# wp.mrt3arm: Statistical Power Analysis for Multisite Randomized Trials... In WebPower: Basic and Advanced Statistical Power Analysis

 wp.mrt3arm R Documentation

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

### Description

Multisite randomized trials (MRT) 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 MRT can be analyzed in a two-level hierarchical linear model, where the indicator variable for treatment assignment is included in first 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). Three types of tests are considered in the function: (1) The "main" type tests treatment main effect; (2) The "treatment" type tests the difference between the two treatments; and (3) The "omnibus" type tests whether the three arms are all equivalent. Details leading to power calculation can be found in Raudenbush (1997) and Liu (2013).

### Usage

``````wp.mrt3arm(n = NULL, f1 = NULL, f2 = NULL, J = NULL, tau = NULL,
sg2 = 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. `f1` Effect size for treatment main effect. Effect size must be positive. `f2` Effect size for the difference between two treatments. Effect size must be positive. `J` Number of clusters / sites. It tells how many clusters are considered in the study design. At least two clusters are required. `tau` Variance of treatment effects across sites/clusters. `sg2` Level-one error Variance. The residual variance in the first level. `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 three 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:
#For main effect
wp.mrt3arm(n = 30, f1 = 0.43, J = 20, tau = 0.4,
sg2 = 2.25, alpha = 0.05, power = NULL)
#    Multisite randomized trials with 3 arms
#
#       J  n   f1 tau  sg2     power alpha
#      20 30 0.43 0.4 2.25 0.8066964  0.05
#
#    NOTE: n is the number of subjects per cluster
#    URL: http://psychstat.org/mrt3arm

#For tesing difference between effects
wp.mrt3arm(n = 30, f2 = 0.2, J = 20, tau = 0.4, sg2 = 2.25,
alpha = 0.05, power = NULL, type="treatment")
#    Multisite randomized trials with 3 arms
#
#      J  n  f2 tau  sg2     power alpha
#      20 30 0.2 0.4 2.25 0.2070712  0.05
#
#    NOTE: n is the number of subjects per cluster
#    URL: http://psychstat.org/mrt3arm

#For testing site variablity
wp.mrt3arm(n = 30, f1=0.43, f2 = 0.2, J = 20, tau = 0.4, sg2 = 2.25,
alpha = 0.05, power = NULL, type="omnibus")
#    Multisite randomized trials with 3 arms
#
#       J  n   f1  f2 tau  sg2     power alpha
#      20 30 0.43 0.2 0.4 2.25 0.7950757  0.05
#
#    NOTE: n is the number of subjects per cluster
#    URL: http://psychstat.org/mrt3arm

#To generate a power curve given a sequence of numbers of sites/clusters:
res <- wp.mrt3arm(n = 30, f2 = 0.2, J = seq(20,120,10), tau = 0.4,
sg2 = 2.25, alpha = 0.05, power = NULL, type="treatment")
res
#    Multisite randomized trials with 3 arms
#
#       J  n  f2 tau  sg2     power alpha
#      20 30 0.2 0.4 2.25 0.2070712  0.05
#      30 30 0.2 0.4 2.25 0.2953799  0.05
#      40 30 0.2 0.4 2.25 0.3804554  0.05
#      50 30 0.2 0.4 2.25 0.4603091  0.05
#      60 30 0.2 0.4 2.25 0.5337417  0.05
#      70 30 0.2 0.4 2.25 0.6001544  0.05
#      80 30 0.2 0.4 2.25 0.6593902  0.05
#      90 30 0.2 0.4 2.25 0.7116052  0.05
#     100 30 0.2 0.4 2.25 0.7571648  0.05
#     110 30 0.2 0.4 2.25 0.7965644  0.05
#     120 30 0.2 0.4 2.25 0.8303690  0.05
#
#    NOTE: n is the number of subjects per cluster
#    URL: http://psychstat.org/mrt3arm

#To plot the power curve:
plot(res, "J", "power")

#To calculate the required sample size given power and effect size:
wp.mrt3arm(n = NULL, f1 = 0.43, J = 20, tau = 0.4,
sg2 = 2.25, alpha = 0.05, power = 0.8)
#    Multisite randomized trials with 3 arms
#
#       J        n   f1 tau  sg2 power alpha
#      20 28.61907 0.43 0.4 2.25   0.8  0.05
#
#    NOTE: n is the number of subjects per cluster
#    URL: http://psychstat.org/mrt3arm

``````

WebPower documentation built on Oct. 14, 2023, 1:06 a.m.