sci.ratioVH {mratios} | R Documentation |
This function constructs simultaneous confidence intervals for ratios of linear combinations of normal means in a one-way model, allowing that the variances differ among groups. Different methods are available for multiplicity adjustment.
sci.ratioVH(formula, data, type = "Dunnett", base = 1, method = "Plug", Num.Contrast = NULL, Den.Contrast = NULL, alternative = "two.sided", conf.level = 0.95, names = TRUE)
formula |
A formula specifying a numerical response and a grouping factor as e.g. response ~ treatment |
data |
A dataframe containing the response and group variable |
type |
type of contrast, with the following options:
|
base |
a single integer specifying the control (i.e. denominator) group for the Dunnett contrasts, ignored otherwise |
method |
a character string, specifying the method to be used for confidence interval construction:
|
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 |
alternative |
a character string
|
conf.level |
simultaneous confidence level in case of method="Plug","Bonf", or "MtI", and comparisonwise confidence level in case of method="Unadj" |
names |
logical, indicating whether rownames of the contrast matrices shall be retained in the output |
Given a one-way ANOVA model, the interest is in simultaneous confidence intervals for several ratios of linear combinations of the treatment means. It is assumed that the responses are normally distributed with possibly heterogeneous variances. Multivariate t-distributions are applied with a correlation matrix depending on the unknown ratios and sample variances and degress of freedom according to Satterthwaite (1946).
Using method="Unadj"
results in the methods described in Hasler, Vonk and Hothorn (2007).
An object of class "sci.ratio", containing a list with elements:
estimate |
the point estimates of the ratios |
CorrMat.est |
the estimated correlation matrix |
Num.Contrast |
matrix of contrasts used for the numerator of ratios |
Den.Contrast |
matrix of contrasts used for the denominator of ratios |
conf.int |
the estimated confidence intervals |
NSD |
a logical indicating whether any denominator occured, which were not significantly difference from 0 |
and some of the input arguments.
Mario Hasler, Frank Schaarschmidt
For the univariate confidence intervals, see
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.
For the simultaneous confidence intervals, there is so far no peer-reviewed publication available.
Satterthwaite, FE (1946). An approximate distribution of estimates of variance components. Biometrics 2, 110-114.
plot.sci.ratio
for plots of confidence intervals and simtest.ratioVH
for raw and multiplicity-adjusted p-values
data(Mutagenicity, package="mratios") boxplot(MN~Treatment, data=Mutagenicity) # Unless it is hard to assume Gaussian distribution # in this example this is an attempt to take # heterogeneous variances into account. # Comparisons to the vehicle control, # Proof of Hazard, using multiplicity adjusted # confidence intervals: sci.ratioVH(MN~Treatment, data=Mutagenicity, type="Dunnett", base=6, method="Plug") # Unadjusted confidence intervals for an # intersection union test to proof safety # for all doses of the compound. sci.ratioVH(MN~Treatment, data=Mutagenicity, type="Dunnett", base=6, method="Unadj", alternative="less") # # # # # User-defined contrasts: # 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 CIs<-sci.ratioVH(MN~Treatment, data=Mutagenicity, Num.Contrast=NC, Den.Contrast=DC) # # # # # 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: sci.ratioVH(formula=MN~Treatment, data=Mutagenicity, Num.Contrast=NC, Den.Contrast=DC, method="Unadj", alternative="less", conf.level=0.95)