# Plotting 2D confidence sets

### Description

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

### Usage

1 2 3 |

### 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 |

`alpha` |
A numeric value giving the type I error level to be controlled. Default is |

`equi` |
A numeric vector of length 2 specifying the equivalence region (lower and upper equivalence threshold) to be shaded in grey. When set to |

`axnames` |
A vector of two character strings giving the x and y axis labels. When set to |

`main` |
A character string giving the plot title. |

`xlim` |
A numeric vector of length two specifying the plotting range on the x-axis. Default is |

`ylim` |
A numeric vector of length two specifying the plotting range on the y-axis. Default is |

`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. |

`nboot` |
An integer giving the number of bootstrap replications, which is only required for |

`TsengBrownA` |
A numeric giving the parameter A to be used when |

`TsengBrownB` |
A numeric giving the parameter B to be used when |

### Details

Available `method`

s are: `bootkern`

for the bootstrap kernel density region described in Pallmann & Jaki (2016); `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).

The default choices of `equi`

, `xlim`

, and `ylim`

are convenient for many bioequivalence settings but can of course be modified as needed.

White dot and white cross (the latter only where theta0 appears).

### Value

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

### Note

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

### Author(s)

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

### 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.

### See Also

`confset`

and `confints`

for confidence boundaries; `plotMV2D`

for confidence regions for a normal mean and variance.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
## Not run:
# 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
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")
plot2D(dat=mydata, method="bootkern", alpha=0.1, axnames=ax, main="Bootstrap")
# Plot simultaneous 90
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")
## End(Not run)
``` |