiveness and efficiency.


"I enjoyed reviewing the new CRC Press/Chapman Hall book entitled Power Analysis of Trials with Multilevel Data, by Mirjam Moerbeek and Steven Teerenstra. This book addresses a critical need in the scientific community for a well-organized, easily accessible guide to performing power analysis and computing required sample sizes for randomized trials embedded in multilevel study designs, where observations of interest are nested within higher level units (e.g. patients within clinics or repeated measures on participants). …

This book effectively compiles all the published literature on this specialized topic, putting it in one place for researchers who design these types of studies and could benefit from a concise and practical resource on this important aspect of study design. The two Dutch authors are experts in this area and are very well-equipped to provide more general education and practical advice on this topic. Multilevel study designs in which power analysis methods for independent observations do not apply are quite common, but no prior books have attempted to organize all the possible power analysis approaches for these types of studies into a single reference. …

In sum, this will be a very useful book for researchers, statisticians, and consultants responsible for designing various types of randomized trials in multilevel settings. My minor quibbles are far outweighed by the important contributions that this single resource on power analysis in multilevel designs will make to the scientific community."

—Brady T. West, University of Michigan, Biometrical Journal, May 2017

"…the appearance of the book, Power Analysis of Trials with Multilevel Data, is well timed…Another nice feature of the book is the example power analyses that conclude most chapters (and sometimes appear earlier in chapters as well). The authors have done a very good job finding articles in the literature that use a particular design, extracting relevant parameters from those articles, and then illustrating how to use those parameters to plan a replication study…I think this book deserves a place on the bookshelf of both researchers who plan experimental studies and statisticians who advise them."

—Christopher H. Rhoads, University of Connecticut, The American Statistician, November 2016

Table of Contents

List of figures

List of tables




Hierarchical data structures

Research design

Power analysis for experimental research

Aim and contents of the book

Multilevel statistical models

The basic two-level model

Estimation and hypothesis test

Intraclass correlation coefficient

Multilevel models for dichotomous outcomes

More than two levels of nesting

Software for multilevel analysis

Concepts of statistical power analysis

Background of power analysis

Types of power analysis

Timing of power analysis

Methods for power analysis

Robustness of power and sample size calculations

Procedure for a priori power analysis

The optimal design of experiments

Sample size and precision analysis

Sample size and accuracy of parameter estimates

Cluster randomized trials


Multilevel model

Sample size calculations for continuous outcomes

Sample size calculations for dichotomous outcomes

An example

Improving statistical power in cluster randomized trials

Inclusion of covariates

Minimization, matching, pre-stratification

Taking repeated measurements

Crossover in cluster randomized trials

Stepped wedge designs

Multisite trials


Multilevel model

Sample size calculations for continuous outcomes

Sample size calculations for dichotomous outcomes

An example

Pseudo cluster randomized trials


Multilevel model

Sample size calculations for continuous outcomes

Sample size calculations for binary outcomes

An example

Individually randomized group treatment trials


Multilevel model

Sample size calculations for continuous outcomes

Sample size calculations for dichotomous outcomes

An example

Longitudinal intervention studies


Multilevel model

Sample size calculations for continuous outcomes

Sample size calculations for dichotomous outcomes

The effect of drop-out on statistical power

An example

Extensions: three levels of nesting and factorial designs


Three-level cluster randomized trials

Multisite cluster randomized trials

Repeated measures in cluster randomized trials and multisite trials

Factorial designs

The problem of unknown intraclass correlation coefficients

Estimates from previous research

Sample size re-estimation

Bayesian sample size calculation

Maximin optimal designs

Computer software for power calculations


Computer program SPA-ML


Author Index

Subject Index

About the Authors

Mirjam Moerbeek is an associate professor at Utrecht University, the Netherlands. She obtained her master’s degree (cum laude) in biometrics from Wageningen Agricultural University in 1996 and her PhD in applied statistics from Maastricht University in 2000. She has received prestigious research grants from the Netherlands’ Organisation for Scientific Research (NWO) as well as grants to hire PhD students. Her research interests are statistical power analysis and optimal experimental design, especially for hierarchical and survival data. She was involved in organizing a colloquium and class on cost-efficient and optimal designs for the Royal Netherlands Academy of Arts and Sciences (KNAW) and is a joint organizer of the biennial International Conference on Multilevel Analysis.

Steven Teerenstra received his MSc and PhD in mathematics at Radboud University in 1996 and 2004, respectively, as well as his MSc in theoretical physics in 2006. He is currently a biostatistician at Radboud University Nijmegen Medical Center, involved in research, consultation and conduct of cluster randomized trials. He is appointed assessor of statistics and methodology at the Dutch Medicines Evaluation Board and a member of the Biostatistics Working Party at the European Medicines Agency.

About the Series

Chapman & Hall/CRC Interdisciplinary Statistics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General