UNTANGLING EFFECT AND SIDE EFFECT: CONSIS-TENT CAUSAL INFERENCE IN NON-TARGETED TRIALS

Abstract

A treatment is usually appropriate for some group (the "sick" group) on whom it has an effect, but it can also have a side-effect when given to subjects from another group (the "healthy" group). In a non-targeted trial both sick and healthy subjects may be treated, producing heterogeneous effects within the treated group. Inferring the correct treatment effect on the sick population is then difficult, because the effect and side-effect are tangled. We propose an efficient nonparametric approach to untangling the effect and side-effect, called PCM (pre-cluster and merge). We prove its asymptotic consistency in a general setting and show, on synthetic data, more than a 10x improvement in accuracy over existing state-of-the-art.

1. INTRODUCTION

A standard approach to causal effect estimation is the targeted randomized controlled trial (RCT), see (8; 13; 15; 17; 23) . To test a treatment's effect on a sick population, subjects are recruited and admitted into the trial based on eligibility criteria designed to identify sick subjects. The trial subjects are then randomly split into a treated group that receives the treatment and a control group that receives the best alternative treatment (or a placebo). "Targeted" means only sick individuals are admitted into the trial via the eligibility criteria, with the implicit assumption that only a single treatment-effect is to be estimated. This ignores the possibility of treated subgroups among the sick population with heterogeneous effects. Further, one often does not have the luxury of a targeted RCT. For example, eligibility criteria for admittance to the trial may not unambiguously identify sick subjects, or one may not be able to control who gets into the trial. When the treatment is not exclusively applied on sick subjects, we say the trial is non-targeted and new methods are needed to extract the treatment effect on the sick, (25). Non-targeted trials are the norm whenever subjects self-select into an intervention, which is often the case across domains stretching from healthcare to advertising. We propose a nonparametric approach to causal inference in non-targeted trials, based on a pre-cluster and merge strategy. Assume a population is broken into ℓ groups with different expected treatment effects in each group. Identify each group with the level of its treatment effect, so there are effect levels c = 0, 1, . . . , ℓ-1. For example, a population's subjects can be healthy, c = 0, or sick, c = 1. We use the Rubin-Neyman potential outcome framework, (19). A subject is a tuple s = (x, c, t, y) sampled from a distribution D, where x ∈ [0, 1] d is a feature-vector such as [age, weight], c indicates the subject's level, t indicates the subjects treatment cohort, and y is the observed outcome. The observed outcome is one of two potential outcomes, v if treated or v if not treated. We consider strongly ignorable trials: given x, the propensity to treat is strictly between 0 and 1 and the potential outcomes {v, v} depend only on x, independent of t. In a strongly ignorable trial, one can use the features to identify counterfactual controls for estimating effect. The level c is central to the scope of our work. Mathematically, c is a hidden effect modifier which determines the distribution of the potential outcomes (c is an unknown and possibly complex function of x). The level c dichotomizes the feature space into subpopulations with different effects. One tries to design the eligibility criteria for the trial to ensure that the propensity to treat is non-zero only for subjects in one level. What to do when the eligibility criteria allow more than one level into the trial is exactly the problem we address. Though our work applies to a general number of levels, all the main ideas can be illustrated with just two levels, c ∈ {0, 1}. For the sake of concreteness, we denote these two levels healthy and sick.

