Package 'ETC'

Title: Equivalence to Control
Description: Treatments of a one-way layout, being equivalent to a control, can be selected with this package. Bonferroni adjusted "two one-sided t-tests" (TOST) and related simultaneous confidence intervals are given for both differences or ratios of means of normally distributed data. For the case of equal variances and balanced sample sizes for the treatment groups, the single-step procedure of Bofinger and Bofinger (1995) <doi:10.1111/j.2517-6161.1995.tb02058.x> can be chosen. For non-normal data, the Wilcoxon test is applied.
Authors: Mario Hasler
Maintainer: Mario Hasler <[email protected]>
License: GPL
Version: 1.5
Built: 2024-12-05 06:45:12 UTC
Source: CRAN

Help Index

Equivalence to Control

Description

Treatments of a one-way layout, being equivalent to a control, can be selected with this package. Bonferroni adjusted "two one-sided t-tests" (TOST) and related simultaneous confidence intervals are given for both differences or ratios of means of normally distributed data. For the case of equal variances and balanced sample sizes for the treatment groups, the single-step procedure of Bofinger and Bofinger (1995) <doi:10.1111/j.2517-6161.1995.tb02058.x> can be chosen. For non-normal data, the Wilcoxon test is applied.

Details

Package: ETC
Type: Package
Version: 1.5
Date: 2022-03-02
License: GPL
LazyLoad: yes

  • etc.diffSimultaneous equivalence tests and related confidence intervals for differences to control

  • etc.ratSimultaneous equivalence tests and related confidence intervals for ratios to control

  • BWData set of body weights measured in a toxicological study

Author(s)

Mario Hasler

Maintainer: Mario Hasler <[email protected]>

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. and Bofinger M. (1995): Equivalence with respect to a control: Stepwise tests, Journal of the Royal Statistical Society B 57 (4), 721-733;

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

Examples

data(BW)

comp <- etc.diff(formula=Weight~Dose, data=BW, margin.up=30, method="Bofinger")
summary(comp)

Body weights measured in a toxicological study

Description

Body weights of a 90-day chronic toxicological study on rats with a control and three dose groups.

Usage

data(BW)

Format

A data frame with 60 observations on the following 2 variables.

Weight

a numeric vector containing the bodyweights of rats

Dose

a factor with levels 1 2 3 4, specifying the dose groups, where 1 is the control group

Source

Hothorn, L.A. (2004): Statistische Auswerteverfahren. In: Regulatorische Toxikologie (Reichl, F.X., ed.). Springer Verlag Heidelberg, pp. 167-181.

Examples

library(ETC)

data(BW)
boxplot(Weight~Dose, data=BW)

Simultaneous equivalence to control for differences of means

Description

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

Usage

etc.diff(formula, data, base = 1, margin.up = NULL, margin.lo = -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 absolute 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 absolute lower margins under the null hypotheses, set to -margin.up by default if not given

method

a character string:

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

  • "var.equal": equal group variances,

  • "Bofinger": equal group variances and equal sample sizes for the non-control groups

  • "non.par": non-normally distributed data

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 in a one-way layout, 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 differences 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"). If the sample sizes of the treatment groups are balanced in the case of equal variances, the single-step procedure of Bofinger and Bofinger (1995) can be chosen with p-values and quantiles coming from a multivariate t-distribution (method="Bofinger"). A warning is given in the output if the Bofinger method is applied for unbalanced treatment groups. For non-normal data, tests based on wilcox.test(..., exact=FALSE, correct=TRUE, ...) are used (method="non.par").

Value

An object of class etc.diff containing:

estimate

a (named) vector of estimated differences

test.stat

a (named) vector of the calculated test statistics

degr.fr

either a single degree of freedom (method="var.equal" and method="Bofinger") or a (named) vector of degrees of freedom (method="var.unequal")

corr.mat

if method="Bofinger", the correlation matrix of the multivariate t-distribution

crit.value

either a single critical value (method="var.equal" and method="Bofinger") or a (named) vector of critical values (method="var.unequal")

p.value

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

conf.int

a (named) matrix of simultaneous confidence intervals

Note

The confidence intervals related to the TOST method (method="var.equal", method="var.unequal", and method="non.par") have simultaneous coverage probability (1-2alpha), while the intervals according to Bofinger and Bofinger (1995) (method="Bofinger") have (1-alpha). All 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. and Bofinger M. (1995): Equivalence with Respect to a Control: Stepwise Tests, Journal of the Royal Statistical Society B 57 (4), 721-733;

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

See Also

etc.rat

Examples

data(BW)

comp <- etc.diff(formula=Weight~Dose, data=BW, margin.up=30, method="Bofinger")
summary(comp)

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)

Print out of the results of etc.diff

Description

A short print out of the results of etc.diff.

Usage

## S3 method for class 'etc.diff'
print(x, digits = 4, ...)

Arguments

x

an object of class "etc.diff" as obtained by calling etc.diff

digits

digits for rounding the results

...

arguments to be passed to print

Value

A print out containing the margins, estimates, confidence intervals, and p.values computed by etc.diff.

Author(s)

Mario Hasler

See Also

print.etc.rat

Print out of the results of etc.rat

Description

A short print out of the results of etc.rat.

Usage

## S3 method for class 'etc.rat'
print(x, digits = 4, ...)

Arguments

x

an object of class "etc.rat" as obtained by calling etc.rat

digits

digits for rounding the results

...

arguments to be passed to print

Value

A print out containing the margins, estimates, confidence intervals, and p.values computed by etc.rat.

Author(s)

Mario Hasler

See Also

print.etc.diff

Summary function for etc.diff

Description

A detailed print out of the results of etc.diff.

Usage

## S3 method for class 'etc.diff'
summary(object, digits = 4, ...)

Arguments

object

an object of class "etc.diff" as obtained by calling etc.diff

digits

digits for rounding the results

...

arguments to be passed to print

Value

A print out containing the margins, degrees of freedom (not for method="non.par"), correlation matrix (if method="Bofinger"), estimates, critical values (not for method="non.par"), test statistics, confidence intervals, and p.values computed by etc.diff.

Author(s)

Mario Hasler

See Also

summary.etc.rat

Summary function for etc.rat

Description

A detailed print out of the results of etc.rat.

Usage

## S3 method for class 'etc.rat'
summary(object, digits = 4, ...)

Arguments

object

an object of class "etc.rat" as obtained by calling etc.rat

digits

digits for rounding the results

...

arguments to be passed to print

Value

A print out containing the margins, degrees of freedom, estimates, critical values, test statistics, confidence intervals, and p.values computed by etc.rat.

Author(s)

Mario Hasler

See Also

summary.etc.diff