R Graphical Manual

Browse All

Last data update: 2014.03.03

R: Simultaneous Confidence Intervals for Differences of Means of...

SimCiDiff

R Documentation

Simultaneous Confidence Intervals for Differences of Means of Multiple Endpoints

Description

Simultaneous confidence intervals 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

SimCiDiff(data, grp, resp = NULL, type = "Dunnett", base = 1, ContrastMat = NULL,
          alternative = "two.sided", covar.equal = FALSE, conf.level = 0.95)

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"`
`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)
`conf.level`	a numeric value defining the simultaneous confidence level

Details

The interest is in simultaneous confidence intervals for several linear combinations (contrasts) of treatment means in a one-way ANOVA model, and simultaneously for multiple endpoints. For example, corresponding intervals for 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 lower and upper limits (see Hasler and Hothorn, 2011). Simultaneous tests based on these intervals control 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 SimCi containing:

`estimate`	a matrix of estimated differences
`lower.raw`	a matrix of raw (unadjusted) lower limits
`upper.raw`	a matrix of raw (unadjusted) upper limits
`lower`	a matrix of lower limits adjusted for multiplicity
`upper`	a matrix of upper limits 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 intervals have the same direction for all comparisons and endpoints (alternative="..."). In case of doubt, use "two.sided".

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.

Examples

# Example 1:
# Simultaneous confidence intervals related to 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-
# intervals to the case of heteroscedasticity.

data(coagulation)

interv1 <- SimCiDiff(data=coagulation, grp="Group", resp="Thromb.count",
  type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
interv1

# Example 2:
# Simultaneous confidence intervals related to a comparisons 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-intervals to the case of heteroscedasticity and multiple
# endpoints.

data(coagulation)

interv2 <- SimCiDiff(data=coagulation, grp="Group", resp=c("Thromb.count","ADP","TRAP"),
  type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
summary(interv2)

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/SimCiDiff.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SimCiDiff
> ### Title: Simultaneous Confidence Intervals for Differences of Means of
> ###   Multiple Endpoints
> ### Aliases: SimCiDiff
> ### Keywords: htest
> 
> ### ** Examples
> 
> # Example 1:
> # Simultaneous confidence intervals related to 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-
> # intervals to the case of heteroscedasticity.
> 
> data(coagulation)
> 
> interv1 <- SimCiDiff(data=coagulation, grp="Group", resp="Thromb.count",
+   type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
> interv1
 
Simultaneous 95% confidence intervals for differences of means of multiple endpoints 
Assumption: Heterogeneous covariance matrices for the groups 
 
  comparison     endpoint estimate lower.raw upper.raw   lower upper
1      B - S Thromb.count   0.1217   -0.0367       Inf -0.0681   Inf
2      H - S Thromb.count   0.0435   -0.1344       Inf -0.1695   Inf
 
> 
> # Example 2:
> # Simultaneous confidence intervals related to a comparisons 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-intervals to the case of heteroscedasticity and multiple
> # endpoints.
> 
> data(coagulation)
> 
> interv2 <- SimCiDiff(data=coagulation, grp="Group", resp=c("Thromb.count","ADP","TRAP"),
+   type="Dunnett", base=3, alternative="greater", covar.equal=FALSE)
> summary(interv2)
 
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
 
  comparison     endpoint estimate lower.raw upper.raw   lower upper
1      B - S Thromb.count   0.1217   -0.0367       Inf -0.1115   Inf
2      B - S          ADP   0.2121    0.0691       Inf  0.0068   Inf
3      B - S         TRAP   0.1053   -0.1395       Inf -0.2580   Inf
4      H - S Thromb.count   0.0435   -0.1344       Inf -0.2136   Inf
5      H - S          ADP   0.0842   -0.0398       Inf -0.0927   Inf
6      H - S         TRAP   0.0711   -0.1784       Inf -0.2938   Inf
 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>