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Multivariate frailty models for multi-type recurrent event data and its application to cancer prevention trial

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  • Bedair, Khaled
  • Hong, Yili
  • Li, Jie
  • Al-Khalidi, Hussein R.

Abstract

Multi-type recurrent event data arise in many situations when two or more different event types may occur repeatedly over an observation period. For example, in a randomized controlled clinical trial to study the efficacy of nutritional supplements for skin cancer prevention, there can be two types of skin cancer events occur repeatedly over time. The research objectives of analyzing such data often include characterizing the event rate of different event types, estimating the treatment effects on each event process, and understanding the correlation structure among different event types. In this paper, we propose the use of a proportional intensity model with multivariate random effects to model such data. The proposed model can take into account the dependence among different event types within a subject as well as the treatment effects. Maximum likelihood estimates of the regression coefficients, variance–covariance components, and the nonparametric baseline intensity function are obtained via a Monte Carlo Expectation–Maximization (MCEM) algorithm. The expectation step of the algorithm involves the calculation of the conditional expectations of the random effects by using the Metropolis–Hastings sampling. Our proposed method can easily handle recurrent event data that have more than two types of events. Simulation studies were used to validate the performance of the proposed method, followed by an application to the skin cancer prevention data.

Suggested Citation

  • Bedair, Khaled & Hong, Yili & Li, Jie & Al-Khalidi, Hussein R., 2016. "Multivariate frailty models for multi-type recurrent event data and its application to cancer prevention trial," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 161-173.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:161-173
    DOI: 10.1016/j.csda.2016.01.018
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    References listed on IDEAS

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    1. Hussein R. Al-Khalidi & Yili Hong & Thomas R. Fleming & Terry M. Therneau, 2011. "Insights on the Robust Variance Estimator under Recurrent-Events Model," Biometrics, The International Biometric Society, vol. 67(4), pages 1564-1572, December.
    2. Luc Duchateau & Paul Janssen & Iva Kezic & Catherine Fortpied, 2003. "Evolution of recurrent asthma event rate over time in frailty models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(3), pages 355-363, July.
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    4. Rondeau, Virginie & Marzroui, Yassin & Gonzalez, Juan R., 2012. "frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i04).
    5. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    6. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 69-82, May.
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    Cited by:

    1. Hsiang Yu & Yu‐Jen Cheng & Ching‐Yun Wang, 2018. "Methods for multivariate recurrent event data with measurement error and informative censoring," Biometrics, The International Biometric Society, vol. 74(3), pages 966-976, September.
    2. Xiaowei Sun & Jieli Ding & Liuquan Sun, 2020. "A semiparametric additive rates model for the weighted composite endpoint of recurrent and terminal events," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 471-492, July.

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