Dirac Delta Regression: Conditional Density Estimation with Clinical Trials

TL;DR

Dirac Delta Regression (DDR) is a novel method for estimating the entire conditional outcome density in clinical trials, enabling personalized treatment insights and outperforming existing methods especially with small samples.

Contribution

DDR introduces a new approach to estimate full conditional outcome densities from RCT data, capturing patient-specific outcome distributions beyond mean effects.

Findings

DDR accurately estimates conditional densities in clinical trial data.

DDR outperforms existing algorithms in small sample scenarios.

DDR can detect significant patient-specific effects even without population-level effects.

Abstract

Personalized medicine seeks to identify the causal effect of treatment for a particular patient as opposed to a clinical population at large. Most investigators estimate such personalized treatment effects by regressing the outcome of a randomized clinical trial (RCT) on patient covariates. The realized value of the outcome may however lie far from the conditional expectation. We therefore introduce a method called Dirac Delta Regression (DDR) that estimates the entire conditional density from RCT data in order to visualize the probabilities across all possible outcome values. DDR transforms the outcome into a set of asymptotically Dirac delta distributions and then estimates the density using non-linear regression. The algorithm can identify significant differences in patient-specific outcomes even when no population level effect exists. Moreover, DDR outperforms state-of-the-art algorithms in conditional density estimation by a large margin even in the small sample regime. An R package is available at https://github.com/ericstrobl/DDR.