TY - JOUR
T1 - Comparing multiple treatments to both positive and negative controls
AU - Dasgupta, Nairanjana
AU - Solorzano, Eleanne
AU - TONG, Tiejun
N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2010/1/1
Y1 - 2010/1/1
N2 - In the past, most comparison to control problems have dealt with comparing k test treatments to either positive or negative controls. Dasgupta et al. [2006. Using numerical methods to find the least favorable configuration when comparing k test treatments to both positive and negative controls. Journal of Statistical Computation and Simulation 76, 251-265] enumerate situations where it is imperative to compare several test treatments to both a negative as well as a positive control simultaneously. Specifically, the aim is to see if the test treatments are worse than the negative control, or if they are better than the positive control when the two controls are sufficiently apart. To find critical regions for this problem, one needs to find the least favorable configuration (LFC) under the composite null. In their paper, Dasgupta et al. [2006. Using numerical methods to find the least favorable configuration when comparing k test treatments to both positive and negative controls. Journal of Statistical Computation and Simulation 76, 251-265] came up with a numerical technique to find the LFC. In this paper we verify their result analytically. Via Monte Carlo simulation we compare the proposed method to the logical single step alternatives: Dunnett's [1955. A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association 50, 1096-1121] or the Bonferroni correction. The proposed method is superior in terms of both the Type I error and the marginal power.
AB - In the past, most comparison to control problems have dealt with comparing k test treatments to either positive or negative controls. Dasgupta et al. [2006. Using numerical methods to find the least favorable configuration when comparing k test treatments to both positive and negative controls. Journal of Statistical Computation and Simulation 76, 251-265] enumerate situations where it is imperative to compare several test treatments to both a negative as well as a positive control simultaneously. Specifically, the aim is to see if the test treatments are worse than the negative control, or if they are better than the positive control when the two controls are sufficiently apart. To find critical regions for this problem, one needs to find the least favorable configuration (LFC) under the composite null. In their paper, Dasgupta et al. [2006. Using numerical methods to find the least favorable configuration when comparing k test treatments to both positive and negative controls. Journal of Statistical Computation and Simulation 76, 251-265] came up with a numerical technique to find the LFC. In this paper we verify their result analytically. Via Monte Carlo simulation we compare the proposed method to the logical single step alternatives: Dunnett's [1955. A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association 50, 1096-1121] or the Bonferroni correction. The proposed method is superior in terms of both the Type I error and the marginal power.
KW - Least favorable configuration
KW - Log concavity
KW - Multiple comparison
KW - Negative control
KW - Positive control
UR - http://www.scopus.com/inward/record.url?scp=70349306609&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2009.07.001
DO - 10.1016/j.jspi.2009.07.001
M3 - Journal article
AN - SCOPUS:70349306609
SN - 0378-3758
VL - 140
SP - 180
EP - 188
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1
ER -