Dirac Delta Regression: Conditional Density Estimation with Clinical Trials

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 treatment outcomes. 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 patient-specific treatment effects even when no population level effect exists. Moreover, DDR outperforms state-of-the-art algorithms in conditional density estimation on average regardless of the need for causal inference.