A simulation-based approach to estimate joint model of longitudinal and event-time data with many missing longitudinal observations

Joint models of longitudinal and event-time data have been extensively studied and applied in many different fields. Estimation of joint models is challenging, most present procedures are computational expensive and have a strict requirement on data quality. In this study, a novel simulation-based procedure is proposed to estimate a general family of joint models, which include many widely-applied joint models as special cases. Our procedure can easily handle low-quality data where longitudinal observations are systematically missed for some of the covariate dimensions. In addition, our estimation procedure is compatible with parallel computing framework when combining with stochastic descending algorithm, it is perfectly applicable to massive data and therefore suitable for many financial applications. Consistency and asymptotic normality of our estimator are proved, a simulation study is conducted to illustrate its effectiveness. Finally, as an application, the procedure is applied to estimate pre-payment probability of a massive consumer-loan dataset drawn from one biggest P2P loan platform of China.

[1]  Robin Henderson,et al.  Joint modelling of repeated measurements and time-to-event outcomes: flexible model specification and exact likelihood inference , 2014, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[2]  P. Osmera,et al.  Parallel evolutionary algorithms , 2003, Proceedings 2003 IEEE International Symposium on Computational Intelligence in Robotics and Automation. Computational Intelligence in Robotics and Automation for the New Millennium (Cat. No.03EX694).

[3]  P. Andersen,et al.  Repeated assessment of risk factors in survival analysis , 1992, Statistical methods in medical research.

[4]  Yi Li,et al.  Joint Modeling of Longitudinal and Cure-Survival Data , 2013, Journal of statistical theory and practice.

[5]  Joseph G Ibrahim,et al.  Joint modeling of longitudinal and survival data with missing and left‐censored time‐varying covariates , 2014, Statistics in medicine.

[6]  Bradley P Carlin,et al.  Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages , 2004 .

[7]  M. Wulfsohn,et al.  Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS , 1995 .

[8]  Siem Jan Koopman,et al.  The Multi-State Latent Factor Intensity Model for Credit Rating Transitions , 2005 .

[9]  Achim Wambach,et al.  Incentive effects in the demand for health care: a bivariate panel count data estimation , 2003 .

[10]  L. Perko.  Differential Equations and Dynamical Systems , 1991 .

[11]  Zhiliang Ying,et al.  Semiparametric regression for the mean and rate functions of recurrent events , 2000 .

[12]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .

[13]  Jeremy M. G. Taylor,et al.  A Stochastic Model for Analysis of Longitudinal AIDS Data , 1994 .

[14]  Xiaoqi Zhang,et al.  Understanding Dynamic Status Change of Hospital Stay and Cost Accumulation via Combining Continuous and Finitely Jumped Processes , 2018, Comput. Math. Methods Medicine.

[15]  Keith R. Abrams,et al.  Joint Modeling of Longitudinal and Survival Data , 2013 .

[16]  N M Laird,et al.  Model-based approaches to analysing incomplete longitudinal and failure time data. , 1997, Statistics in medicine.

[17]  Donglin Zeng,et al.  Maximum likelihood estimation in semiparametric regression models with censored data , 2007, Statistica Sinica.

[18]  A. Karr.  Point Processes and Their Statistical Inference. , 1994 .

[19]  Abdus Sattar,et al.  Joint modeling of longitudinal and survival data with a covariate subject to a limit of detection , 2019, Statistical methods in medical research.

[20]  Michael Sherris,et al.  The Impact of Systematic Trend and Uncertainty on Mortality and Disability in a Multi-State Latent Factor Model for Transition Rates , 2016 .

[21]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[22]  Gert Cauwenberghs,et al.  A Fast Stochastic Error-Descent Algorithm for Supervised Learning and Optimization , 1992, NIPS.

[23]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[24]  Hulin Wu,et al.  Joint inference for nonlinear mixed-effects models and time to event at the presence of missing data. , 2007, Biostatistics.

[25]  Yan Wang,et al.  Jointly Modeling Longitudinal and Event Time Data With Application to Acquired Immunodeficiency Syndrome , 2001 .

[26]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[27]  Stephen J. Wright,et al.  An asynchronous parallel stochastic coordinate descent algorithm , 2013, J. Mach. Learn. Res..

[28]  Jianguo Sun.  Panel Count Data , 2014 .

[29]  Guangbao Guo,et al.  Parallel Statistical Computing for Statistical Inference , 2012 .

[30]  Dimitris Rizopoulos,et al.  Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time‐to‐Event Data , 2011, Biometrics.

[31]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[32]  N M Laird,et al.  Missing data in longitudinal studies. , 1988, Statistics in medicine.

[33]  Dimitris Rizopoulos,et al.  JM: An R package for the joint modelling of longitudinal and time-to-event data , 2010 .