WebPower (version 0.9.4)

wp.mrt3arm: 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)

Value

An object of the power analysis.

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.

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