clusterPower (version 0.7.0)

cps.ma.normal: Simulation-based power estimation for continuous outcome multi-arm cluster-randomized trials.

Description

This function uses iterative simulations to determine approximate power for multi-arm cluster-randomized controlled trials with a normally-distributed outcome of interest. Users can modify a variety of parameters to suit the simulations to their desired experimental situation. This function returns the summary power values for each arm.

Usage

cps.ma.normal(
  nsim = 1000,
  nsubjects = NULL,
  narms = NULL,
  nclusters = NULL,
  means = NULL,
  sigma_sq = NULL,
  sigma_b_sq = NULL,
  alpha = 0.05,
  quiet = FALSE,
  ICC = NULL,
  method = "glmm",
  multi_p_method = "bonferroni",
  allSimData = FALSE,
  seed = NA,
  cores = NULL,
  poorFitOverride = FALSE,
  lowPowerOverride = FALSE,
  tdist = FALSE,
  return.all.models = FALSE,
  optmethod = "nlminb",
  nofit = FALSE,
  timelimitOverride = TRUE
)

Arguments

nsim

Number of datasets to simulate; accepts integer (required).

nsubjects

Number of subjects per cluster (required); accepts an integer if all are equal and narms and nclusters are provided. Alternately, the user can supply a list with one entry per arm if the cluster sizes are the same within the arm, or, if they are not the same within the arms, the user can supply a list of vectors where each vector represents an arm and each entry in the vector is the number of subjects per cluster.

narms

Integer value representing the number of arms.

nclusters

An integer or vector of integers representing the number of clusters in each arm.

means

Expected absolute treatment effect for each arm; accepts a vector of length narms (required).

sigma_sq

Within-cluster variance; accepts a vector of length narms (required).

sigma_b_sq

Between-cluster variance; accepts a vector of length narms (required).

alpha

Significance level; default = 0.05.

quiet

When set to FALSE, displays simulation progress and estimated completion time; default is FALSE.

ICC

The intra-cluster correlation coefficient

method

Analytical method, either Generalized Linear Mixed Effects Model (GLMM) or Generalized Estimating Equation (GEE). Accepts c('glmm', 'gee') (required); default = 'glmm'.

multi_p_method

A string indicating the method to use for adjusting p-values for multiple comparisons. Choose one of "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", or "none" to leave p-values unadjusted. The default is "bonferroni". See ?p.adjust for additional details.

allSimData

Option to output list of all simulated datasets; default = FALSE.

seed

Option to set.seed. Default is NULL.

cores

a string ("all") or numeric value indicating the number of cores to be used for parallel computing.

poorFitOverride

Option to override stop() if more than 25% of fits fail to converge; default = FALSE.

lowPowerOverride

Option to override stop() if the power is less than 0.5 after the first 50 simulations and every ten simulations thereafter. On function execution stop, the actual power is printed in the stop message. Default = FALSE. When TRUE, this check is ignored and the calculated power is returned regardless of value.

tdist

Logical; use t-distribution instead of normal distribution for simulation values, default = FALSE.

return.all.models

Logical; Returns all of the fitted models, the simulated data, the overall model comparisons, and the convergence report vector. This is equivalent to the output of cps.ma.normal.internal(). See ?cps.ma.normal.internal() for details.

optmethod

Option to fit with a different optimizer. Default is 'nlminb', but some incompatible model types will trigger a list of compatible optimizer options.

nofit

Option to skip model fitting and analysis and return the simulated data. Defaults to FALSE.

timelimitOverride

Logical. When FALSE, stops execution if the estimated completion time is more than 2 minutes. Defaults to TRUE.

Value

A list with the following components:

power

Data frame with columns "Power" (Estimated statistical power), "lower.95.ci" (Lower 95% confidence interval bound), "upper.95.ci" (Upper 95% confidence interval bound). Note that non-convergent models are returned for review, but not included in this calculation.

model.estimates

Produced only when allSimData=TRUE, data frame with columns corresponding to each arm with the suffixes as follows: ".Estimate" (Estimate of treatment effect for a given simulation), "Std.Err" (Standard error for treatment effect estimate), ".tval" (for GLMM) | ".wald" (for GEE), ".pval"

overall.power.table

Produced only when allSimData=TRUE, table of F-test (when method="glmm") or chi-squared (when method="gee") significance test results.

overall.power.summary

Overall power of model compared to H0. Omits non-convergent models.

simulated.data

If allSimData = TRUE, a list of nsim data frames, each containing: "y" (Simulated response value), "trt" (Indicator for arm), "clust" (Indicator for cluster).

model.fit.warning.percent

Character string containing the percent of nsim in which the glmm fit was singular or failed to converge, produced only when method == "glmm" & allSimData==FALSE.

model.fit.warning.incidence

Vector of length nsim denoting whether or not a simulation glmm fit triggered a "singular fit" or "non-convergence" error, produced only when method = "glmm" & allSimData=TRUE.

If nofit = T, a data frame of the simulated data sets, containing:

• "arm" (Indicator for treatment arm)

• "cluster" (Indicator for cluster)

• "y1" ... "yn" (Simulated response value for each of the nsim data sets).

Testing details

This function has been verified, where possible, against reference values from the NIH's GRT Sample Size Calculator, PASS11, CRTsize::n4means, clusterPower::cps.normal, and clusterPower::cpa.normal.

Details

Users must specify the desired number of simulations, the group/arm means, and two of the following: ICC, within-cluster variance, or between-cluster variance. Significance level, analytic method, progress updates, poor/singular fit override, and simulated data set output may also be specified. This function validates the user's input and passes the necessary arguments to an internal function, which performs the simulations. The internal function can be called directly by the user to return the fitted models rather than the power summaries (see ?cps.ma.normal.internal for details).

Users must also supply the number of arms, the subjects per cluster, and the number of clusters per arm. For a balanced design, users can provide these values with the arguments narms, nsubjects, and nclusters, respectively. For unbalanced designs, the user may provide a list of vectors with one vector per arm, with each vector containing the number of subjects per cluster. See the examples provided below for a demonstration of the various input options.

Non-convergent models are not included in the calculation of exact confidence intervals.

Examples

# NOT RUN {
nsubjects.example <- list(c(20,20,20,25), c(15, 20, 20, 21), c(17, 20, 21))
means.example <- c(22, 21, 21.5)
sigma_sq.example <- c(1, 1, 0.9)
sigma_b_sq.example <- c(0.1, 0.15, 0.1)

multi.cps.normal.models <- cps.ma.normal(nsim = 100,
                              narms = 3,
                              nsubjects = nsubjects.example,
                              means = means.example,
                              sigma_sq = sigma_sq.example,
                              sigma_b_sq = sigma_b_sq.example,
                              alpha = 0.05,
                              quiet = FALSE, method = 'glmm',
                              seed = 123, cores = "all",
                              lowPowerOverride = FALSE,
                              poorFitOverride = FALSE,
                              optmethod = "nlm")

 multi.cps.normal <- cps.ma.normal(nsim = 100, narms = 3,
                                   nclusters = c(10,11,10), nsubjects = 25,
                                   means = c(1, 0.25, 1.75),
                                   sigma_sq = c(1.2, 1, 1.9),
                                   sigma_b_sq = c(0.5, 1, 0.75),
                                   quiet = FALSE, ICC=NULL, method = 'glmm',
                                   allSimData = FALSE, seed = 123,
                                   poorFitOverride = TRUE,
                                   cores = NULL,
                                   optmethod = "nlminb")

multi.cps.normal.simple <- cps.ma.normal(nsim = 100, narms = 3,
                                  nclusters = 5, nsubjects = 10,
                                  means = c(22.0, 22.5, 22.9),
                                  sigma_sq = 0.2,
                                  sigma_b_sq = 0.2, alpha = 0.05,
                                  quiet = FALSE, ICC=NULL, method = 'glmm',
                                  allSimData = FALSE, seed = 123,
                                  poorFitOverride = TRUE, cores="all",
                                  optmethod = "NLOPT_LN_NELDERMEAD")
# }