POWER AND

PRECISION

A computer program forstatistical power analysisand confidence intervals

“Stunning in its clarity and efficiency.”

— Dr. Sal Manuzza, New York University School of Medicine

Means � Proportions � Correlations � ANOVA � Regression � Logistic � Su­rvival � Cluster

Power Analysis forCluster-randomized Trials

SAVE MONEY!!

GET THE BIGPICTURE IN SECONDS!!

WORK INTERACTIVELY

This program will automatically find the most cost-effective number of persons percluster. This number, based on a wide array of factors and unique to each study, can easilyreduce the study cost by 50% or more as compared with a less cost-effective design.

Create a graph that shows power as a function of the number of clusters, the number of persons per cluster, the ICC, the effect size, the covariates, and more—in justseconds—and get a clear picture of each factor’simpact in your study.

� � �F I N D O U T H O WWORK IN MINUTES RATHER THAN HOURS!

Enter the effect sizeand the ICC

Enter the cost per clusterand the cost per subject

The program computes the most cost-effective number of clustersand individuals needed to yield thedesired power.

The program displaysthe cost and power

CREATE a report which explains the studydesign and assumptions.

VERIFY that all elements of the study havebeen specified correctly.

USE the report as a teaching tool, and as anexample of how a power analysis should bedescribed.

EDIT the report and include it in your study planor grant application.

Suppose you are planning a trial that will enroll patients within hospitals, and will randomize hospitals toeither treatment or control. You assume an effect size (d) of 0.30, ICC of 0.10, covariates accounting

for 35% of hospital-level variance and 20% of the patient-level variance. The cost is estimated at $2,000per hospital and $200 per patient.

You might decide to enroll 18 hospitals with 100 patients per hospital, which will yield power of 90%. The costwould be $792,000.

However, with one click the program tells you to enroll 32 hospitals with 11 patients per hospital. Power is thesame, but the cost is only $268,800 (a savings of 65%).

Create a Report with a single click!

Reduce the study cost by 50% or more. With one click.

�

Power is 90%Cost is

$792,000

Power is 90%Cost is

$268,800

Power for a test of the null hypothesis

One­goal­of­the­proposed­study­is­to­test­the­null­hypothesis­that­the­population­means­in­the­two­groups

(treated­and­control)­are­identical,­or­(equivalently)­that­the­true­effect­size­(d)­is­zero.­

Study design. This­hypothesis­will­be­tested­in­a­study­that­enrolls­patients­within­hospitals.

Effect size. Power­is­computed­for­an­effect­size­(d)­of­0.30.­The­computations­assume­an­intraclass

correlation­(ICC)­of­0.100.

The­standard­deviation­is­assumed­to­be­the­same­in­the­two­groups.

Sample size. For­each­group­we­will­enroll­18­hospitals­with­100­patients­per­hospital­for­a­total­of­1,800

patients­per­group.­

Patient-level covariates. There­are­2­patient-level­covariates.­The­R-squared­between­these­covariates

and­outcome­is­assumed­to­be­0.20

Hospital-level covariates. There­are­2­hospital-level­covariates.­The­R-squared­between­these­covariates

and­outcome­is­assumed­to­be­0.35

Alpha and Tails. The­criterion­for­significance­(alpha)­has­been­set­at­0.05.­The­test­is­2-tailed,­which

means­that­an­effect­in­either­direction­will­be­interpreted.­­

Power. Given­these­assumptions­(for­the­effect­size,­ICC,­and­covariates),­criteria­(for­alpha­and­tails),­and

plans­(for­the­number­of­clusters­and­sample­size­within­cluster),­the­study­will­have­power­of­90.1%­­to

Assess the impact of all parameters in just seconds!

1. Click “Tables and Graphs.”The program picks up allparameters from the mainscreen and uses these toselect a plausible range ofvalues for the sample size.The initial table and graphare created immediately. Total time: 1 second

2.Add any number of factors with a few clicks.Here, we used three values for n per cluster (10, 20, 30) and two valuesfor the ICC (0.10, 0.15). The program automaticallynests the factors,populates the table, andcreates the graphs. Total time: 20 seconds

• Use these graphs atmeetings to develop anappropriate study plan

• Include the graphs in your reports andgrant applications

Simply drag and drop columns in the table to instantly highlight theimpact of any parameter. For example...

Assess the impact of the ICC. Assess the impact of the number of patients.

Based on an ICC of 0.10 we plan to enroll 32 hospitals per treat-ment to yield power of 90%. The graph shows that if the ICC is0.15 rather than 0.10, we would need to enroll 39 hospitals pertreatment to ensure the same level of power.

Based on 10 patients per treatment for each hospital, we plan toenroll 32 hospitals per treatmet to yield power of 90%. This graphshows that if we doubled the number of patients per hospital wecould reduce the number of hospitals to 25.

POWER AND

PRECISIONTools and Features

OptionsLevelsTwo levels (e.g., patients within hospitals, or students withinschools)

CovariatesAllowed at both levels (subject and cluster)

Costs. May be set separately for each group (treated and control)or may be linked to each other

Number of clusters. May be set separately for each group (treated and control)or may be linked to each other

Number of subjects. May be set separately for each group (treated and control)or may be linked to each other

Effect sizeStandardized mean difference (d)

Statistical modelsRandom effects at both levels

GraphsExport as WMF, EMF, BMP, Copy to clipboard

ReportsExport as RTF, copy to clipboard

TablesExport as data or as picture, copy to clipboard

Includes the procedures you needIn addition to cluster-randomized trials, includes modules tocompute power for survival studies, means, proportions,correlations, analysis of variance, multiple regression.logistic regression, tests of equivalence, and more.

PDF manualIncludes step-by-step instructions, worked examples, anddetailed discussion of formulas

Developed by a team of expertsMichael Borenstein, Larry V Hedges, Hannah R Rothstein

FIND THE OPTIMALRATIO OF SUBJECTSTO CLUSTERSClick “Find optimal n percluster” and the programdisplays the most cost-effective n per cluster,which can reduce costs by50% or more as comparedwith less efficient designs.

FIND THE NUMBER OFCLUSTERS (ORSUBJECTS) FOR THEREQUIRED POWERClick “Find” and theprogram displays thenumber of hospitals (orpatients) required forpower of 80%, 90%, andso on.

INTERACTIVE GUIDEThis guide walks youthrough every step ofthe analysis and offerssuggestions forincreasing power andreducing costs.

©1997-2010 Biostat, Inc. All rights reserved. Unauthorized use is a violation of applicable laws. Made in USA.RequiresWindows XP, Windows Vista, or Windows 7. Will run on MAC© using emulator. Screen resolution XGA orbetter

Program developed with funding from the National Institutes of Health (NIMH/SBIR)Program official at NIDA—Dr. Augie DianaGrant # R44 DA 025366 Power Analysis for Cluster-randomized trialsBiostatTM

14 North Dean Street, Englewood, NJ 07631 • USA Tel: 201-541-5688 • TOLL-FREE: 1-877-BIOSTATFax: 201-541-5526 • Info@PowerAnalysis.com

www.PowerAnalysis.com

Three-level and four-level designsThe program described in this brochure is for two-level hierarchical designs.

A program with three-level and four-level designs (both hierarchical and randomized blocks), options for fixed-effect and random-effects at each level, and newer graphics is in development. For details, send an e-mail toInfo@PowerAndPrecision.com