wp.crt3arm | R Documentation |

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).

```
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)
```

`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 ( |

`type` |
Type of effect ( |

`interval` |
A vector containing the end-points of the interval to be searched for the root. |

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.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
```

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