Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations

Nabeel Seedat, Fergus Imrie, Alexis Bellot, Zhaozhi Qian, Mihaela van der Schaar
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:19497-19521, 2022.

Abstract

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer "what-if" questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all scenarios with irregular sampling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-seedat22b, title = {Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations}, author = {Seedat, Nabeel and Imrie, Fergus and Bellot, Alexis and Qian, Zhaozhi and van der Schaar, Mihaela}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {19497--19521}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/seedat22b/seedat22b.pdf}, url = {https://proceedings.mlr.press/v162/seedat22b.html}, abstract = {Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer "what-if" questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all scenarios with irregular sampling.} }
Endnote
%0 Conference Paper %T Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations %A Nabeel Seedat %A Fergus Imrie %A Alexis Bellot %A Zhaozhi Qian %A Mihaela van der Schaar %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-seedat22b %I PMLR %P 19497--19521 %U https://proceedings.mlr.press/v162/seedat22b.html %V 162 %X Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer "what-if" questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all scenarios with irregular sampling.
APA
Seedat, N., Imrie, F., Bellot, A., Qian, Z. & van der Schaar, M.. (2022). Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:19497-19521 Available from https://proceedings.mlr.press/v162/seedat22b.html.

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