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Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)

Author

Listed:
  • Yiming Chen

    (Department of Epidemiology and Biostatistics, University of Maryland, College Park, MD 20742, USA)

  • Paul J. Smith

    (Department of Mathematics, University of Maryland, College Park, MD 20742, USA)

  • Mei-Ling Ting Lee

    (Department of Epidemiology and Biostatistics, University of Maryland, College Park, MD 20742, USA)

Abstract

The first-hitting-time based model conceptualizes a random process for subjects’ latent health status. The time-to-event outcome is modeled as the first hitting time of the random process to a pre-specified threshold. Threshold regression with linear predictors has numerous benefits in causal survival analysis, such as the estimators’ collapsibility. We propose a neural network extension of the first-hitting-time based threshold regression model. With the flexibility of neural networks, the extended threshold regression model can efficiently capture complex relationships among predictors and underlying health processes while providing clinically meaningful interpretations, and also tackle the challenge of high-dimensional inputs. The proposed neural network extended threshold regression model can further be applied in causal survival analysis, such as performing as the Q-model in G-computation. More efficient causal estimations are expected given the algorithm’s robustness. Simulations were conducted to validate estimator collapsibility and threshold regression G-computation. The performance of the neural network extended threshold regression model is also illustrated by using simulated and real high-dimensional data from an observational study.

Suggested Citation

  • Yiming Chen & Paul J. Smith & Mei-Ling Ting Lee, 2023. "Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)," Stats, MDPI, vol. 6(2), pages 1-24, April.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:2:p:36-575:d:1135599
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    References listed on IDEAS

    as
    1. Sander Greenland & Judea Pearl, 2011. "Adjustments and their Consequences—Collapsibility Analysis using Graphical Models," International Statistical Review, International Statistical Institute, vol. 79(3), pages 401-426, December.
    2. Mei-Ling Ting Lee & John Lawrence & Yiming Chen & G. A. Whitmore, 2022. "Accounting for delayed entry into observational studies and clinical trials: length-biased sampling and restricted mean survival time," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 637-658, October.
    3. Riccardo De Bin & Vegard Grødem Stikbakke, 2023. "A boosting first-hitting-time model for survival analysis in high-dimensional settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 420-440, April.
    4. Sven Ove Samuelsen, 2023. "Cox regression can be collapsible and Aalen regression can be non-collapsible," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 403-419, April.
    5. Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    Full references (including those not matched with items on IDEAS)

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