Some examples of situations with multiple comparisons are given in the special context of dose finding. Procedures controlling the multiple level (or the experimentwise error in the strong sense) are emphasized. The closed testing principle is explained as a general tool for deriving concrete multiple tests with this property. The resulting procedures are sketched in the field of dose finding. Finally, one outlook on dealing with adaptive designs is provided.
WilliamsDA. A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics. 1971;27: 103–117.
2.
BuddeMBauerP. Multiple test procedures in clinical dose finding studies. J Am Stat Assoc. 1989;407: 792–796.
3.
HochbergYTamhaneAC. Multiple Comparison Procedures. New York: John Wiley & Sons; 1987.
4.
MarcusRPeritzEGabrielKR. On closed testing procedures with special reference to ordered analysis of variance. Biometrika. 1976;63: 655–660.
5.
SpjøtvolleE. On the optimality of some multiple comparison procedures. Ann Math Stat. 1972;48: 398–411.
6.
BechhoferRE. A single sample multiple decision procedure for ranking means of normal populations with known variances. Ann Math Stat. 1954;25: 16–39.
7.
DuncanDB. A Bayesian approach to multiple comparisons. Technometrics. 1965;7: 171–222.
8.
FinnerHGianiG. Closed subset selection procedures for selecting good populations. J Stat Plan Inf. 1993; in press.
9.
BauerP. Multistage testing with adaptive designs. Biometrie und Inf in Med u Biol. 1989a; 20(4):130–148.
10.
BauerP. A sequential elimination procedure for choosing the best population(s) based on multiple testing. J Stat Plan Inf. 1989b;21: 245–252.
11.
SonnemannE. Allegmeine Lösung multipler Testprobleme. EDV in Medizin und Biologie. 1982;13: 120–128.
12.
SonnemannEFinnerH. Vollständigkeitssätze für multiple Testprobleme. Proceedings of the symposion in Gerolstein “Multiple Hypotheses Testing.” BauerP.HommelG.SonnemannE., eds. Heidelberg: Springer-Verlag; 1988.
13.
BauerP. Multiple testing in clinical trials. Stat Med.1991;10: 871–890.
14.
HolmS. A simple sequentially rejective multiple test procedure. Scand J Stat. 1979;6: 65–70.
RubergSJ. Contrasts for identifying the minimum effective dose. J Am Stat Assoc. 1989;407: 816–822.
17.
BauerPHacklP. The use of Hunter's inequality in simultaneous testing. Biom J.1986;27: 25–38.
18.
BauerP. On the assessment of the performance of multiple test procedures. Biom J.1987;29(8):895–906.
19.
BauerPKöhneK. Evaluation of experiments with adaptive interim analyses. Department of Medical Statistics, University of Cologne, Technical Report: 1992.
