cset function

Confidence regions and intervals around multivariate normal means

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

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).

Returns

An object of class JOC.

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

Author(s)

Philip Pallmann (p.pallmann@lancaster.ac.uk )

Note

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

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)