Type: | Package |
Title: | Equivalence to Control |
Version: | 1.5 |
Date: | 2022-03-02 |
Author: | Mario Hasler |
Suggests: | SimComp, multcomp, mratios |
Imports: | mvtnorm, stats |
Maintainer: | Mario Hasler <hasler@email.uni-kiel.de> |
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. |
License: | GPL-2 | GPL-3 [expanded from: GPL] |
LazyLoad: | yes |
NeedsCompilation: | no |
Packaged: | 2022-03-02 13:48:41 UTC; Administrator |
Repository: | CRAN |
Date/Publication: | 2022-03-02 15:30:14 UTC |
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 <hasler@email.uni-kiel.de>
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, where1
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:
|
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
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:
|
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)
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 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
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 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