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September 6, 2026JAMIA OpenOpen Access

Deep Learning Survival Analysis with Time-Varying Covariates: Extending PyCox to Assess COVID-19 Antiviral Treatments and Long-COVID Associations

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Authors

SBSeo Hyon BaikHXHaotian XianFBFitsum Baye

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Overview

Retrospective cohort study demonstrates reduced long-COVID risk from antivirals in older adults, suggesting modified deep learning matches standard accuracy with superior speed.

Key Points

  • To extend the PyCox deep learning survival analysis framework to handle counting-process data structures with time-varying covariates, mitigating immortal time bias in observational healthcare studies.
  • Modified PyCox to accommodate longitudinal counting-process records and evaluated it on 2,246,913 Medicare beneficiaries aged ≥65 diagnosed with COVID-19 between January and September 2022 (2,785,807 total records).
  • Compared modified PyCox against standard time-varying Cox regression and original time-fixed PyCox to evaluate associations between early antiviral treatment (nirmatrelvir or molnupiravir) and long-COVID.
  • Assessed model performance using concordance index, integrated Brier score, integrated negative binomial log-likelihood, and time-dependent AUC.
  • In the cohort (19.5% receiving nirmatrelvir, 2.6% receiving molnupiravir, and 14.0% developing long-COVID), modified PyCox produced hazard ratios concordant with time-varying Cox regression for nirmatrelvir (HR 0.878 vs 0.874) and molnupiravir (HR 0.918 vs 0.909), whereas time-fixed PyCox estimated stronger associations (HR 0.822 and 0.879).
  • Modified PyCox achieved higher time-dependent AUCs (0.536–0.609) than time-fixed PyCox (0.481–0.519) while demonstrating comparable overall discrimination and calibration to traditional Cox modeling.
  • Modified PyCox achieved the fastest computational runtime, training in 1 minute 14 seconds compared to 3 minutes 18 seconds for original PyCox and 5 minutes for traditional Cox regression.

Cite This Study

Baik et al. (2026) studied this question.

synapsesocial.com/papers/6a9d1e3328139818eab20e2bhttps://doi.org/10.1093/jamiaopen/ooag186
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