TY - JOUR
T1 - Closed Testing in Pharmaceutical Research
T2 - Historical and Recent Developments
AU - Henning, Kevin S.S.
AU - Westfall, Peter H.
N1 - Publisher Copyright:
© 2015, © American Statistical Association.
PY - 2015/4/3
Y1 - 2015/4/3
N2 - In pharmaceutical research, making multiple statistical inferences is standard practice. Unless adjustments are made for multiple testing, the probability of making erroneous determinations of significance increases with the number of inferences. Closed testing is a flexible and easily explained approach to controlling the overall error rate that has seen wide use in pharmaceutical research, particularly in clinical trials settings. In this article, we first give a general review of the uses of multiple testing in pharmaceutical research, with particular emphasis on the benefits and pitfalls of closed testing procedures. We then provide a more technical examination of a class of closed tests that use additive-combination-based and minimum-based p-value statistics, both of which are commonly used in pharmaceutical research. We show that, while the additive combination tests are generally far superior to minimum p-value tests for composite hypotheses, the reverse is true for multiple comparisons using closure-based testing. The loss of power of additive combination tests is explained in terms worst-case “hurdles” that must be cleared before significance can be determined via closed testing. We prove mathematically that this problem can result in the power of a closure-based minimum p-value test approaching 1, while the power of a closure-based additive combination test approaches 0. Finally, implications of these results to pharmaceutical researchers are given.
AB - In pharmaceutical research, making multiple statistical inferences is standard practice. Unless adjustments are made for multiple testing, the probability of making erroneous determinations of significance increases with the number of inferences. Closed testing is a flexible and easily explained approach to controlling the overall error rate that has seen wide use in pharmaceutical research, particularly in clinical trials settings. In this article, we first give a general review of the uses of multiple testing in pharmaceutical research, with particular emphasis on the benefits and pitfalls of closed testing procedures. We then provide a more technical examination of a class of closed tests that use additive-combination-based and minimum-based p-value statistics, both of which are commonly used in pharmaceutical research. We show that, while the additive combination tests are generally far superior to minimum p-value tests for composite hypotheses, the reverse is true for multiple comparisons using closure-based testing. The loss of power of additive combination tests is explained in terms worst-case “hurdles” that must be cleared before significance can be determined via closed testing. We prove mathematically that this problem can result in the power of a closure-based minimum p-value test approaching 1, while the power of a closure-based additive combination test approaches 0. Finally, implications of these results to pharmaceutical researchers are given.
KW - Clinical trials
KW - Closure-based multiple testing
KW - Power
KW - Simulation
KW - p-Value combination tests
UR - http://www.scopus.com/inward/record.url?scp=84932600444&partnerID=8YFLogxK
U2 - 10.1080/19466315.2015.1004270
DO - 10.1080/19466315.2015.1004270
M3 - Article
AN - SCOPUS:84932600444
SN - 1946-6315
VL - 7
SP - 126
EP - 147
JO - Statistics in Biopharmaceutical Research
JF - Statistics in Biopharmaceutical Research
IS - 2
ER -