etc.rat: Simultaneous equivalence to control for ratios of means

etc.ratR Documentation

Simultaneous equivalence to control for ratios of means

Description

Performs simultaneous equivalence tests and related confidence intervals for ratios to control in a one-way layout.

Usage

etc.rat(formula, data, base = 1, margin.up = NULL, margin.lo = 1/margin.up,
        method = "var.unequal", FWER = 0.05)

Arguments

formula

a formula specifying a numerical response and a grouping factor (e.g., response ~ treatment)

data

a data frame containing the response and group variable as columns

base

a single integer specifying the control group

margin.up

a single numerical value or a numeric vector (of lenght equal to the number of comparisons) for relative upper margins under the null hypotheses

margin.lo

a single numerical value or a numeric vector (of lenght equal to the number of comparisons) for relative lower margins under the null hypotheses, set to 1/margin.up by default if not given

method

a character string:

  • "var.unequal": possibly unequal group variances,

  • "var.equal": equal group variances

FWER

a single numeric value specifying the familywise error rate to be controlled by the simultaneous confidence intervals

Details

Having several treatment groups and a control, the object is to simultaneously select those treatments being equivalent to the control. Bonferroni adjusted "two one-sided t-tests" (TOST) and related simultaneous confidence intervals are used for ratios of means of normally distributed data with equal group variances (method="var.equal"). A pooled sample variance over all treatments is taken in this case. Welch-t-Tests are applied for unequal variances (method="var.unequal").

Value

An object of class etc.rat containing:

estimate

a (named) vector of estimated ratios

test.stat

a (named) vector of the calculated test statistics (method="var.equal")

test.stat.up

a (named) vector of the calculated test statistics (up) (method="var.unequal")

test.stat.do

a (named) vector of the calculated test statistics (do) (method="var.unequal")

degr.fr

a single degree of freedom (method="var.equal")

degr.fr.up

a (named) vector of degrees of freedom for test statistics (up) (method="var.unequal")

degr.fr.do

a (named) vector of degrees of freedom for test statistics (do) (method="var.unequal")

degr.fr.ci

a (named) vector of degrees of freedom used for the confidence intervals (method="var.unequal")

crit.value

a single critical value (method="var.equal")

crit.value.up

a (named) vector of critical values for test statistics (up) (method="var.unequal")

crit.value.do

a (named) vector of critical values for test statistics (do) (method="var.unequal")

crit.value.ci

a (named) vector of critical values for the confidence intervals (method="var.unequal")

p.value

a (named) vector of p-values adjusted for multiplicity

conf.int

a (named) matrix of simultaneous confidence intervals

Note

Because related to the TOST method, the confidence intervals have simultaneous coverage probability (1-2alpha). The intervals are "expanded", see Bofinger (1985).

Author(s)

Mario Hasler

References

Hothorn, L.A. and Hasler, M. (2008): Proof of hazard and proof of safety in toxicological studies using simultaneous confidence intervals for differences and ratios to control, Journal of Biopharmaceutical Statistics 18, 915-933;

Bofinger, E. (1985): Expanded confidence intervals, Communications in Statistics - Theory and Methods 14 (8), 1849-1864

See Also

etc.diff

Examples

data(BW)

comp <- etc.rat(formula=Weight~Dose, data=BW, margin.up=1.25, method="var.equal")
summary(comp)

ETC documentation built on March 18, 2022, 5:57 p.m.