R: Simultaneous Tests for Differences of Means of Multiple...
SimTestDiff
R Documentation
Simultaneous Tests for Differences of Means of Multiple Endpoints
Description
Simultaneous tests for general contrasts (linear functions) of normal means (e.g.,
"Dunnett", "Tukey", "Williams" ect.) when there is more than one primary response
variable (endpoint). The procedure of Hasler and Hothorn (2011) is applied for
differences of means of normally distributed data. The covariance matrices
(containing the covariances between the endpoints) may be assumed to be equal or
possibly unequal for the different groups (Hasler, 2014). For the case of only a
single endpoint and unequal covariance matrices (variances), the procedure
coincides with the PI procedure of Hasler and Hothorn (2008).
Usage
SimTestDiff(data, grp, resp = NULL, type = "Dunnett", base = 1, ContrastMat = NULL,
alternative = "two.sided", Margin = NULL, covar.equal = FALSE)
Arguments
data
a data frame containing a grouping variable and the endpoints as
columns
grp
a character string with the name of the grouping variable
resp
a vector of character strings with the names of the endpoints; if
resp=NULL (default), all column names of the data frame
without the grouping variable are chosen automatically
type
a character string, defining the type of contrast, with the following
options:
"Dunnett": many-to-one comparisons
"Tukey": all-pair comparisons
"Sequen": comparisons of consecutive groups
"AVE": comparison of each group with average of all others
"GrandMean": comparison of each group with grand mean of all
groups
"Changepoint": differences of averages of groups of higher
order to averages of groups of lower order
"Marcus": Marcus contrasts
"McDermott": McDermott contrasts
"Williams": Williams trend tests
"UmbrellaWilliams": Umbrella-protected Williams trend tests
note that type is ignored if ContrastMat is specified
by the user (see below)
base
a single integer specifying the control group for Dunnett contrasts,
ignored otherwise
ContrastMat
a contrast matrix, where columns correspond to groups and rows
correspond to contrasts
alternative
a character string specifying the alternative hypothesis,
must be one of "two.sided" (default), "greater"
or "less"
Margin
a single numeric value, or a numeric vector corresponding to
endpoints, or a matrix where columns correspond to endpoints and
rows correspond to contrasts, default is 0
covar.equal
a logical variable indicating whether to treat the covariance
matrices (containing the covariances between the endpoints)
for the different groups as being equal;
if TRUE then the pooled covariance matrix is used,
otherwise the Satterthwaite approximation to the degrees of
freedom is used according to Hasler and Hothorn (2008)
Details
The interest is in simultaneous tests for several linear combinations (contrasts) of
treatment means in a one-way ANOVA model, and simultaneously for multiple endpoints.
For example, the all-pair comparison of Tukey (1953) and the many-to-one comparison
of Dunnett (1955) are implemented, but allowing for multiple endpoints. Also, the
user is free to create other interesting problem-specific contrasts. An approximate
multivariate t-distribution is used to calculate (adjusted) p-values
(see Hasler and Hothorn, 2011). This approach controls the familywise error rate in
an admissible range and in the strong sense. The covariance matrices of the
treatment groups (containing the covariances between the endpoints) can be assumed
to be equal (covar.equal=TRUE) or unequal (covar.equal=FALSE). If
being equal, the pooled covariance matrix is used, otherwise approximations to the
degrees of freedom (Satterthwaite, 1946) are used (see Hasler, 2014). Unequal
covariance matrices occure if variances or correlations of some endpoints differ
depending on the treatment groups.
Value
An object of class SimTest containing:
estimate
a matrix of estimated differences
statistic
a matrix of the calculated test statistics
p.val.raw
a matrix of raw p-values
p.val.adj
a matrix of p-values adjusted for multiplicity
CorrMatDat
either the estimated common correlation matrix of the data
(covar.equal=TRUE) or the list of the different (one for
each treatment) estimated correlation matrices of the data
(covar.equal=FALSE)
CorrMatComp
the estimated correlation matrix to be used for the multivariate
t-distribution
degr.fr
either a single degree of freedom (covar.equal=TRUE) or a
vector of degrees of freedom (covar.equal=FALSE) related
to the comparisons
Note
All measurement objects of each treatment group must have values for each endpoint.
If there are missing values then the procedure stops. If covar.equal=TRUE,
then the number of endpoints must not be greater than the total sample size minus
the number of treatment groups. If covar.equal=FALSE, the number of endpoints
must not be greater than the minimal sample size minus 1. Otherwise the procedure
stops.
All hypotheses are tested with the same test direction for all comparisons and
endpoints (alternative="..."). In case of doubt, use "two.sided".
If Margin is a single numeric value or a numeric vector, then the same
value(s) are used for the remaining comparisons or endpoints. If Margin is
not specified, the default is 0.
Author(s)
Mario Hasler
References
Hasler, M. (2014): Multiple contrast tests for multiple endpoints in the presence of
heteroscedasticity. The International Journal of Biostatistics 10, 17–28.
Hasler, M. and Hothorn, L.A. (2011): A Dunnett-type procedure for multiple endpoints.
The International Journal of Biostatistics 7, Article 3.
Hasler, M. and Hothorn, L.A. (2008): Multiple contrast tests in the presence of
heteroscedasticity. Biometrical Journal 50, 793–800.
Satterthwaite, F.E. (1946): An approximate distribution of estimates of variance
components. Biometrics 2, 110–114.
See Also
SimTestRat, SimCiDiff,
SimCiRat
Examples
# Example 1:
# A comparison of the groups B and H against the standard S, on endpoint
# Thromb.count, assuming unequal variances for the groups. This is an
# extension of the well-known Dunnett-test to the case of heteroscedasticity.
data(coagulation)
comp1 <- SimTestDiff(data=coagulation, grp="Group", resp="Thromb.count",
type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
comp1
# Example 2:
# A comparison of the groups B and H against the standard S, simultaneously
# on all endpoints, assuming unequal covariance matrices for the groups. This is
# an extension of the well-known Dunnett-test to the case of heteroscedasticity
# and for multiple endpoints.
data(coagulation)
comp2 <- SimTestDiff(data=coagulation, grp="Group", resp=c("Thromb.count","ADP","TRAP"),
type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
summary(comp2)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(SimComp)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/SimComp/SimTestDiff.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SimTestDiff
> ### Title: Simultaneous Tests for Differences of Means of Multiple
> ### Endpoints
> ### Aliases: SimTestDiff
> ### Keywords: htest
>
> ### ** Examples
>
> # Example 1:
> # A comparison of the groups B and H against the standard S, on endpoint
> # Thromb.count, assuming unequal variances for the groups. This is an
> # extension of the well-known Dunnett-test to the case of heteroscedasticity.
>
> data(coagulation)
>
> comp1 <- SimTestDiff(data=coagulation, grp="Group", resp="Thromb.count",
+ type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
> comp1
Test for differences of means of multiple endpoints
Assumption: Heterogeneous covariance matrices for the groups
Alternative hypotheses: True differences greater than the margins
comparison endpoint margin estimate statistic p.value.raw p.value.adj
1 B - S Thromb.count 0 0.1217 1.3327 0.0997 0.1778
2 H - S Thromb.count 0 0.0435 0.4244 0.3382 0.5224
>
> # Example 2:
> # A comparison of the groups B and H against the standard S, simultaneously
> # on all endpoints, assuming unequal covariance matrices for the groups. This is
> # an extension of the well-known Dunnett-test to the case of heteroscedasticity
> # and for multiple endpoints.
>
> data(coagulation)
>
> comp2 <- SimTestDiff(data=coagulation, grp="Group", resp=c("Thromb.count","ADP","TRAP"),
+ type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
> summary(comp2)
Contrast matrix:
Multiple Comparisons of Means: Dunnett Contrasts
B H S
B - S 1 0 -1
H - S 0 1 -1
Estimated covariance matrices of the data:
$B
Thromb.count ADP TRAP
Thromb.count 0.0626 0.0565 -0.0102
ADP 0.0565 0.0638 0.0054
TRAP -0.0102 0.0054 0.0963
$H
Thromb.count ADP TRAP
Thromb.count 0.0943 0.0637 0.0663
ADP 0.0637 0.0518 0.0446
TRAP 0.0663 0.0446 0.1157
$S
Thromb.count ADP TRAP
Thromb.count 0.0318 0.0132 0.0598
ADP 0.0132 0.0079 0.0269
TRAP 0.0598 0.0269 0.1376
Estimated correlation matrices of the data:
$B
Thromb.count ADP TRAP
Thromb.count 1.0000 0.8937 -0.1314
ADP 0.8937 1.0000 0.0687
TRAP -0.1314 0.0687 1.0000
$H
Thromb.count ADP TRAP
Thromb.count 1.0000 0.9121 0.6348
ADP 0.9121 1.0000 0.5770
TRAP 0.6348 0.5770 1.0000
$S
Thromb.count ADP TRAP
Thromb.count 1.0000 0.8338 0.9033
ADP 0.8338 1.0000 0.8161
TRAP 0.9033 0.8161 1.0000
Estimated correlation matrix of the comparisons:
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.0000 0.8494 0.3122 0.2833 0.1708 0.3755
[2,] 0.8494 1.0000 0.2387 0.1335 0.1158 0.1917
[3,] 0.3122 0.2387 1.0000 0.3417 0.2232 0.5550
[4,] 0.2833 0.1335 0.3417 1.0000 0.8869 0.7054
[5,] 0.1708 0.1158 0.2232 0.8869 1.0000 0.5818
[6,] 0.3755 0.1917 0.5550 0.7054 0.5818 1.0000
Alternative hypotheses: True differences greater than the margins
comparison endpoint margin estimate statistic p.value.raw p.value.adj
1 B - S Thromb.count 0 0.1217 1.3327 0.0997 0.3204
2 B - S ADP 0 0.2121 2.6398 0.0106 0.0434
3 B - S TRAP 0 0.1053 0.7402 0.2337 0.5877
4 H - S Thromb.count 0 0.0435 0.4244 0.3382 0.7293
5 H - S ADP 0 0.0842 1.1949 0.1258 0.3748
6 H - S TRAP 0 0.0711 0.4894 0.3147 0.7018
>
>
>
>
>
> dev.off()
null device
1
>