plot2D: Plotting 2D confidence sets

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

Creates graphs of (simultaneous) confidence regions and intervals around multivariate normal means using different methods for computing the confidence sets.

Usage

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plot2D(dat, method, alpha=0.1, equi=1.25, plotrange=c(0.77, 1.3),
       axnames=NULL, main="Title", col="black", steps=400, searchwidth=8,
       nboot=1e4, TsengBrownA=1, TsengBrownB=1)

Arguments

dat

A matrix or data.frame with independent units in rows and multivariate outcomes in columns. It must have two columns.

method

A character string specifying the method to be used. See details for available methods.

alpha

A numeric value giving the type I error level to be controlled. Default is 0.1.

equi

A numeric value specifying the equivalence region to be shaded in grey. The value itself defines the upper equivalence threshold and its inverse the lower threshold. When set to NULL no equivalence region is drawn. Default is 1.25.

plotrange

A numeric vector of length two specifying the plotting area in both directions (x and y). Default is c(0.77, 1.3).

axnames

A vector of two character strings giving the x and y axis labels. When set to NULL the column names of dat are used as axis labels. Default is NULL.

main

A character string giving the plot title.

col

A character string specifying the colour of the plotted region or intervals.

steps

An integer setting the initial number of steps for the search algorithm.

searchwidth

A numeric specifying the step width for the search algorithm.

nboot

An integer giving the number of bootstrap replications, which is only required for method="bootkern". Default is 10000.

TsengBrownA

A numeric giving the parameter A to be used when method="tseng.brown" (ignored otherwise). Default is 1.

TsengBrownB

A numeric giving the parameter B to be used when method="tseng.brown" (ignored otherwise). Default is 1.

Details

xxx

Available methods are: emp.bayes for the empirical Bayes region described in Casella & Hwang (1983); expanded for the two one-sided test (TOST) procedure (Schuirmann 1987) using the expanded intervals described e.g., in Bofinger (1992) and Hsu et al. (1994); fixseq for the fixed sequence intervals described in Maurer et al (1995) and Hsu & Berger (1999); hotelling for the Hotelling-type region described in Wang et al (1999); limacon.asy for the limacon-shaped mimimum expected volume region described in Brown et al (1995); limacon.fin for the finite-sample variant of the minimum expected volume region described in Berger & Hsu (1996); standard.cor for the standard region incorporating correlation between parameters; standard.ind for the standard region ignoring correlation between parameters; tost for the two one-sided test (TOST) intervals described in Schuirmann (1987); tseng for the mimimum expected interval length region described in Tseng (2002); tseng.brown for the pseudo-empirical Bayes region described in Tseng & Brown (1997). See also an overview and comparison of all methods in Pallmann & Jaki (2016).

bootkern

Value

A graphical display of a (simultaneous) confidence set in two dimensions.

Note

x

Author(s)

Philip Pallmann ([email protected])

References

Roger L. Berger & Jason C. Hsu (1996) Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statistical Science, 11(4), 283–319.

Eve Bofinger (1992) Expanded confidence intervals, one-sided tests, and equivalence testing. Journal of Biopharmaceutical Statistics, 2(2), 181–188.

Lawrence D. Brown, George Casella, J. T. Gene Hwang (1995) Optimal confidence sets, bioequivalence, and the limacon of Pascal. Journal of the American Statistical Association, 90(431), 880–889.

George Casella & Jiunn T. Hwang (1983) Empirical Bayes confidence sets for the mean of a multivariate normal distribution. Journal of the American Statistical Association, 78(383), 688–698.

Jason C. Hsu & Roger L. Berger (1999) Stepwise confidence intervals without multiplicity adjustment for dose-response and toxicity studies. Journal of the American Statistical Association, 94(446), 468–482.

Jason C. Hsu, J. T. Gene Hwang, Hung-Kung Liu, Stephen J. Ruberg (1994) Confidence intervals associated with tests for bioequivalence. Biometrika, 81(1), 103–114.

Willi Maurer, Ludwig A. Hothorn, Walter Lehmacher (1995) Multiple comparisons in drug clinical trials and preclinical assays: a priori ordered hypotheses. In: Joachim Vollmar (editor), Biometrie in der Chemisch-Pharmazeutischen Industrie, vol. 6, pp. 3–18. Fischer-Verlag, Stuttgart, Germany.

Philip Pallmann & Thomas Jaki (2016) Simultaneous confidence regions and intervals for multivariate bioequivalence. Submitted to Statistics in Medicine.

Donald J. Schuirmann (1987) A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657–680.

Yu-Ling Tseng (2002) Optimal confidence sets for testing average bioequivalence. Test, 11(1), 127–141.

Yu-Ling Tseng & Lawrence D. Brown (1997) Good exact confidence sets for a multivariate normal mean. The Annals of Statistics, 25(5), 2228–2258.

Weizhen Wang, J. T. Gene Hwang, Anirban DasGupta (1999) Statistical tests for multivariate bioequivalence. Biometrika, 86(2), 395–402.

# bootkern not included so far

See Also

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Examples

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# Generate bivariate normal data

mydata <- mvtnorm::rmvnorm(n=50, mean=rep(0.1, 2), sigma=diag(2) * 0.05)

# Specify axis labels

ax <- c(expression(paste(Delta, " log(AUC)")), expression(paste(Delta, " log(Cmax)")))

# Plot simultaneous 90% confidence regions

#plot2D(dat=mydata, method="standard.ind", alpha=0.1, axnames=ax, main="Standard")
#plot2D(dat=mydata, method="standard.cor", alpha=0.1, axnames=ax, main="Standard")
#plot2D(dat=mydata, method="hotelling", alpha=0.1, axnames=ax, main="Hotelling")
#plot2D(dat=mydata, method="limacon.asy", alpha=0.1, axnames=ax, main="Limacon")
#plot2D(dat=mydata, method="limacon.fin", alpha=0.1, axnames=ax, main="Limacon")
#plot2D(dat=mydata, method="tseng", alpha=0.1, axnames=ax, main="Tseng")

# Plot simultaneous 90% confidence intervals

#plot2D(dat=mydata, method="tost", alpha=0.1, axnames=ax, main="TOST")
#plot2D(dat=mydata, method="expanded", alpha=0.1, axnames=ax, main="Expanded TOST")
#plot2D(dat=mydata, method="fixseq", alpha=0.1, axnames=ax, main="Fixed Sequence")

PhilipPallmann/simbe documentation built on May 8, 2019, 1:34 a.m.