The Annals of Applied Statistics

Pairwise comparison of treatment levels in functional analysis of variance with application to erythrocyte hemolysis

Olga Vsevolozhskaya, Mark Greenwood, and Dmitri Holodov

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Motivated by a practical need for the comparison of hemolysis curves at various treatment levels, we propose a novel method for pairwise comparison of mean functional responses. The hemolysis curves—the percent hemolysis as a function of time—of mice erythrocytes (red blood cells) by hydrochloric acid have been measured among different treatment levels. This data set fits well within the functional data analysis paradigm, in which a time series is considered as a realization of the underlying stochastic process or a smooth curve. Previous research has only provided methods for identifying some differences in mean curves at different times. We propose a two-level follow-up testing framework to allow comparisons of pairs of treatments within regions of time where some difference among curves is identified. The closure multiplicity adjustment method is used to control the family-wise error rate of the proposed procedure.

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Ann. Appl. Stat., Volume 8, Number 2 (2014), 905-925.

First available in Project Euclid: 1 July 2014

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Functional data analysis FANOVA multiple comparison permutation method pairwise comparison


Vsevolozhskaya, Olga; Greenwood, Mark; Holodov, Dmitri. Pairwise comparison of treatment levels in functional analysis of variance with application to erythrocyte hemolysis. Ann. Appl. Stat. 8 (2014), no. 2, 905--925. doi:10.1214/14-AOAS723.

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Supplemental materials

  • Supplementary material: Additional simulation results. Additional simulation results for the two models (M1 or M2), two different number of intervals ($m=5$ or $m=10$), and either 5 or 20 subjects per group are summarized in the tables below. Overall, these results indicate that the procedure tends to lose power as the number of intervals increases but gains power as the number of subjects per group increases.