etc.rat {ETC} | R 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:
|
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
Examples
data(BW)
comp <- etc.rat(formula=Weight~Dose, data=BW, margin.up=1.25, method="var.equal")
summary(comp)