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

## 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 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 3 arms (i.e., two treatments and a control). Details leading to power calculation can be found in Raudenbush (1997) and Liu (2013).

## Usage

 ```1 2 3``` ```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")) ```

## 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 tratment arms and the control arm; Type "treatment" tests the differnce between the two treament arms; and Type "omnibus" tests whether the tree arms are all equivalent.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42``` ```#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 1, 2019, 8:19 p.m.