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Analysis of Longitudinal Data in the Presence of Informative Observational Times and a Dependent Terminal Event, with Application to Medical Cost Data

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  • Lei Liu
  • Xuelin Huang
  • John O'Quigley

Abstract

Summary In longitudinal observational studies, repeated measures are often taken at informative observation times. Also, there may exist a dependent terminal event such as death that stops the follow‐up. For example, patients in poorer health are more likely to seek medical treatment and their medical cost for each visit tends to be higher. They are also subject to a higher mortality rate. In this article, we propose a random effects model of repeated measures in the presence of both informative observation times and a dependent terminal event. Three submodels are used, respectively, for (1) the intensity of recurrent observation times, (2) the amount of repeated measure at each observation time, and (3) the hazard of death. Correlated random effects are incorporated to join the three submodels. The estimation can be conveniently accomplished by Gaussian quadrature techniques, e.g., SAS Proc NLMIXED. An analysis of the cost‐accrual process of chronic heart failure patients from the clinical data repository at the University of Virginia Health System is presented to illustrate the proposed method.

Suggested Citation

  • Lei Liu & Xuelin Huang & John O'Quigley, 2008. "Analysis of Longitudinal Data in the Presence of Informative Observational Times and a Dependent Terminal Event, with Application to Medical Cost Data," Biometrics, The International Biometric Society, vol. 64(3), pages 950-958, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:950-958
    DOI: 10.1111/j.1541-0420.2007.00954.x
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    4. Zhao, Xiaobing & Zhou, Xian, 2012. "Estimation of medical costs by copula models with dynamic change of health status," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 480-491.
    5. Dimitris Rizopoulos & Geert Verbeke & Geert Molenberghs, 2010. "Multiple-Imputation-Based Residuals and Diagnostic Plots for Joint Models of Longitudinal and Survival Outcomes," Biometrics, The International Biometric Society, vol. 66(1), pages 20-29, March.
    6. Miao Han & Liuquan Sun & Yutao Liu & Jun Zhu, 2018. "Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 523-547, July.
    7. Qing Cai & Mei‐Cheng Wang & Kwun Chuen Gary Chan, 2017. "Joint modeling of longitudinal, recurrent events and failure time data for survivor's population," Biometrics, The International Biometric Society, vol. 73(4), pages 1150-1160, December.
    8. Sundaram Rajeshwari & Ma Ling & Ghoshal Subhashis, 2017. "Median Analysis of Repeated Measures Associated with Recurrent Events in Presence of Terminal Event," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-16, May.
    9. Liang Zhu & Hui Zhao & Jianguo Sun & Wendy Leisenring & Leslie L. Robison, 2015. "Regression analysis of mixed recurrent-event and panel-count data with additive rate models," Biometrics, The International Biometric Society, vol. 71(1), pages 71-79, March.
    10. Charles E. McCulloch & John M. Neuhaus & Rebecca L. Olin, 2016. "Biased and unbiased estimation in longitudinal studies with informative visit processes," Biometrics, The International Biometric Society, vol. 72(4), pages 1315-1324, December.
    11. Graeme L. Hickey & Pete Philipson & Andrea Jorgensen & Ruwanthi Kolamunnage‐Dona, 2018. "A comparison of joint models for longitudinal and competing risks data, with application to an epilepsy drug randomized controlled trial," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1105-1123, October.
    12. Lei Liu & Xuelin Huang, 2009. "Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 65-81, February.
    13. Alessandro Gasparini & Keith R. Abrams & Jessica K. Barrett & Rupert W. Major & Michael J. Sweeting & Nigel J. Brunskill & Michael J. Crowther, 2020. "Mixed‐effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(1), pages 5-23, February.
    14. Na Cai & Wenbin Lu & Hao Helen Zhang, 2012. "Time-Varying Latent Effect Model for Longitudinal Data with Informative Observation Times," Biometrics, The International Biometric Society, vol. 68(4), pages 1093-1102, December.
    15. Yimei Li & Liang Zhu & Lei Liu & Leslie L. Robison, 2021. "Regression Analysis of Mixed Panel-Count Data with Application to Cancer Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 178-195, April.
    16. Zhao, Xingqiu & Tong, Xingwei & Sun, Jianguo, 2013. "Robust estimation for panel count data with informative observation times," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 33-40.
    17. Laura M. Yee & Kwun Chuen Gary Chan, 2017. "Nonparametric inference for the joint distribution of recurrent marked variables and recurrent survival time," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 207-222, April.
    18. Xiaoyu Wang & Liuquan Sun, 2023. "Joint modeling of generalized scale-change models for recurrent event and failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 1-33, January.
    19. Wang, Shikun & Li, Zhao & Lan, Lan & Zhao, Jieyi & Zheng, W. Jim & Li, Liang, 2022. "GPU accelerated estimation of a shared random effect joint model for dynamic prediction," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

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