multeq.rat {MultEq}

Equivalence for ratios of means of multiple endpoints

Description

Performs equivalence tests and related confidence intervals for ratios of two normal means of multiple endpoints.

Usage

multeq.rat(data, grp, resp = NULL, base = 1, margin.lo = NULL, margin.up = NULL,
           method = "single.step", var.equal = FALSE, FWER = 0.05)

Arguments

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:

• "step.up": method of Quan et al. (2001),

• "single.step": Bonferroni-adjusted single-step procedure

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

Details

The objective is to show equivalence for two treatment groups on multiple primary, normally distributed response variables (endpoints). If margin.up is not given, one-sided 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 two-sided equivalence tests for ratios is done. Bonferroni adjusted "two one-sided t-tests" (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 t-tests and related confidence intervals are used for var.equal=FALSE.

Value

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 p-values adjusted for multiplicity

lower

a (named) vector of lower confidence limits

upper

a (named) vector of upper confidence limits

Note

Because related to the TOST method, the two-sided confidence intervals for method="single.step" have simultaneous coverage probability (1-2alpha). 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.

Author(s)

Mario Hasler

References

Quan et al. (2001): Assessmant of equivalence on multiple endpoints, Statistics in Medicine 20, 3159-3173

See Also

multeq.diff

Examples

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)