cps.did.binary: Power simulations for cluster-randomized trials: Difference...

In clusterPower: Power Calculations for Cluster-Randomized and Cluster-Randomized Crossover Trials

Description

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This function utilizes iterative simulations to determine approximate power for cluster-randomized controlled trials. Users can modify a variety of parameters to suit the simulations to their desired experimental situation.

Runs the power simulation for difference in difference RCTs with binary outcomes.

Users must specify the desired number of simulations, number of subjects per cluster, number of clusters per arm, pre-treatment between-cluster variance, and two of the following three terms: expected probability of outcome in arm 1, expected probability of outcome in arm 2, expected difference in probabilities between groups ; post-treatment between-cluster variance, significance level, analytic method, progress updates, and simulated data set output may also be specified.

The following equations are used to estimate intra-cluster correlation coefficients:

P_h: \mjsdeqnICC = \frac\sigma_b\sigma_b + \pi^2/3 P_c: \mjsdeqnICC = \fracP(Y_ij = 1, Y_ih = 1) - \pi_j\pi_h\sqrt\pi_j(1 - \pi_j)\pi_h(1 - \pi_h) P_lmer: \mjsdeqnICC = \frac\sigma_b\sigma_b + \sigma_w

Usage

cps.did.binary(
  nsim = NULL,
  nsubjects = NULL,
  nclusters = NULL,
  p.diff = NULL,
  p1t0 = 0,
  p2t0 = NULL,
  p1t1 = NULL,
  p2t1 = NULL,
  or1 = NULL,
  or2 = NULL,
  or.diff = NULL,
  sigma_b_sq0 = NULL,
  sigma_b_sq1 = NULL,
  alpha = 0.05,
  method = "glmm",
  quiet = TRUE,
  allSimData = FALSE,
  poorFitOverride = FALSE,
  lowPowerOverride = FALSE,
  timelimitOverride = TRUE,
  seed = NA,
  nofit = FALSE
)

Arguments

nsim	Number of datasets to simulate; accepts integer (required).
nsubjects	Number of subjects per cluster; accepts integer (required).
nclusters	Number of clusters per arm; accepts integer (required).
p.diff	Optional if p1t1 and p2t0 are provided. Expected difference in outcome proportion between groups, defined as p.diff = (p1t1 - p1t0) - (p2t1 - p2t0). At least 2 of the following 3 arguments must be specified when using expected odds ratios:
p1t0	Required. Expected outcome proportion in arm 1 at baseline. Default is 0.
p2t0	Optional. Expected outcome proportion in arm 2 at baseline. If no quantity is provided, p2t0 = p1t0 is assumed.
p1t1	Optional. Expected outcome proportion in arm 1 at follow-up. If no quantity is provided, p1t1 = p1t0 is assumed.
p2t1	Required. Expected outcome proportion in arm 2 at follow-up.
or1	Expected odds ratio for outcome in arm 1
or2	Expected odds ratio for outcome in arm 2
or.diff	Expected difference in odds ratio for outcome between groups, defined as or.diff = or1 - or2.
sigma_b_sq0	Pre-treatment (time == 0) between-cluster variance; accepts numeric scalar (indicating equal between-cluster variances for both arms) or a vector of length 2 specifying treatment-specific between-cluster variances.
sigma_b_sq1	Post-treatment (time == 1) between-cluster variance; accepts numeric scalar (indicating equal between-cluster variances for both arms) or a vector of length 2 specifying treatment-specific between-cluster variances. If not provided by the user, sigma_b_sq1 = sigma_b_sq0.
alpha	Significance level. Default = 0.05
method	Analytical method, either Generalized Linear Mixed Effects Model (GLMM) or Generalized Estimating Equation (GEE). Accepts c('glmm', 'gee') (required); default = 'glmm'.
quiet	When set to FALSE, displays simulation start time and completion time. Default is TRUE.
allSimData	Option to output list of all simulated datasets. Default = FALSE.
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.
timelimitOverride	Logical. When FALSE, stops execution if the estimated completion time is more than 2 minutes. Defaults to TRUE.
seed	Option to set the seed. Default is NA.
nofit	Option to skip model fitting and analysis and only return the simulated data. Default = FALSE.

Value

A list with the following components

• Character string indicating total number of simulations, simulation type, and number of convergent models

• Number of simulations

• Data frame with columns "Power" (Estimated statistical power), "lower.95.ci" (Lower 95 "upper.95.ci" (Upper 95

• Analytic method used for power estimation

• Significance level

• Vector containing user-defined cluster sizes

• Vector containing user-defined number of clusters

• Data frame reporting sigma_b_sq for each group at each time point

• Vector containing expected difference in probabilities based on user inputs

• Data frame with columns: "Period" (Pre/Post-treatment indicator), "Arm" (Arm indicator), "Value" (Mean response value)

• Data frame containing three estimates of ICC

• Data frame with columns: "Estimate" (Estimate of treatment effect for a given simulation), "Std.err" (Standard error for treatment effect estimate), "Test.statistic" (z-value (for GLMM) or Wald statistic (for GEE)), "p.value", "converge" (Did simulated model converge?), "sig.val" (Is p-value less than alpha?)

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

• List of warning messages produced by non-convergent models. Includes model number for cross-referencing against model.estimates

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).

Author(s)

Alexander R. Bogdan

Alexandria C. Sakrejda ([e-mail]

Ken Kleinman ([e-mail])

References

Snjiders, T. & Bosker, R. Multilevel Analysis: an Introduction to Basic and Advanced Multilevel Modelling. London, 1999: Sage.

Elridge, S., Ukoumunne, O. & Carlin, J. The Intra-Cluster Correlation Coefficient in Cluster Randomized Trials: A Review of Definitions. International Statistical Review (2009), 77, 3, 378-394. doi: 10.1111/j.1751-5823.2009.00092.x

Examples

# Estimate power for a trial with 10 clusters in both arms, those clusters having
# 20 subjects each, with sigma_b_sq0 = 1. We have estimated arm proportions of 0.2
# and 0.3 in the first and second arms, respectively, and we use
# 100 simulated data sets analyzed by the GLMM method. The resulting estimated power 
# (if you set seed = 123) should be about 0.78.

## Not run: 
did.binary.sim = cps.did.binary(nsim = 100, nsubjects = 20, nclusters = 10, 
                                p1t0 = 0.1, p2t0 = 0.1,  
                                p1t1 = 0.2, p2t1 = 0.45, sigma_b_sq0 = 1, 
                                sigma_b_sq1 = 1, alpha = 0.05,
                                method = 'glmm', allSimData = FALSE, seed = 123)

## End(Not run)

clusterPower documentation built on Jan. 29, 2021, 1:06 a.m.