R: Approximate simultaneous tests for ratios of normal means...

simtest.ratioVH {mratios} | R Documentation

## Approximate simultaneous tests for ratios of normal means with heterogeneous variances

### Description

Performs simultaneous tests for several ratios of linear combinations of treatment means in a normal one-way layout, assuming normal distribution of the data allowing heterogeneous variances.

### Usage

    simtest.ratioVH(formula, data,
     type = "Dunnett", base = 1, alternative = "two.sided",
     Margin.vec = NULL, FWER = 0.05,
     Num.Contrast = NULL, Den.Contrast = NULL,
     names = TRUE)

### Arguments

`formula` | A formula specifying a numerical response and a grouping factor (e.g., response ~ treatment)
`data` | A dataframe containing the response and group variable
`type` | type of contrast, with the following options: "Dunnett": many-to-one comparisons, with control in the denominator "Tukey": all-pair comparisons "Sequen": comparison 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 "Changepoint": ratio 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 Note: 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 the Dunnett contrasts, ignored otherwise
`alternative` | a character string: "two.sided": for two-sided tests "less": for lower tail tests "greater": for upper tail tests
`Margin.vec` | a single numerical value or vector of Margins under the null hypotheses, default is 1
`FWER` | a single numeric value specifying the family-wise error rate to be controlled
`Num.Contrast` | Numerator contrast matrix, where columns correspond to groups and rows correspond to contrasts
`Den.Contrast` | Denominator contrast matrix, where columns correspond to groups and rows correspond to contrasts
`names` | a logical value: if TRUE, the output will be named according to names of user defined contrast or factor levels

### Details

The associated ratio test statistic T[i] has a t-distribution. Multiplicity adjustment is achieved by using quantiles of r r-variate t-distributions, which differ in the degree of freedom and share the correlation structure. The compariso-specific degrees of freedom are derived using the approximation according to Satterthwaite (1946).

### Value

An object of class simtest.ratio containing:

`estimate` | a (named) vector of estimated ratios
`teststat` | a (named) vector of the calculated test statistics
`Num.Contrast` | the numerator contrast matrix
`Den.Contrast` | the denominator contrast matrix
`CorrMat` | the correlation matrix of the multivariate t-distribution calculated under the null hypotheses
`critical.pt` | the equicoordinate critical value of the multi-variate t-distribution for a specified FWER
`p.value.raw` | a (named) vector of unadjusted p-values
`p.value.adj` | a (named) vector of p-values adjusted for multiplicity
`Margin.vec` | the vector of margins under the null hypotheses

and some other input arguments.

### Author(s)

Mario Hasler

### References

Simultaneous tests (adjusted p-values)

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

Unadjusted tests (raw p-values)

Hasler M, Vonk R, Hothorn LA (2007). Assessing non-inferiority of a new treatment in a three-arm trial in the presence of heteroscedasticity. Statistics in Medicine 27, 490-503.

Satterthwaite, FE (1946). An approximate distribution of estimates of variance components. Biometrics 2, 110-114.

### See Also

sci.ratioVH for corresponding confidence intervals

### Examples

    ###############################################

    data(Mutagenicity, package="mratios")

    boxplot(MN~Treatment, data=Mutagenicity)

    Mutas<-subset(Mutagenicity, Treatment!="Cyclo25")

    simtest.ratioVH(MN~Treatment, data=Mutagenicity,
     type="Dunnett", base=6, Margin.vec=1.2, alternative="less")

    ###############################################

    # Unadjusted confidence intervals for multiple ratios
    # of means assuming heterogeneous group variances.
    # The following code produces the results given in Table
    # V of Hasler, Vonk and Hothorn (2007).
    # The upper confidence limits in Table V can produced
    # by calling:

    # Mutagenicity of the doses of the new compound,
    # expressed as ratio (DoseX-Vehicle)/(Cyclo25-Vehicle):

    # Check the order of the factor levels:

    levels(Mutagenicity$Treatment)

    # numerators:

    NC<-rbind(
    "Hydro30-Vehicle"=c(0,0,1,0,0,-1),
    "Hydro50-Vehicle"=c(0,0,0,1,0,-1),
    "Hydro75-Vehicle"=c(0,0,0,0,1,-1),
    "Hydro100-Vehicle"=c(0,1,0,0,0,-1)
    )

    DC<-rbind(
    "Cyclo25-Vehicle"=c(1,0,0,0,0,-1),
    "Cyclo25-Vehicle"=c(1,0,0,0,0,-1),
    "Cyclo25-Vehicle"=c(1,0,0,0,0,-1),
    "Cyclo25-Vehicle"=c(1,0,0,0,0,-1)
    )

    colnames(NC)<-colnames(DC)<-levels(Mutagenicity$Treatment)

    NC

    DC

    # The raw p-values are those presented in Table V:

    simtest.ratioVH(formula=MN~Treatment, data=Mutagenicity,
     Num.Contrast=NC, Den.Contrast=DC,
     alternative="less", Margin.vec=0.5, FWER=0.05)

[Package mratios version 1.3.17 Index]