multeq.rat  R Documentation 
Performs equivalence tests and related confidence intervals for ratios of two normal means of multiple endpoints.
multeq.rat(data, grp, resp = NULL, base = 1, margin.lo = NULL, margin.up = NULL, method = "single.step", var.equal = FALSE, FWER = 0.05)
data 
a data frame containing response variables (endpoints) and the group variable as columns, the data must have exactly two treatment groups 
grp 
the name of the group variable in " " 
resp 
a vector of names of the response variables (endpoints) in " " 
base 
a single integer specifying the base/control group 
margin.lo 
a vector of relative lower margins under the null hypotheses relating to the endpoints 
margin.up 
a vector of relative upper margins under the null hypotheses relating to the endpoints 
method 
a character string:

var.equal 
a logical indicating homogeneous or heterogeneous variances of the data 
FWER 
a single numeric value specifying the familywise error rate to be controlled by the simultaneous confidence intervals 
The objective is to show equivalence for two treatment groups on multiple primary, normally distributed response variables (endpoints). If margin.up is not given, onesided tests are applied for the alternative hypothesis that the ratios (to the base group) of the means is larger than margin.lo. Analogously, same vice versa. Only if both margin.lo and margin.up are given, a twosided equivalence tests for ratios is done. Bonferroni adjusted "two onesided ttests" (TOST) and related simultaneous confidence intervals are used for method "single.step"; an extended version of the method of Quan et al. (2001) is applied for "step.up". Welch ttests and related confidence intervals are used for var.equal=FALSE.
An object of class multeq.rat containing:
estimate 
a (named) vector of estimated ratios 
test.stat 
a (named) vector of the calculated test statistics (var.equal=TRUE) 
test.stat.up 
a (named) vector of the calculated test statistics (up) (var.equal=FALSE) 
test.stat.do 
a (named) vector of the calculated test statistics (do) (var.equal=FALSE) 
degr.fr 
a single degree of freedom (var.equal=TRUE) 
degr.fr.up 
a (named) vector of degrees of freedom for test statistics (up) (var.equal=FALSE) 
degr.fr.do 
a (named) vector of degrees of freedom for test statistics (do) (var.equal=FALSE) 
degr.fr.ci 
a (named) vector of degrees of freedom used for the confidence intervals (var.equal=FALSE) 
p.value 
a (named) vector of pvalues adjusted for multiplicity 
lower 
a (named) vector of lower confidence limits 
upper 
a (named) vector of upper confidence limits 
Because related to the TOST method, the twosided confidence intervals for method="single.step" have simultaneous coverage probability (12alpha). The intervals for method="step.up" are stepwise adjusted and only applicable for test decisions, not for a simultaneous parameter estimation or comparing among each other.
Mario Hasler
Quan et al. (2001): Assessmant of equivalence on multiple endpoints, Statistics in Medicine 20, 31593173
multeq.diff
data(clinic) comp < multeq.rat(data=clinic,grp="fact",method="step.up",margin.up=rep(1.25,5), margin.lo=1/rep(1.25,5)) summary(comp)
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