Measuring the individual benefit of a medical or behavioral treatment using generalized linear mixed-effects models

Abstract

We propose statistical definitions of the individual benefit of a medical or behavioral treatment and of the severity of a chronic illness. These definitions are used to develop a graphical method that can be used by statisticians and clinicians in the data analysis of clinical trials from the perspective of personalized medicine. The method focuses on assessing and comparing individual effects of treatments rather than average effects and can be used with continuous and discrete responses, including dichotomous and count responses. The method is based on new developments in generalized linear mixed-effects models, which are introduced in this article. To illustrate, analyses of data from the Sequenced Treatment Alternatives to Relieve Depression clinical trial of sequences of treatments for depression and data from a clinical trial of respiratory treatments are presented. The estimation of individual benefits is also explained. Copyright © 2016 John Wiley & Sons, Ltd.

Trial registration: ClinicalTrials.gov NCT00021528.

Keywords: chronic diseases; clinical trials; disease severity; empirical Bayesian prediction; generalized linear mixed-effects models; random effects linear models.

Conflict of interest statement

The Author declares that there is no conflict of interest.

Copyright © 2016 John Wiley & Sons, Ltd.

Figures

Figure 1

Illustration of a basal severity function and benefit functions for a 1-PM model with a Gaussian response with identity link, using an incremental therapeutic target with y = 1 and σε=σε′=1. (A) Basal severity function. (B) Benefit function for βQ1 = 3. (C) Benefit function for βQ2 = −2. (D) Superimposition of the functions in A and B and another benefit function for which βQ3 = 1.7.

Figure 2

Illustration of a basal severity function and benefit functions for a 1-PM model with a Gaussian response with identity link, using a closed target with y* = 1, δ = 1.64 and σε=σε′=1. (A) Basal severity function. (B) Benefit function for βQ1 = 3. (C) Benefit function for βQ2 = −2. (D) Superimposition of the functions in A, B and C. (E) Superimposition of the functions in A and B and an additional benefit function with βQ3 = 1.7.

Figure 2

Illustration of a basal severity function and benefit functions for a 1-PM model with a Gaussian response with identity link, using a closed target with y* = 1, δ = 1.64 and σε=σε′=1. (A) Basal severity function. (B) Benefit function for βQ1 = 3. (C) Benefit function for βQ2 = −2. (D) Superimposition of the functions in A, B and C. (E) Superimposition of the functions in A and B and an additional benefit function with βQ3 = 1.7.

Figure 3

Comparison of benefit functions of Bupropion and Venlafaxine in patients refractory to Citalopram treatment. (A) Black patients. (B) Non-black patients.

Figure 4

Benefit functions for Drug A and Placebo in a clinical trial aiming at improving respiratory status. The vertical lines mark average values of Λ for subjects of particular ages. The illustrated ages are the youngest age in the patient sample (11), the oldest (63), the median age (28), and the 10% and 90% percentiles (15 and 47).