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:
  • "var.unequal": possibly unequal group variances,
  • "var.equal": equal group variances
  • FWER a single numeric value specifying the familywise error rate to be controlled

    Details

    Given 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. (submitted): Proof of hazard and proof of safety in toxicological studies using simultaneous confidence intervals for differences and ratios to control; 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)
    

    [Package ETC version 1.1 Index]