n4incidence {CRTSize}

Number of Subjects Required for a Cluster Randomized Trial Comparing Incidence Rates

Description

This function provides detailed sample size estimation information to determine the number of subjects that must be enrolled in a cluster randomized trial to test for a significant difference in incidence rates.

Usage

n4incidence(le, lc, m, t, CV, alpha=0.05, power = 0.80, AR=1, two.tailed=TRUE, digits=3)

Arguments

le

The anticipated incidence rate, \lambda_E, in the experimental group with the outcome.

lc

The anticipated incidence rate, \lambda_C, in the control group with the outcome.

m

The anticipated average (or actual) cluster size.

t

The planned follow-up time for the study (in weeks, months, etc.)

CV

The coefficient of variation, assumed constant over both the treatment and control groups. Note that CV = \sigma_1/\lambda_E = \sigma_2/\lambda_C, where \sigma_E and \sigma_C represent the between-cluster variation in incidence rates for each group.

AR

The Allocation Ratio: AR=1 implies an equal number of subjects per treatment and control group (maximum efficiency), > 1, implies more subjects will be enrolled in the control group (e.g. in the case of costly intervention), < 1 implies more subjects in the tretment 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 an incidence rate. A simple example may include whether a new treatment can successfully reduce the incidence of heart attacks over a six month period. In epidemiological terms, \lambda_E and \lambda_C are the expected incidence rate 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 until convergence. In some cases, such as small ICC values, the algorithm may fail 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.

le

The anticipated incidence rate, \lambda_E, in the experimental group with the outcome.

lc

The anticipated incidence rate, \lambda_C, in the control group with the outcome.

m

The anticipated average (or actual) cluster size.

t

The planned follow-up time for the study.

CV

The coefficient of variation.

AR

The Allocation Ratio: One implies an equal number of subjects per treatment and control groups.

alpha

The desired type I error rate.

power

The desired level of power.

AR

The Allocation Ratio.

Author(s)

Michael Rotondi, [e-mail]

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.

See Also

n4means, n4props

Examples

## Not run: 
Suppose a new drug is thought to reduce the incidence of HIV from 0.01 per person-year to 0.005
per person-year. Assume the coefficient of variation is 0.25 and that 1000 subjects will be 
followed for a two year period.  Calculate the required number of subjects that must be enrolled 
in a study to detect this difference with alpha = 0.05 and power = 0.80.

## End(Not run)
n4incidence(le=0.01, lc=0.005, m=1000, t=2, CV=0.25);