Tree-based methods for individualized treatment regimes

Abstract

Individualized treatment rules recommend treatments on the basis of individual patient characteristics. A high-quality treatment rule can produce better patient outcomes, lower costs and less treatment burden. If a treatment rule learned from data is to be used to inform clinical practice or provide scientific insight, it is crucial that it be interpretable; clinicians may be unwilling to implement models they do not understand, and black-box models may not be useful for guiding future research. The canonical example of an interpretable prediction model is a decision tree. We propose a method for estimating an optimal individualized treatment rule within the class of rules that are representable as decision trees. The class of rules we consider is interpretable but expressive. A novel feature of this problem is that the learning task is unsupervised, as the optimal treatment for each patient is unknown and must be estimated. The proposed method applies to both categorical and continuous treatments and produces favourable marginal mean outcomes in simulation experiments. We illustrate it using data from a study of major depressive disorder.

Keywords: Continuous treatment; Exploratory analysis; Personalized medicine; Treatment regime; Tree-based method.

Fig. 1

A decision rule composed of rectangles r₁ = {(1, 1, 1)} and r₂ = {(2,−3,−1)} with rectangular regions ${ℛ}_0=r_1^c\cap r_2$ and ${ℛ}_1=(r_1^c\cap r_2)\cup r_1$.

Fig. 2

Heatmaps of true and estimated optimal treatment rules: (a) average treatment assignment as a function of x₁ and x₂ over 25 learned decision rules for (7), with p = 25 and n = 250; (b) optimal treatment assignment as a function of x₁ and x₂ for (7); optimal treatment assignment for (7) depends exclusively on x₁ and x₂.

Fig. 3

Learned decision rule for nafazodone study: patients with high mood disturbance (MOOD), poor sleep (SLEEPD2), or more severe depression symptoms (HAMD) are assigned nefazodone and cognitive behavioural therapy (Drug + CBT); others are assigned nefazodone only.