n4props {CRTSize} R Documentation

## Number of Subjects Required for a Cluster Randomized Trial with a Binary Outcome

### Description

This function provides detailed sample size estimation information to determine the number of subjects that must be enrolled in a cluster randomized trial with a binary outcome.

### Usage

n4props(pe, pc, m, ICC, alpha=0.05, power = 0.80, AR=1, two.tailed=TRUE, digits=3)

### Arguments

 pe The anticipated proportion of individuals with the outcome of interest in the experimental group. pc The anticipated proportion of individuals with the outcome of interest in the control group. m The anticipated average (or actual) cluster size. ICC The anticipated value of the intraclass correlation coefficient, ICC. AR The Allocation Ratio: AR$=$1 implies an equal number of subjects per treatment and control group (maximum efficiency), AR $>$ 1, implies more subjects will be enrolled in the control group (e.g. in the case of costly intervention), AR $<$ 1 implies more subjects in the treatment group (rarely used). alpha The desired type I error rate. power The desired level of power, recall power = 1 - type II error. two.tailed Logical, If TRUE calculations are based on a two-tailed type I error, if FALSE, a one-sided calculation is performed. digits Number of digits to round calculations

### Details

This function provides detailed information, similar to PROC POWER in SAS, but with less functionality and more concise output. It is used for sample size estimation in a cluster randomized trial where the outcome of interest is binary. A simple example may include whether an individual dies from a heart attack. In epidemiological terms, pe and pc can be thought of as the expected prevalence of the outcome in the experimental and control group. Note that if the results suggest a small number of clusters is required, an iterative procedure will include the T distribution instead of the normal critical value for alpha, iterating the procedure until convergence. Thus on some occasions, the algorithm may not converge. In some cases, such as small ICC values or proportions, this fails to converge and may need to be stopped.

### Value

 nE The minimum number of clusters required in the experimental group. nC The minimum number of clusters required in the control group. pe The anticipated proportion of individuals in the experimental group with the outcome. pc The anticipated proportion of individuals in the control group with the outcome. alpha The desired type I error rate. power The desired level of power, recall power = 1 - type II error. AR The Allocation Ratio.

### Author(s)

Michael Rotondi, mrotondi@yorku.ca

### References

Matthews JNS. Introduction to Randomized Controlled Clinical Trials (2nd Ed.) Chapman & Hall: New York, 2006.

Donner A and Klar N. Design and Analysis of Cluster Randomization Trials in Health Research. Arnold: London, 2000.