## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 11, Number 3 (2017), 1513-1536.

### Latent class modeling using matrix covariates with application to identifying early placebo responders based on EEG signals

Bei Jiang, Eva Petkova, Thaddeus Tarpey, and R. Todd Ogden

#### Abstract

Latent class models are widely used to identify unobserved subgroups (i.e., latent classes) based upon one or more manifest variables. The probability of belonging to each subgroup is typically modeled as a function of a set of measured covariates. In this paper, we extend existing latent class models to incorporate matrix covariates. This research is motivated by a randomized placebo-controlled depression clinical trial. One study goal is to identify a subgroup of subjects who experience symptoms improvement early on during antidepressant treatment, which is considered to be an indication of a placebo rather than a true pharmacological response. We want to relate the likelihood of belonging to this subgroup of early responders to baseline electroencephalography (EEG) measurement that takes the form of a matrix. The proposed method is built upon a low-rank Candecomp/Parafac (CP) decomposition of the target coefficient matrix through low-dimensional latent variables, which effectively reduces the model dimensionality. We adopt a Bayesian hierarchical modeling approach to estimate the latent variables, which allows a flexible way to incorporate prior knowledge about covariate effect heterogeneity and offers a data-driven method of regularization. Simulation studies suggest that the proposed method is robust against potentially misspecified rank in the CP decomposition. With the motivating example we show how the proposed method can be applied to extract valuable information from baseline EEG measurements that explains the likelihood of belonging to the early responder subgroup, helping to identify placebo responders and suggesting new targets for the study of placebo response.

#### Article information

**Source**

Ann. Appl. Stat., Volume 11, Number 3 (2017), 1513-1536.

**Dates**

Received: February 2016

Revised: March 2017

First available in Project Euclid: 5 October 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1507168838

**Digital Object Identifier**

doi:10.1214/17-AOAS1044

**Mathematical Reviews number (MathSciNet)**

MR3709568

**Zentralblatt MATH identifier**

1380.62254

**Keywords**

Candecomp/Parafac (CP) matrix decomposition Bayesian hierarchical modeling data-driven regularization major depression placebo effect

#### Citation

Jiang, Bei; Petkova, Eva; Tarpey, Thaddeus; Ogden, R. Todd. Latent class modeling using matrix covariates with application to identifying early placebo responders based on EEG signals. Ann. Appl. Stat. 11 (2017), no. 3, 1513--1536. doi:10.1214/17-AOAS1044. https://projecteuclid.org/euclid.aoas/1507168838

#### Supplemental materials

- Supplement to “Latent class modeling using matrix covariates with application to identifying early placebo responders based on EEG signals”. Web Appendices A and B referenced in Sections 2.5 and 4 are available with this paper at the journal website.Digital Object Identifier: doi:10.1214/17-AOAS1044SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.