SimCiRat {SimComp}R Documentation

Simultaneous Confidence Intervals for Ratios of Means of Multiple Endpoints

Description

Simultaneous confidence intervals for ratios of 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 (2009) is applied for ratios 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.

Usage

SimCiRat(data, grp, resp = NULL, type = "Dunnett", base = 1, Num.Contrast = NULL,
          Den.Contrast = 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, with control in the denominator
  • "Tukey": all-pair comparisons
  • "Sequen": comparisons of consecutive groups, where the group with lower order is the denomniator
  • "AVE": comparison of each group with average of all others, where the average is taken as denominator
  • "GrandMean": comparison of each group with grand mean of all groups, where the grand mean is taken as denominator
  • "Changepoint": ratios of averages of groups of higher order divided by averages of groups of lower order
  • "Marcus": Marcus contrasts as ratios
  • "McDermott": McDermott contrasts as ratios
  • "Williams": Williams contrasts as ratios
  • "UmbrellaWilliams": Umbrella-protected Williams contrasts as ratios
note that type is ignored if Num.Contrast and Den.Contrast are specified by the user (see below)
base a single integer specifying the control (i.e. denominator) group for Dunnett contrasts, ignored otherwise
Num.Contrast a numerator contrast matrix, where columns correspond to groups and rows correspond to contrasts
Den.Contrast a denominator 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 ratios of 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) for ratios of means 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, 2009). Simultaneous tests based on these intervals control the familywise error rate 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 the Satterthwaite approximation to the degrees of freedom is used according to Hasler and Hothorn (2008). Unequal covariance matrices occure if either 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 matrix of degrees of freedom (covar.equal=FALSE)

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 the intervals have the same direction for all comparisons and endpoints (alternative="..."). In case of doubts, use "two.sided".

In contrast to simultaneous confidence intervals for differences, the correlation matrix for the multivariate t-distribution depends on the unknown ratios. The same problem also arises for the degrees of freedom if the covariance matrices for the different groups are assumed to be unequal (covar.equal=FALSE). Both problems can be handled by a plug-in approach, see the references therefore.

Author(s)

Mario Hasler

References

Hasler, M. (2009): Extensions of Multiple Contrast Tests. PhD Thesis, Gottfried-Wilhelm-Leibniz-Universitaet Hannover.

Hasler, M. and Hothorn, L.A. (submitted): A Dunnett-type Procedure for Multiple Endpoints

Hasler, M. and Hothorn, L.A. (2008): Multiple contrast tests in the presence of heteroscedasticity. Biometrical Journal 50, 793-800.

Dilba, G., Bretz, F., and Guiard, V. (2006): Simultaneous confidence sets and confidence intervals for multiple ratios. Journal of Statistical Planning and Inference 136, 2640-2658.

See Also

SimCiDiff, SimTestRat, SimTestDiff,

Examples

data(iris)

interv <- SimCiRat(data=iris, grp="Species")
summary(interv)

[Package SimComp version 1.3 Index]