Cautionary Tales on Synthetic Controls in Survival Analyses

Alicia Curth, Hoifung Poon, Aditya V. Nori, Javier González
Proceedings of the Third Conference on Causal Learning and Reasoning, PMLR 236:143-159, 2024.

Abstract

Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs – even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v236-curth24a, title = {Cautionary Tales on Synthetic Controls in Survival Analyses}, author = {Curth, Alicia and Poon, Hoifung and Nori, Aditya V. and Gonz\'alez, Javier}, booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning}, pages = {143--159}, year = {2024}, editor = {Locatello, Francesco and Didelez, Vanessa}, volume = {236}, series = {Proceedings of Machine Learning Research}, month = {01--03 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v236/curth24a/curth24a.pdf}, url = {https://proceedings.mlr.press/v236/curth24a.html}, abstract = {Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs – even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches.} }
Endnote
%0 Conference Paper %T Cautionary Tales on Synthetic Controls in Survival Analyses %A Alicia Curth %A Hoifung Poon %A Aditya V. Nori %A Javier González %B Proceedings of the Third Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2024 %E Francesco Locatello %E Vanessa Didelez %F pmlr-v236-curth24a %I PMLR %P 143--159 %U https://proceedings.mlr.press/v236/curth24a.html %V 236 %X Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs – even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches.
APA
Curth, A., Poon, H., Nori, A.V. & González, J.. (2024). Cautionary Tales on Synthetic Controls in Survival Analyses. Proceedings of the Third Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 236:143-159 Available from https://proceedings.mlr.press/v236/curth24a.html.

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