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Temporal process regression

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  • J. P. Fine

Abstract

We consider regression for response and covariates which are temporal processes observed over intervals. A functional generalised linear model is proposed which includes extensions of standard models in multi-state survival analysis. Simple nonparametric estimators of time-indexed parameters are developed using 'working independence' estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. The procedure does not require smoothing or a Markov assumption, unlike approaches based on transition intensities. The usual definition of optimal estimating equations for parametric models is then generalised to the functional model and the optimum is identified in a class of functional generalised estimating equations. Simulations demonstrate large efficiency gains relative to working independence at times where censoring is heavy. The estimators are the basis for new tests of the covariate effects and for the estimation of models in which greater structure is imposed on the parameters, providing novel goodness-of-fit tests. The methodology's practical utility is illustrated in a data analysis. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • J. P. Fine, 2004. "Temporal process regression," Biometrika, Biometrika Trust, vol. 91(3), pages 683-703, September.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:3:p:683-703
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    Cited by:

    1. Minjung Kwak, 2017. "Estimation and inference of the joint conditional distribution for multivariate longitudinal data using nonparametric copulas," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 491-514, July.
    2. Shuang Ji & Limin Peng & Yu Cheng & HuiChuan Lai, 2012. "Quantile Regression for Doubly Censored Data," Biometrics, The International Biometric Society, vol. 68(1), pages 101-112, March.
    3. Limin Peng & Jason P. Fine, 2007. "Regression Modeling of Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 63(1), pages 96-108, March.
    4. Tianyu Zhan & Douglas E. Schaubel, 2019. "Semiparametric temporal process regression of survival-out-of-hospital," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 322-340, April.
    5. J. E. Soh & Yijian Huang, 2021. "A varying-coefficient model for gap times between recurrent events," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 437-459, July.
    6. Yijian Huang, 2017. "Restoration of Monotonicity Respecting in Dynamic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 613-622, April.
    7. Jun Yan & Jian Huang, 2009. "Partly Functional Temporal Process Regression with Semiparametric Profile Estimating Functions," Biometrics, The International Biometric Society, vol. 65(2), pages 431-440, June.
    8. Wang, Jixian & Quartey, George, 2013. "A semi-parametric approach to analysis of event duration and prevalence," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 248-257.
    9. Jun Yan & Yu Cheng & Jason P. Fine & HuiChuan J. Lai, 2010. "Uncovering Symptom Progression History from Disease Registry Data with Application to Young Cystic Fibrosis Patients," Biometrics, The International Biometric Society, vol. 66(2), pages 594-602, June.

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