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

In ETC: Equivalence to Control

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.