# wp.crt3arm: Statistical Power Analysis for Cluster Randomized Trials with... In WebPower: Basic and Advanced Statistical Power Analysis

 wp.crt3arm R Documentation

## Statistical Power Analysis for Cluster Randomized Trials with 3 Arms

### Description

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 control arm (Liu, 2013). The data from CRT can be analyzed in a two-level hierarchical linear model, where the indicator variable for treatment assignment is included in second level. If a study contains multiple treatments, then multiple indicators will be used. This function is for designs with 3 arms (i.e., two treatments and a control). Details leading to power calculation can be found in Raudenbush (1997) and Liu (2013).

### Usage

```wp.crt3arm(n = NULL, f = NULL, J = NULL, icc = NULL, power = NULL,
alpha = 0.05, alternative = c("two.sided", "one.sided"),
type = c("main", "treatment", "omnibus"), interval = NULL)
```

### Arguments

 `n` Sample size. It is the number of individuals within each cluster. `f` Effect size. It specifies one of the three types of effects: the main effect of treatment, 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". `type` Type of effect (`"main"` or `"treatment"` or `"omnibus"`) with "main" as default. The type "main" tests the difference between the average treatment arms and the control arm; Type "treatment" tests the difference between the two treatment arms; and Type "omnibus" tests whether the tree arms are all equivalent. `interval` A vector containing the end-points of the interval to be searched for the root.

### Value

An object of the power analysis.

### References

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.

### Examples

```
#To calculate the statistical power given sample size and effect size:
wp.crt3arm(f = 0.5, n = 20, J = 10, icc = 0.1, alpha = 0.05, power = NULL)
#  Cluster randomized trials with 3 arms
#
#     J  n   f icc     power alpha
#    10 20 0.5 0.1 0.3940027  0.05
#
#  NOTE: n is the number of subjects per cluster.
#  URL: http://psychstat.org/crt3arm

#To generate a power curve given a sequence of sample sizes:
res <- wp.crt3arm(f = 0.5, n = seq(20, 100, 10), J = 10,
icc = 0.1, alpha = 0.05, power = NULL)
res
#  Cluster randomized trials with 3 arms
#
#     J   n   f icc     power alpha
#    10  20 0.5 0.1 0.3940027  0.05
#    10  30 0.5 0.1 0.4304055  0.05
#    10  40 0.5 0.1 0.4513376  0.05
#    10  50 0.5 0.1 0.4649131  0.05
#    10  60 0.5 0.1 0.4744248  0.05
#    10  70 0.5 0.1 0.4814577  0.05
#    10  80 0.5 0.1 0.4868682  0.05
#    10  90 0.5 0.1 0.4911592  0.05
#    10 100 0.5 0.1 0.4946454  0.05
#
#  NOTE: n is the number of subjects per cluster.
#  URL: http://psychstat.org/crt3arm

#To plot the power curve:
plot(res)

#To calculate the required sample size given power and effect size:
wp.crt3arm(f = 0.8, n = NULL, J = 10, icc = 0.1, alpha = 0.05, power = 0.8)
#  Cluster randomized trials with 3 arms
#
#     J        n   f icc power alpha
#    10 27.25145 0.8 0.1   0.8  0.05
#
#  NOTE: n is the number of subjects per cluster.
#  URL: http://psychstat.org/crt3arm

```

WebPower documentation built on May 21, 2022, 5:05 p.m.