etc.rat {ETC}

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)