simtest.ratio {mratios} | R Documentation |
Performs simultaneous tests for several ratios of linear combinations of treatment means in the normal one-way ANOVA model with homogeneous variances.
simtest.ratio(formula, data, type = "Dunnett", base = 1, alternative = "two.sided", Margin.vec = NULL, FWER = 0.05, Num.Contrast = NULL, Den.Contrast = NULL, names = TRUE)
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:
|
base |
a single integer specifying the control (i.e. denominator) group for the Dunnett contrasts, ignored otherwise |
alternative |
a character string:
|
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 |
Given a one-way ANOVA model, the interest is in simultaneous tests for several ratios of linear combinations of the treatment means. Let us denote the ratios by gamma_i, i=1,...,r, and let psi_i, i=1,...,r, denote the relative margins against which we compare the ratios. For example, upper-tail simultaneous tests for the ratios are stated as
H_0i: gamma_i <= psi_i
versus
H_1i: gamma_i > psi_i, i=1,...,r
.
The associated likelihood ratio test statistic T_i has a t-distribution. For multiplicity adjustments, we use the joint distribution of the T_i , i=1,...,r, which under the null hypotheses follows a central r-variate t-distribution. Adjusted p-values can be calculated by adapting the results of Westfall et al. (1999) for ratio formatted hypotheses.
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.
Gemechis Dilba, Frank Schaarschmidt
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.
Westfall, P.H., Tobias, R.D., Rom, D., Wolfinger, R.D., and Hochberg, Y. (1999): Multiple comparisons and multiple tests using the SAS system. SAS Institute Inc. Cary, NC, 65-81.
While print.simtest.ratio
produces a small default print-out of the results,
summary.simtest.ratio
can be used to produce a more detailed print-out, which is recommended if user-defined contrasts are used,
sci.ratio
for constructing simultaneous confidence intervals for ratios in oneway layout
See summary.glht(multcomp)
for multiple tests for parameters of lm
, glm
.
library(mratios) # # # # User-defined contrasts for comparisons # between Active control, Placebo and three dosage groups: data(AP) AP boxplot(pre_post~treatment, data=AP) # Test whether the differences of doses 50, 100, 150 vs. Placebo # are non-inferior to the difference of Active control vs. Placebo # User-defined contrasts: # Numerator Contrasts: NC <- rbind( "(D100-D0)" = c(0,-1,1,0,0), "(D150-D0)" = c(0,-1,0,1,0), "(D50-D0)" = c(0,-1,0,0,1)) # Denominator Contrasts: DC <- rbind( "(AC-D0)" = c(1,-1,0,0,0), "(AC-D0)" = c(1,-1,0,0,0), "(AC-D0)" = c(1,-1,0,0,0)) NC DC noninf <- simtest.ratio(pre_post ~ treatment, data=AP, Num.Contrast=NC, Den.Contrast=DC, Margin.vec=c(0.9,0.9,0.9), alternative="greater") summary( noninf ) # # # # Some more examples on standard multiple comparison procedures # stated in terms of ratio hypotheses: # Comparisons vs. Control: many21 <- simtest.ratio(pre_post ~ treatment, data=AP, type="Dunnett") summary(many21) # Let the Placebo be the control group, which is the second level # in alpha-numeric order. A simultaneous test for superiority of # the three doses and the Active control vs. Placebo could be # done as: many21P <- simtest.ratio(pre_post ~ treatment, data=AP, type="Dunnett", base=2, alternative="greater", Margin.vec=1.1) summary(many21P) # All pairwise comparisons: allpairs <- simtest.ratio(pre_post ~ treatment, data=AP, type="Tukey") summary(allpairs) # # # # Comparison to grand mean of all strains # in the Penicillin example: data(Penicillin) CGM <- simtest.ratio(diameter~strain, data=Penicillin, type="GrandMean") CGM summary(CGM)