cset {jocre}

Confidence regions and intervals around multivariate normal means

Description

Computes boundaries of (simultaneous) confidence regions and intervals around multivariate normal means using different methods.

Usage

cset(dat, method, alpha=0.1, steps=NULL, nboot=1e4, TsengBrownA=1, TsengBrownB=1)

Arguments

dat

A matrix or data.frame with independent units in rows and multivariate outcomes in 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.

steps

An integer setting the initial number of steps for the search algorithm. Default is NULL, which chooses 300 for two-dimensional and 50 for higher-dimensional problems.

nboot

A numeric giving the number of bootstrap replications to be used when method="bootkern" (ignored otherwise). Default is 1e4.

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

Available methods for confidence regions are: boot.kern for the nonparametric bootstrap method using kernel density estimation described in Pallmann & Jaki (2017); emp.bayes for the empirical Bayes region described in Casella & Hwang (1983); 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 described in Chew (1966); 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).

Available methods for confidence intervals are: 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); fix.seq for the fixed sequence intervals described in Maurer et al (1995) and Hsu & Berger (1999); tost for the two one-sided test (TOST) intervals described in Schuirmann (1987).

See also an overview and comparison of all methods in Pallmann & Jaki (2017).

Value

An object of class JOC.

Note

Warning: please use with care! Some of the functionality has not yet been thoroughly tested.

Author(s)

Philip Pallmann ([e-mail])

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.

Victor Chew (1966) Confidence, prediction, and tolerance regions for the multivariate normal distribution. Journal of the American Statistical Association, 61(315), 605–617.

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 (2017) 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

csetMV for (simultaneous) confidence regions for normal mean and variance.

Examples

## Not run: 
# Example 1: simultaneous 90% confidence intervals for trivariate data

trivar <- mvtnorm::rmvnorm(n=20, mean=rep(0.05, 3), sigma=toeplitz(c(0.05, 0.04, 0.03)))
colnames(trivar) <- c("AUCinf", "AUCt", "Cmax")

tost <- cset(dat=trivar, method="tost", alpha=0.1)
summary(tost)

# Example 2: simultaneous 90% confidence regions for bivariate data

bivar <- mvtnorm::rmvnorm(n=20, mean=rep(0.05, 2), sigma=toeplitz(c(0.05, 0.04)))
colnames(bivar) <- c("AUC", "Cmax")

hotelling <- cset(dat=bivar, method="hotelling", alpha=0.1)
summary(hotelling)
plot(hotelling, main="90% Hotelling Region")

limacon <- cset(dat=bivar, method="limacon.asy", alpha=0.1)
summary(limacon)
plot(limacon, main="90% Limacon Region")

tseng <- cset(dat=bivar, method="tseng", alpha=0.1)
summary(tseng)
plot(tseng, main="90% Tseng Region")

## End(Not run)