TY - JOUR

T1 - Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables

AU - Schaarschmidt, Frank

N1 - Funding Information: I thank the anonymous referees as well as L.A. Hothorn and M. Hasler for their helpful and constructive comments on earlier versions of this manuscript. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n ∘ HEALTH-F5-2008-201619 , and the German Science Foundation DFG-H01678/9 .

PY - 2013/2

Y1 - 2013/2

N2 - In biological and medical research, continuous, strictly positive, right-skewed data, possibly with heterogeneous variances, are common, and can be described by log-normal distributions. In experiments involving multiple treatments in a one-way layout, various sets of multiple comparisons among the treatments and corresponding simultaneous confidence intervals can be of interest. The focus is on multiple contrasts of the expected values of the treatments. Previously published methods based on normal approximations and generalized pivotal quantities are extended to the case of multiple contrasts. These methods are evaluated in a simulation study that involves comparisons to a control group, all pairwise comparisons and, to illustrate more general multiple contrast types, a non-standard type of contrast matrix. A method based on generalized pivotal quantities is recommended because it is superior to all other methods in terms of simultaneous coverage probability and because the type-I-errors are distributed almost equally between lower and upper confidence bounds. Methods based on normal approximations are found to be very liberal and biased with respect to directional type-I-errors. These methods are illustrated with an example from pharmaceutical research.

AB - In biological and medical research, continuous, strictly positive, right-skewed data, possibly with heterogeneous variances, are common, and can be described by log-normal distributions. In experiments involving multiple treatments in a one-way layout, various sets of multiple comparisons among the treatments and corresponding simultaneous confidence intervals can be of interest. The focus is on multiple contrasts of the expected values of the treatments. Previously published methods based on normal approximations and generalized pivotal quantities are extended to the case of multiple contrasts. These methods are evaluated in a simulation study that involves comparisons to a control group, all pairwise comparisons and, to illustrate more general multiple contrast types, a non-standard type of contrast matrix. A method based on generalized pivotal quantities is recommended because it is superior to all other methods in terms of simultaneous coverage probability and because the type-I-errors are distributed almost equally between lower and upper confidence bounds. Methods based on normal approximations are found to be very liberal and biased with respect to directional type-I-errors. These methods are illustrated with an example from pharmaceutical research.

KW - Coverage probability

KW - Generalized pivotal quantity

KW - Multiple contrasts

KW - One-way layout

UR - http://www.scopus.com/inward/record.url?scp=84869096852&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2012.08.011

DO - 10.1016/j.csda.2012.08.011

M3 - Article

AN - SCOPUS:84869096852

VL - 58

SP - 265

EP - 275

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 1

ER -