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Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive Gaussian quadrature rule

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  • Rizopoulos, Dimitris

Abstract

Joint models for longitudinal and time-to-event data have recently attracted a lot of attention in statistics and biostatistics. Even though these models enjoy a wide range of applications in many different statistical fields, they have not yet found their rightful place in the toolbox of modern applied statisticians mainly due to the fact that they are rather computationally intensive to fit. The main difficulty arises from the requirement for numerical integration with respect to the random effects. This integration is typically performed using Gaussian quadrature rules whose computational complexity increases exponentially with the dimension of the random-effects vector. A solution to overcome this problem is proposed using a pseudo-adaptive Gauss–Hermite quadrature rule. The idea behind this rule is to use information for the shape of the integrand by separately fitting a mixed model for the longitudinal outcome. Simulation studies show that the pseudo-adaptive rule performs excellently in practice, and is considerably faster than the standard Gauss–Hermite rule.

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  • Rizopoulos, Dimitris, 2012. "Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive Gaussian quadrature rule," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 491-501.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:491-501
    DOI: 10.1016/j.csda.2011.09.007
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    2. Philipson, Pete & Hickey, Graeme L. & Crowther, Michael J. & Kolamunnage-Dona, Ruwanthi, 2020. "Faster Monte Carlo estimation of joint models for time-to-event and multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    3. Murray, James & Philipson, Pete, 2023. "Fast estimation for generalised multivariate joint models using an approximate EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    4. Maria Marino & Marco Alfó, 2015. "Latent drop-out based transitions in linear quantile hidden Markov models for longitudinal responses with attrition," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(4), pages 483-502, December.
    5. Vock, David & Davidian, Marie & Tsiatis, Anastasios, 2014. "SNP_NLMM: A SAS Macro to Implement a Flexible Random Effects Density for Generalized Linear and Nonlinear Mixed Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(c02).
    6. Bernhardt, Paul W. & Zhang, Daowen & Wang, Huixia Judy, 2015. "A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 37-53.
    7. Molei Liu & Jiehuan Sun & Jose D. Herazo-Maya & Naftali Kaminski & Hongyu Zhao, 2019. "Joint Models for Time-to-Event Data and Longitudinal Biomarkers of High Dimension," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 614-629, December.
    8. Carles Serrat & Montserrat Ru� & Carmen Armero & Xavier Piulachs & H�ctor Perpi��n & Anabel Forte & �lvaro P�ez & Guadalupe G�mez, 2015. "Frequentist and Bayesian approaches for a joint model for prostate cancer risk and longitudinal prostate-specific antigen data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(6), pages 1223-1239, June.
    9. Murray, James & Philipson, Pete, 2022. "A fast approximate EM algorithm for joint models of survival and multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    10. Zhang, Cuihong & Ning, Jing & Cai, Jianwen & Squires, James E. & Belle, Steven H. & Li, Ruosha, 2024. "Dynamic risk score modeling for multiple longitudinal risk factors and survival," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    11. Marino, Maria Francesca & Alfó, Marco, 2016. "Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 193-209.
    12. Lisa M. McCrink & Adele H. Marshall & Karen J. Cairns, 2013. "Advances in Joint Modelling: A Review of Recent Developments with Application to the Survival of End Stage Renal Disease Patients," International Statistical Review, International Statistical Institute, vol. 81(2), pages 249-269, August.
    13. Xavier Piulachs & Ramon Alemany & Montserrat Guillen, 2014. "A joint longitudinal and survival model with health care usage for insured elderly," Working Papers 2014-07, Universitat de Barcelona, UB Riskcenter.
    14. Zhang, Zili & Charalambous, Christiana & Foster, Peter, 2023. "A Gaussian copula joint model for longitudinal and time-to-event data with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

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