Dirac Delta Regression: Conditional Density Estimation with Clinical Trials
This work addresses personalized medicine by enabling visualization of outcome probabilities for individual patients, which is incremental as it builds on existing regression methods for treatment effects.
The paper tackles the problem of estimating personalized treatment effects in clinical trials by introducing Dirac Delta Regression (DDR), a method that estimates the entire conditional density from randomized clinical trial data, outperforming state-of-the-art algorithms in conditional density estimation by a large margin even with small samples.
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.