MetaAnalysisSimulations: MetaAnalysisSimulations

In reproducer: Reproduce Statistical Analyses and Meta-Analyses

MetaAnalysisSimulations

Description

This function simulates data from many families of experiments. The number of families simulated is defined by the Replications parameter. The parameter Exp determines the number of experiments in each family. The function simulates data from one of four distributions and uses the data to construct two of groups of equal size (GroupSize). The experimental design of individual experiments in each family is determined by the FourGroup parameter. If FourGroup=FALSE, the basic experimental design is a balanced two group randomized experiment, otherwise the experimental design is a balanced four group experiment corresponding to a randomized blocks experiment. The function calls either NP2GMetaAnalysisSimulation or NP2GMetaAnalysisSimulation to generate and analyse data for each individual family. The function either returns the meta-analysed data from each experiment or provides summary statistics.

Usage

MetaAnalysisSimulations(
  mean = 0,
  sd = 1,
  diff = 0.5,
  GroupSize = 10,
  type = "n",
  Replications = 50,
  Exp = 5,
  seed = 456,
  alpha = 0.05,
  FourGroup = FALSE,
  StdAdj = 0,
  BlockEffect = 0,
  BlockStdAdj = 0,
  StdExp = 0,
  MAMethod = "PM",
  returnES = FALSE,
  AlwaysTwoSidedTests = FALSE
)

Arguments

mean	the value used for the mean of control group in the simulated data. It can be any real number including zero.
sd	the value used for the spread of the control group and the spread of the treatment group in the simulated data. The value must be a real value greater than 0.
diff	mean+diff is the value used for the mean of the treatment group. It can be zero.
GroupSize	is the size of each of the groups comprising one experiment. Groupsize should be an integer of 4 or more
type	specifies the distribution being simulated. The permitted values are 'n' for the normal distribution (default), 'l' for the lognormal distribution, 'g' for the gamma distribution and 'lap' for the Laplace distribution.
Replications	The number of times the set of experiments is simulated.
Exp	is the number of experiments in each family of experiments being simulated. Exp should be an integer of 2 or more (default 5).
seed	specifies the seed to be used to initiate the simulation, so the simulation is repeatable.
alpha	The significance level used for tests and confidence intervals (default 0.05)
FourGroup	is a Boolean variable that determines whether the experiment is a two group experiments or a 4-Group randomised block experiment. It defaults to FALSE which means a two-group experiment is the default condition
StdAdj	If non-zero that can be used to introduced variability into the treatment spread/variance (default 0). Not appropriate for gamma data.
BlockEffect	A factor used to change the mean difference between blocks (default 0.5)
BlockStdAdj	if non-zero this can be used to change the BlockEffect from a fixed to random effect (default 0).
StdExp	if non-zero it simulates a random effect between experiments in the same family (default 0).
MAMethod	specifies the model to be used when experimental effect sizes ar aggregated using the R metafor package.
returnES	if TRUE the function outputs the summary statistics otherwise it outputs the meta-analysis results for each family (default FALSE)
AlwaysTwoSidedTests	This parameter can be used to override the one-sided tests used as default if the diff parameter is non-zero (default FALSE). This should only be set to TRUE to check simulation reported in other papers that seem to have used two-sided tests.

Value

The parameter either returns the meta-analysis values obtained from each family or the average values of the meta-analysis over all replications.

Author(s)

Barbara Kitchenham and Lech Madeyski

Examples

as.data.frame(
  MetaAnalysisSimulations(
    mean=0, sd=1, diff=0.5, GroupSize=10, type='n', Replications=5, Exp=5,
    seed=456, alpha=0.05, FourGroup=FALSE, StdAdj=0, BlockEffect=0.5,
    BlockStdAdj=0,StdExp=0,MAMethod='PM',returnES=FALSE))
#  AverageCliffd AverageCliffdvar AverageCliffdsig Averagephat Averagephatvar
#1        0.3336        0.0132419              0.8      0.6668    0.003214756
#Averagephatsig  AveMDStd AveMDStdvar AveMDStdsig MAMean.phat  MAphat.var
#1          0.9 0.6176206  0.04278117         0.9    0.689908 0.003888047
#MAphat.sig MAMean.Cliffd MACliffd.var MACliffd.sig Mean.StdMDUnweighted
#1      0.9       0.37984   0.01575063          0.9            0.6449963
#StdMDUnweighted.var StdMDUnweighted.sig Mean.StdMDAdjUnweighted
#1        0.04299001                 0.9               0.6145034
#StdMDAdjUnweighted.var StdMDAdjUnweighted.sig Mean.HedgesMA Hedges.var
#1           0.04192908                    0.9     0.6150575 0.04455833
#Hedges.sig Mean.StdMDAdjMA.exact StdMDAdjMA.exact.var StdMDAdjMA.exact.sig
#1      0.9             0.5834754           0.05171067                  0.8
#Mean.StdMDAdjMA.approx StdMDAdjMA.approx.var StdMDAdjMA.approx.sig
#1              0.58643            0.04749064                   0.9
#Mean.StdMDMA.exact StdMDMA.exact.var StdMDMA.exact.sig Mean.StdMDMA.approx
#1        0.6134374        0.05711235               0.8           0.6165884
#StdMDMA.approx.var StdMDMA.approx.sig
#1       0.05242339                0.9
#as.data.frame(
 # MetaAnalysisSimulations(
 #   mean=0, sd=1, diff=0.5, GroupSize=10, type='n', Replications=50, Exp=5,
 #   seed=456, alpha=0.05, FourGroup=FALSE, StdAdj=0, BlockEffect=0.5,
 #   BlockStdAdj=0,StdExp=0,MAMethod='PM',returnES=FALSE))
# AverageCliffd AverageCliffdvar AverageCliffdsig Averagephat Averagephatvar
#1      0.29808       0.01333744             0.74     0.64904    0.003236444
# Averagephatsig  AveMDStd   AveMDStdvar AveMDStdsig MAMean.phat  MAphat.var
#           0.78 0.5450377    0.04217901        0.78   0.6677884 0.004538661
#  MAphat.sig MAMean.Cliffd MACliffd.var MACliffd.sig  Mean.StdMDUnweighted
#1       0.72     0.3356298   0.01833956         0.72             0.5686653
#  StdMDUnweighted.var StdMDUnweighted.sig Mean.StdMDAdjUnweighted
#1          0.04237386                0.82               0.5419554
#StdMDAdjUnweighted.var StdMDAdjUnweighted.sig Mean.HedgesMA Hedges.var
#            0.04138573                   0.78     0.5420552 0.04388383
#  Hedges.sig Mean.StdMDAdjMA.exact StdMDAdjMA.exact.var StdMDAdjMA.exact.sig
#1       0.76             0.5163304           0.05874152                 0.72
#Mean.StdMDAdjMA.approx StdMDAdjMA.approx.var StdMDAdjMA.approx.sig
#1            0.5203279            0.05591752                  0.74
# Mean.StdMDMA.exact StdMDMA.exact.var
#        0.5418705        0.06468786
# StdMDMA.exact.sig Mean.StdMDMA.approx StdMDMA.approx.var StdMDMA.approx.sig
#              0.72           0.5461255         0.06159257               0.74

#as.data.frame(
#   MetaAnalysisSimulations(
#     mean=0, sd=1, diff=0.5, GroupSize=10, type='n', Replications=50, Exp=5,
#     seed=456, alpha=0.05, FourGroup=TRUE, StdAdj=0, BlockEffect=0.5,
#     BlockStdAdj=0, StdExp=0, MAMethod='PM', returnES=FALSE))
#  AverageCliffd AverageCliffdvar AverageCliffdsig Averagephat ...
#1       0.27968       0.00683327             0.92     0.63984 ...
# as.data.frame(
#   MetaAnalysisSimulations(
#     mean=0, sd=1, diff=0.5, GroupSize=10, type='n', Replications=10, Exp=5,
#     seed=456, alpha=0.05, FourGroup=TRUE, StdAdj=0, BlockEffect=0.5,
#     BlockStdAdj=0, StdExp=0, MAMethod='PM', returnES=TRUE))
#Family NumExp GroupSize AveCliffd AveCliffdvar AveCliffdsig Avephat  ...
#     1      1         5        10        0.252  0.007423693    TRUE  ...
# Family NumExp GroupSize AveCliffd AveCliffdvar AveCliffdsig Avephat ...
#1     1      5        10     0.252  0.007423693         TRUE   0.626 ...

reproducer documentation built on Oct. 18, 2023, 5:10 p.m.