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Improved semiparametric estimation of the proportional rate model with recurrent event data

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  • Ming‐Yueh Huang
  • Chiung‐Yu Huang
Abstract
Owing to its robustness properties, marginal interpretations, and ease of implementation, the pseudo‐partial likelihood method proposed in the seminal papers of Pepe and Cai and Lin et al. has become the default approach for analyzing recurrent event data with Cox‐type proportional rate models. However, the construction of the pseudo‐partial score function ignores the dependency among recurrent events and thus can be inefficient. An attempt to investigate the asymptotic efficiency of weighted pseudo‐partial likelihood estimation found that the optimal weight function involves the unknown variance–covariance process of the recurrent event process and may not have closed‐form expression. Thus, instead of deriving the optimal weights, we propose to combine a system of pre‐specified weighted pseudo‐partial score equations via the generalized method of moments and empirical likelihood estimation. We show that a substantial efficiency gain can be easily achieved without imposing additional model assumptions. More importantly, the proposed estimation procedures can be implemented with existing software. Theoretical and numerical analyses show that the empirical likelihood estimator is more appealing than the generalized method of moments estimator when the sample size is sufficiently large. An analysis of readmission risk in colorectal cancer patients is presented to illustrate the proposed methodology.

Suggested Citation

  • Ming‐Yueh Huang & Chiung‐Yu Huang, 2023. "Improved semiparametric estimation of the proportional rate model with recurrent event data," Biometrics, The International Biometric Society, vol. 79(3), pages 1686-1700, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:1686-1700
    DOI: 10.1111/biom.13788
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    References listed on IDEAS

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    1. Maja Miloslavsky & Sündüz Keleş & Mark J. van der Laan & Steve Butler, 2004. "Recurrent events analysis in the presence of time‐dependent covariates and dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 239-257, February.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    4. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-517, October.
    5. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    6. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    7. Zeng, Donglin & Lin, D.Y., 2007. "Semiparametric Transformation Models With Random Effects for Recurrent Events," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 167-180, March.
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