Statistics Papers

Document Type

Journal Article

Date of this Version

2010

Publication Source

The Annals of Applied Statistics

Volume

4

Issue

1

Start Page

366

Last Page

395

DOI

10.1214/09-AOAS282

Abstract

In a clinical trial of a treatment for alcoholism, a common response variable of interest is the number of alcoholic drinks consumed by each subject each day, or an ordinal version of this response, with levels corresponding to abstinence, light drinking and heavy drinking. In these trials, within-subject drinking patterns are often characterized by alternating periods of heavy drinking and abstinence. For this reason, many statistical models for time series that assume steady behavior over time and white noise errors do not fit alcohol data well. In this paper we propose to describe subjects’ drinking behavior using Markov models and hidden Markov models (HMMs), which are better suited to describe processes that make sudden, rather than gradual, changes over time. We incorporate random effects into these models using a hierarchical Bayes structure to account for correlated responses within subjects over time, and we estimate the effects of covariates, including a randomized treatment, on the outcome in a novel way. We illustrate the models by fitting them to a large data set from a clinical trial of the drug Naltrexone. The HMM, in particular, fits this data well and also contains unique features that allow for useful clinical interpretations of alcohol consumption behavior.

Keywords

hidden Markov models, alcoholism clinical trial, longitudinal data, mixed effects models, alcohol relapse, MCMC for mixture models

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Date Posted: 27 November 2017

This document has been peer reviewed.