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An online updating approach for testing the proportional hazards assumption with streams of survival data

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  • Yishu Xue
  • HaiYing Wang
  • Jun Yan
  • Elizabeth D. Schifano

Abstract

The Cox model—which remains the first choice for analyzing time‐to‐event data, even for large data sets—relies on the proportional hazards (PH) assumption. When survival data arrive sequentially in chunks, a fast and minimally storage intensive approach to test the PH assumption is desirable. We propose an online updating approach that updates the standard test statistic as each new block of data becomes available and greatly lightens the computational burden. Under the null hypothesis of PH, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data blocks pooled into one data set. In simulation studies, the test and its variant based on most recent data blocks maintain their sizes when the PH assumption holds and have substantial power to detect different violations of the PH assumption. We also show in simulation that our approach can be used successfully with “big data” that exceed a single computer's computational resources. The approach is illustrated with the survival analysis of patients with lymphoma cancer from the Surveillance, Epidemiology, and End Results Program. The proposed test promptly identified deviation from the PH assumption, which was not captured by the test based on the entire data.

Suggested Citation

  • Yishu Xue & HaiYing Wang & Jun Yan & Elizabeth D. Schifano, 2020. "An online updating approach for testing the proportional hazards assumption with streams of survival data," Biometrics, The International Biometric Society, vol. 76(1), pages 171-182, March.
  • Handle: RePEc:bla:biomet:v:76:y:2020:i:1:p:171-182
    DOI: 10.1111/biom.13137
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    Cited by:

    1. Amalan Mahendran & Helen Thompson & James M. McGree, 2023. "A model robust subsampling approach for Generalised Linear Models in big data settings," Statistical Papers, Springer, vol. 64(4), pages 1137-1157, August.
    2. Lee, JooChul & Wang, HaiYing & Schifano, Elizabeth D., 2020. "Online updating method to correct for measurement error in big data streams," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    3. Lee, JooChul & Schifano, Elizabeth D. & Wang, HaiYing, 2024. "Fast Optimal Subsampling Probability Approximation for Generalized Linear Models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 224-237.

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