Statistics and Its Interface

Volume 9 (2016)

Number 3

Stratified psychiatry via convexity-based clustering with applications towards moderator analysis

Pages: 255 – 266



Thaddeus Tarpey (Department of Mathematics and Statistics, Wright State University, Dayton, Ohio, U.S.A.)

Eva Petkova (Department of Child and Adolescent Psychiatry, New York University, New York, N.Y., U.S.A.; and the Nathan S. Kline Institute for Psychiatric Research, Orangeburg, New York, U.S.A.)

Liangyu Zhu (Department of Statistics, North Carolina State University, Rayleigh, N.C., U.S.A.)


Understanding heterogeneity in phenotypical characteristics, symptoms manifestations and response to treatment of subjects with psychiatric illnesses is a continuing challenge in mental health research. A long-standing goal of medical studies is to identify groups of subjects characterized with a particular trait or quality and to distinguish them from other subjects in a clinically relevant way. This paper develops and illustrates a novel approach to this problem based on a method of optimal-partitioning (clustering) of functional data. The proposed method allows for the simultaneous clustering of different populations (e.g., symptoms of drug and placebo treated patients) in order to identify prototypical outcome profiles that are distinct from one or the other treatment and outcome profiles common to the different treatments. The clustering results are used to discover potential treatment effect modifiers (i.e., moderators), in particular, moderators of specific drug effects and placebo response. A depression clinical trial is used to illustrate the method.


longitudinal data analysis, mixed models, partitioning, personalized medicine, placebo response.

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Published 27 January 2016