Dirac Delta Regression: Conditional Density Estimation with Clinical Trials

Eric V. Strobl, Shyam Visweswaran
Proceedings of The KDD'21 Workshop on Causal Discovery, PMLR 150:78-125, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v150-strobl21a, title = {Dirac Delta Regression: Conditional Density Estimation with Clinical Trials}, author = {Strobl, Eric V. and Visweswaran, Shyam}, booktitle = {Proceedings of The KDD'21 Workshop on Causal Discovery}, pages = {78--125}, year = {2021}, editor = {Le, Thuc Duy and Li, Jiuyong and Cooper, Greg and Triantafyllou, Sofia and Bareinboim, Elias and Liu, Huan and Kiyavash, Negar}, volume = {150}, series = {Proceedings of Machine Learning Research}, month = {15 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v150/strobl21a/strobl21a.pdf}, url = {https://proceedings.mlr.press/v150/strobl21a.html}, 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.} }
Endnote
%0 Conference Paper %T Dirac Delta Regression: Conditional Density Estimation with Clinical Trials %A Eric V. Strobl %A Shyam Visweswaran %B Proceedings of The KDD'21 Workshop on Causal Discovery %C Proceedings of Machine Learning Research %D 2021 %E Thuc Duy Le %E Jiuyong Li %E Greg Cooper %E Sofia Triantafyllou %E Elias Bareinboim %E Huan Liu %E Negar Kiyavash %F pmlr-v150-strobl21a %I PMLR %P 78--125 %U https://proceedings.mlr.press/v150/strobl21a.html %V 150 %X 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.
APA
Strobl, E.V. & Visweswaran, S.. (2021). Dirac Delta Regression: Conditional Density Estimation with Clinical Trials. Proceedings of The KDD'21 Workshop on Causal Discovery, in Proceedings of Machine Learning Research 150:78-125 Available from https://proceedings.mlr.press/v150/strobl21a.html.

Related Material