Proximal Causal Inference for Time Series from N-of-1Mobile Device Data
Abstract
Unmeasured confounding challenges causal inference in intensive longitudinal studies, potentially biasing treatment effect estimates. The proximal causal inference (PCI) framework offers a promising approach to identification using proxies or negative control variables in the presence of hidden confounding bias. While prior literature considers the joint effect of time-varying treatments, our work extends the framework to a time series setting to estimate the contemporaneous or lagged effect of time-varying treatments. We demonstrate that under traditional PCI assumptions, we can recover unbiased effect estimation in the presence of unmeasured confounding by leveraging the intensive longitudinal nature of time series data. Specifically, we develop identifiability conditions and show that past and future observations can be employed as natural proxies for unmeasured confounders. We further develop the bridge function required for valid PCI estimation along with asymptotic variance. Simulation studies illustrate our method's validity and robustness to violation of certain PCI identification assumptions. We demonstrate the potential for studying socio-environmental exposure health effects by applying our method to a smartphone study of bipolar patients. Our work contributes to the growing literature on PCI and provides a powerful tool for analyzing longitudinal data, including in observational mobile health research prone to confounding bias.
Related
- Flexible Doubly Robust Proximal Causal Inference for Censored Outcomes
- Proximal causal inference through cross-proxy balancing
- Simultaneous Inference for Proximal Causal Learning with Weak Proxies
- ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding
- Semiparametric Inference for Dynamic Causal Effects from Observational Time Series
BibTeX
@misc{cui2026proximal,
title = {{Proximal Causal Inference for Time Series from N-of-1Mobile Device Data}},
author = {Fanyu Cui and Charlotte Fowler and Xiaoxuan Cai and Jukka-Pekka Onnela and Justin Baker and Linda Valeri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22647},
eprint = {2610.22647},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22647},
}
RIS
TY - UNPB
TI - Proximal Causal Inference for Time Series from N-of-1Mobile Device Data
AU - Fanyu Cui
AU - Charlotte Fowler
AU - Xiaoxuan Cai
AU - Jukka-Pekka Onnela
AU - Justin Baker
AU - Linda Valeri
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22647
UR - https://arxiv.org/abs/2610.22647
AB - Unmeasured confounding challenges causal inference in intensive longitudinal studies, potentially biasing treatment effect estimates. The proximal causal inference (PCI) framework offers a promising approach to identification using proxies or negative control variables in the presence of hidden confounding bias. While prior literature considers the joint effect of time-varying treatments, our work extends the framework to a time series setting to estimate the contemporaneous or lagged effect of time-varying treatments. We demonstrate that under traditional PCI assumptions, we can recover unbiased effect estimation in the presence of unmeasured confounding by leveraging the intensive longitudinal nature of time series data. Specifically, we develop identifiability conditions and show that past and future observations can be employed as natural proxies for unmeasured confounders. We further develop the bridge function required for valid PCI estimation along with asymptotic variance. Simulation studies illustrate our method's validity and robustness to violation of certain PCI identification assumptions. We demonstrate the potential for studying socio-environmental exposure health effects by applying our method to a smartphone study of bipolar patients. Our work contributes to the growing literature on PCI and provides a powerful tool for analyzing longitudinal data, including in observational mobile health research prone to confounding bias.
ER -