wp.crt2arm: Statistical Power Analysis for Cluster Randomized Trials with...
In WebPower: Basic and Advanced Statistical Power Analysis

Description Usage Arguments Value References Examples

Cluster randomized trials (CRT) are a type of multilevel design for the situation when the entire cluster is randomly assigned to either a treatment arm or a contral arm (Liu, 2013). The data from CRT can be analyzed in a two-level hierachical linear model, where the indicator variable for treatment assignment is included in second level. If a study contains multiple treatments, then mutiple indicators will be used. This function is for designs with 2 arms (i.e., a treatment and a control). Details leading to power calculation can be found in Raudenbush (1997) and Liu (2013).

1 2	wp.crt2arm(n = NULL, f = NULL, J = NULL, icc = NULL, power = NULL, alpha = 0.05, alternative = c("two.sided", "one.sided"))

`n`	Sample size. It is the number of individuals within each cluster.
`f`	Effect size. It specifies either the main effect of treatment, or the mean difference between the treatment clusters and the control clusters.
`J`	Number of clusters / sides. It tells how many clusters are considered in the study design. At least two clusters are required.
`icc`	Intra-class correlation. ICC is calculated as the ratio of between-cluster variance to the total variance. It quantifies the degree to which two randomly drawn observations within a cluster are correlated.
`power`	Statistical power.
`alpha`	significance level chosed for the test. It equals 0.05 by default.
`alternative`	Type of the alternative hypothesis (`"two.sided"` or `"one.sided"`). The default is "two.sided". The option "one.sided" can be either "less" or "greater".

An object of the power analysis.

Liu, X. S. (2013). Statistical power analysis for the social and behavioral sciences: basic and advanced techniques. Routledge.

Raudenbush, S. W. (1997). Statistical analysis and optimal design for cluster randomized trials. Psychological Methods, 2(2), 173.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

#To calculate the statistical power given sample size and effect size:
wp.crt2arm(f = 0.6, n = 20, J = 10, icc = 0.1, alpha = 0.05, power = NULL)
#  Cluster randomized trials with 2 arms
#
#     J  n   f icc     power alpha
#    10 20 0.6 0.1 0.5901684  0.05
#
#  NOTE: n is the number of subjects per cluster.
#  URL: http://psychstat.org/crt2arm

#To generate a power curve given a sequence of sample sizes:
res <- wp.crt2arm(f = 0.6, n = seq(20,100,10), J = 10,
                       icc = 0.1, alpha = 0.05, power = NULL)
res
#  Cluster randomized trials with 2 arms
#
#     J   n   f icc     power alpha
#    10  20 0.6 0.1 0.5901684  0.05
#    10  30 0.6 0.1 0.6365313  0.05
#    10  40 0.6 0.1 0.6620030  0.05
#    10  50 0.6 0.1 0.6780525  0.05
#    10  60 0.6 0.1 0.6890755  0.05
#    10  70 0.6 0.1 0.6971076  0.05
#    10  80 0.6 0.1 0.7032181  0.05
#    10  90 0.6 0.1 0.7080217  0.05
#    10 100 0.6 0.1 0.7118967  0.05
#
#  NOTE: n is the number of subjects per cluster.
#  URL: http://psychstat.org/crt2arm

#To plot the power curve:
plot(res) 

#To calculate the required sample size given power and effect size:
wp.crt2arm(f = 0.8, n = NULL, J = 10,
                 icc = 0.1, alpha = 0.05, power = 0.8)
#  Cluster randomized trials with 2 arms
#
#     J        n   f icc power alpha
#    10 16.02558 0.8 0.1   0.8  0.05
#
#  NOTE: n is the number of subjects per cluster.
#  URL: http://psychstat.org/crt2arm