# swPwr: Power of Stepped Wedge Cluster Randomized Trial (SW CRT) In swCRTdesign: Stepped Wedge Cluster Randomized Trial (SW CRT) Design

## Description

swPwr returns (two-sided) power of treatment effect (θ) for the specified SW CRT design using a linear models weighted least squares (WLS) approach. The response/outcome of interest can be binomial or Gaussian distributed and is assumed to come from a model with random intercepts, random treatment effects, and random cluster-specific time effects. Variance components can be specified using either tau, eta, rho, and gamma, or icc and cac (see details). If a random intercepts only model is used (i.e., eta and gamma are 0 and n is constant over clusters and time), then the power calculation is comparable to the closed-form formula of [Hussey and Hughes, 2007].

## Usage

 1 2 swPwr(design, distn, n, mu0, mu1, sigma, tau, eta, rho, gamma, icc, cac, alpha=0.05, retDATA=FALSE, silent=FALSE) 

## Arguments

 design list: A stepped wedge design object, typically from swDsn, that includes at least the following components: ## swDsn, swDsn.unique.clusters, clusters, n.clusters, total.time distn character: Distribution assumed (gaussian or binomial). Currently, 'Binomial' implies Bernoulli. n integer (scalar, vector, or matrix): Number of observations: (scalar) for all clusters and all time points; (vector) for each cluster at all time points; and (matrix) for each cluster at each time point, where rows correspond to clusters and columns correspond to time. n can also be used to specify a design with transition periods (e.g. in the first time period that each sequence receives treatment, no observations are collected from that sequence). Simply define n as a matrix with a sample size of 0 during every transition period. mu0 numeric (scalar): Mean outcome in the control group. mu1 numeric (scalar): Mean outcome in the treatment group. Note: Treatment effect is the difference in means θ = μ_1 - μ_0. sigma numeric (scalar): Standard deviation when assuming Gaussian distribution (distn=gaussian). For binomial distribution σ^2 is automatically set to \bar{μ}(1-\bar{μ}) where \bar{μ} = (μ_1 + μ_0)/2 tau numeric (scalar): Standard deviation of random intercepts. eta numeric (scalar): Standard deviation of random treatment effects. rho numeric (scalar): Correlation between random intercepts and random treatment effects. gamma numeric (scalar): Standard deviation of random time effects. icc numeric (scalar): Within-period intra-cluster correlation. Can be used with CAC instead of tau, eta, rho, and gamma; see details. cac numeric (scalar): Cluster auto-correlation. Can be used with ICC instead of tau, eta, rho, and gamma; see details. alpha numeric (scalar): Two-sided statistical significance level. retDATA logical: if TRUE, all stored (input, intermediate, and output) values of swPwr are returned. Default value is FALSE. silent logical: if TRUE, hides a warning about differences in argument order between version 3.0 and prior versions. When n is not a scalar, also hides reminder about order of entries in n. Default value is FALSE.

## Details

The two-sided statistical power of treatment effect (θ = μ_1 - μ_0) is

Pwr(θ) = Φ( Z - z_{1 - α /2} ) + Φ( -Z - z_{1 - α /2} )

where

Z = \frac{ |θ| }{ √{Var(\hat{θ}_{WLS})} }

and Φ is the cumulative distribution function of the standard normal N(0,1) distribution.

When eta (and rho) are 0, instead of using tau, eta, rho, and gamma, the icc and cac can be used to define the variability of the random intercepts and time effects. In this model,

ICC = \frac{τ^2+γ^2}{τ^2+γ^2+σ^2}

CAC = \frac{τ^2}{τ^2+γ^2}

## Value

numeric (matrix): swPwr returns the power of treatment effect (θ), where the variance of treatment effect is computed by WLS.

numeric (list): swPwr returns all specified and computed items as objects of a list if retDATA = TRUE.

 design list: The stepped wedge design object as input. distn character: Distribution assumed (gaussian or binomial). n integer (scalar, vector, or matrix): Number of observations: (scalar) for all clusters and all time points; (vector) for each cluster at all time points; and (matrix) for each cluster at each time point, where rows correspond to clusters and columns correspond to time. mu0 numeric (scalar): Mean outcome in the control group. mu1 numeric (scalar): Mean outcome in intervention group. Note: treatment effect is difference in means θ = μ_1 - μ_0. sigma numeric (scalar): Standard deviation input. For binomial distribution, sigma = NA tau numeric (scalar): Standard deviation of random intercepts. eta numeric (scalar): Standard deviation of random treatment effects. rho numeric (scalar): Correlation between random intercepts and random treatment effects. gamma numeric (scalar): Standard deviation of random time effects. icc numeric (scalar): Within-period intra-cluster correlation. Can be used with CAC instead of tau, eta, rho, and gamma; see details. cac numeric (scalar): Cluster auto-correlation. Can be used with ICC instead of tau, eta, rho, and gamma; see details. alpha numeric (scalar): Statistical significance level. Xmat numeric (matrix): Design matrix for this SW CRT design. Wmat numeric (matrix): Covariance matrix for this SW CRT design. var.theta.WLS numeric (scalar): Variance estimate of θ using weighted least squares (WLS) for this SW CRT design. pwrWLS numeric (scalar): Power of treatment effect (θ) using weighted least squares (WLS) for this SW CRT design.
 pwrCLOSED numeric (scalar): Power of treatment effect (θ) using closed-form formula from Hughes, et al. (2003) for this SW CRT design. Returned if eta and gamma are 0 and n is constant over clusters and time.

## Author(s)

James P Hughes, Navneet R Hakhu, and Emily C Voldal

## References

Hussey MA, Hughes JP. Design and analysis of stepped wedge cluster randomized trials. Contemporary Clinical Trials 2007;28:182-191.

## 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 43 44 45 46 47 48 49 50 51 52 53 54 library(swCRTdesign) # Example 1 (Random Intercepts Only, standard Stepped Wedge (SW) design) swPwr.Ex1.RIO.std <- swPwr(swDsn(c(6,6,6,6)), distn="binomial", n=120, mu0=0.05, mu1=0.035, tau=0.01, eta=0, rho=0, gamma=0, alpha=0.05, retDATA=FALSE) swPwr.Ex1.RIO.std # Example 2 (Random Intercepts Only, extended SW design) swPwr.Ex1.RIO.extend <- swPwr(swDsn(c(6,6,6,6), extra.time=3), distn="binomial", n=120, mu0=0.05, mu1=0.035, tau=0.01, eta=0, rho=0, gamma=0, alpha=0.05, retDATA=FALSE) swPwr.Ex1.RIO.extend # Example 3 (Independent Random Intercepts and Treatment effects, standard SW design) swPwr.Ex1.IRIS <- swPwr(swDsn(c(6,6,6,6)), distn="binomial", n=120, mu0=0.05, mu1=0.035, tau=0.01, eta=0.0045, rho=0, gamma=0, alpha=0.05, retDATA=FALSE) swPwr.Ex1.IRIS # Example 4 (Correlated Random Intercepts and Slopes, standard SW design) swPwr.Ex1.CRIS <- swPwr(swDsn(c(6,6,6,6)), distn="binomial", n=120, mu0=0.05, mu1=0.035, tau=0.01, eta=0.0045, rho=0.4, gamma=0, alpha=0.05, retDATA=FALSE) swPwr.Ex1.CRIS # Example 5 (Random time effect and correlated Random Intercepts and Slopes, standard SW design) swPwr.Ex1.RTCRIS <- swPwr(swDsn(c(6,6,6,6)), distn="binomial", n=120, mu0=0.05, mu1=0.035, tau=0.01, eta=0.0045, rho=0.4, gamma = 0.1, alpha=0.05, retDATA=FALSE) swPwr.Ex1.RTCRIS #Example 6 (Sample size varying by cluster) sample.size.vector <- c(35219,53535,63785,456132,128670,96673, 51454,156667,127440,68615,56502,17719, 75931,58655,52874,75936) swPwr.Ex1.vector <- swPwr(swDsn(c(4,3,5,4)), distn="gaussian", n=sample.size.vector, mu0=2.66, mu1=2.15, sigma=sqrt(1/2.66), tau=0.31, eta=0.2, rho=0, gamma = 0.15, alpha=0.05, retDATA=FALSE) swPwr.Ex1.vector #Example 7 (Sample size varying by cluster and time) sample.size.matrix <- matrix(c(26, 493, 64, 45, 48, 231, 117, 17, 49, 36, 19, 77, 67, 590, 261, 212, 67, 318, 132, 58, 44, 57, 59, 78, 115, 532, 176, 199, 73, 293, 129, 79, 51, 62, 109, 94, 174, 785, 133, 79, 120, 305, 224, 99, 83, 79, 122, 122, 94, 961, 90, 131, 166, 352, 316, 59, 54, 131, 101, 133),nrow=12,ncol=5, byrow=FALSE) swPwr.Ex1.matrix <- swPwr(swDsn(c(3,3,3,3)), distn="binomial", n=sample.size.matrix, mu0=0.08, mu1=0.06, tau=0.017, eta=0.006, rho=-0.5, gamma = 0, alpha=0.05, retDATA=FALSE) swPwr.Ex1.matrix #Example 8 (Using ICC and CAC) swPwr.Ex1.icccac <- swPwr(swDsn(c(6,6,6,6)), distn="gaussian", n=120, mu0=0.05, mu1=0.035, sigma=0.1, icc=0.02, cac=0.125, alpha=0.05, retDATA=FALSE) swPwr.Ex1.icccac 

swCRTdesign documentation built on Oct. 30, 2019, 11:24 a.m.