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Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data


  • An, Mark Yuying


This paper studies the estimation of a semiparametric bivariate proportional hazard model from event time data under interval censoring. As a direct generalization of the bivariate exponential distribution of Marshall and Olkin, the model, on the one hand, controls for the effects of observed covariates, and on the other, achieves great flexibility through nonparametrically specified baseline hazards. The model is most relevant in analyzing the joint distribution of two event times arising from "systems of two components". Examples include the two infection times of the left and the right kidneys of patients and the two retirement times of married couples. To estimate this semiparametric model from grouped data, we propose a maximum likelihood estimator and a minimum chi-square estimator. Both estimation methods exploit the fact that the most flexible model structure that can be identified with grouped data is finite-dimensional. Compared with the maximum likelihood estimation, the minimum chi-square procedure is computationally more attractive but applies only to "many observations per cell" cases where the covariates are either categorical or amendable to sensible grouping. Specification tests for different model assumptions are also discussed.

Suggested Citation

  • An, Mark Yuying, 1996. "Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data," Working Papers 96-06, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:96-06

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    References listed on IDEAS

    1. Mark Yuying An & Roberto Ayala, 1996. "Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data," Econometrics 9611003, EconWPA.
    2. Mark Yuying An, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Econometrics 9611001, EconWPA.
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    Cited by:

    1. Ortega, Jaime, 2000. "Job Rotation as a Mechanism for Learning," CLS Working Papers 00-4, University of Aarhus, Aarhus School of Business, Centre for Labour Market and Social Research.
    2. Westergaard-Nielsen, Niels, 2001. "Danish Labour Market Policy: Is it worth it?," CLS Working Papers 01-10, University of Aarhus, Aarhus School of Business, Centre for Labour Market and Social Research.
    3. Mark Yuying An, 2004. "Likelihood-Based Estimation of a Proportional-Hazard, Competing- Risk Model with Grouped Duration Data," Urban/Regional 0407013, EconWPA.
    4. Pedersen, Peder J. & Smith, Nina, 2001. "International Migration and Migration policy in Denmark," CLS Working Papers 01-5, University of Aarhus, Aarhus School of Business, Centre for Labour Market and Social Research.
    5. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    6. Li, Shuwei & Hu, Tao & Wang, Peijie & Sun, Jianguo, 2017. "Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 75-86.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies


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