Joint Modeling of Multivariate Longitudinal Data and Competing Risks Using Multiphase Sub-models

In many clinical studies that involve follow-up, it is common to observe one or more sequences of longitudinal measurements, as well as one or more time to event outcomes. A competing risks situation arises when the probability of occurrence of one event is altered/hindered by another time to event. Recently, there has been much attention paid to the joint analysis of a single longitudinal response and a single time to event outcome, when the missing data mechanism in the longitudinal process is non-ignorable. We, in this paper, propose an extension where multiple longitudinal responses are jointly modeled with competing risks (multiple time to events). Our shared parameter joint model consists of a system of multiphase non-linear mixed effects sub-models for the multiple longitudinal responses, and a system of cause-specific non-proportional hazards frailty sub-models for competing risks, with associations among multiple longitudinal responses and competing risks modeled using latent parameters. The joint model is applied to a data set of patients who are on mechanical circulatory support and are awaiting heart transplant, using readily available software. While on the mechanical circulatory support, patient liver and renal functions may worsen and these in turn may influence one of the two possible competing outcomes: (i) death before transplant; (ii) transplant. In one application, we propose a system of multiphase cause-specific non-proportional hazard sub-model where frailty can be time varying. Performance under different scenarios was assessed using simulation studies. By using the proposed joint modeling of the multiphase sub-models, one can identify: (i) non-linear trends in multiple longitudinal outcomes; (ii) time-varying hazards and cumulative incidence functions of the competing risks; (iii) identify risk factors for the both types of outcomes, where the effect may or may not change with time; and (iv) assess the association between multiple longitudinal and competing risks outcomes, where the association may or may not change with time.

[1]  Ning Li,et al.  A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types , 2008, Biometrics.

[2]  Gang Li,et al.  A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data , 2007, Statistics in medicine.

[3]  K. Kalantar-Zadeh,et al.  Renal Transplant Outcomes in Waitlist Candidates with a Previous Inactive Status Due to Being Temporarily Too Sick. , 2014, Clinical transplants.

[4]  Samuel T. Edwards,et al.  Ventricular hypertrophy and left atrial dilatation persist and are associated with reduced survival after valve replacement for aortic stenosis. , 2014, The Journal of thoracic and cardiovascular surgery.

[5]  M. Jessup,et al.  Mechanical Circulatory Support as a Bridge to Transplant or for Destination Therapy , 2010, Current heart failure reports.

[6]  D. Bates,et al.  Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model , 1995 .

[7]  E. Vonesh,et al.  A note on the use of Laplace's approximation for nonlinear mixed-effects models , 1996 .

[8]  J. Heltshe,et al.  Estimating species richness using the jackknife procedure. , 1983, Biometrics.

[9]  R. Kolamunnage-Dona,et al.  Joint modelling of longitudinal and competing risks data , 2008, Statistics in medicine.

[10]  D. Bates,et al.  Nonlinear mixed effects models for repeated measures data. , 1990, Biometrics.

[11]  Melania Pintilie,et al.  Competing Risks: A Practical Perspective , 2006 .

[12]  Peter J Diggle,et al.  Joint modelling of repeated measurement and time-to-event data: an introductory tutorial. , 2015, International journal of epidemiology.

[13]  N. Reid,et al.  Estimating Risks of Progressing to Aids when Covariates are Measured , 1993 .

[14]  Gang Li,et al.  Robust Joint Modeling of Longitudinal Measurements and Competing Risks Failure Time Data , 2009, Biometrical journal. Biometrische Zeitschrift.

[15]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[16]  Jeevanantham Rajeswaran,et al.  The natural history of lung function after lung transplantation for α(1)-antitrypsin deficiency. , 2014, American journal of respiratory and critical care medicine.

[17]  Marc Lavielle,et al.  Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm , 2015 .

[18]  Gang Li,et al.  Joint modeling of longitudinal ordinal data and competing risks survival times and analysis of the NINDS rt‐PA stroke trial , 2010, Statistics in medicine.

[19]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

[20]  H Putter,et al.  Tutorial in biostatistics: competing risks and multi‐state models , 2007, Statistics in medicine.

[21]  M C Oz,et al.  Screening scale predicts patients successfully receiving long-term implantable left ventricular assist devices. , 1995, Circulation.

[22]  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 .

[23]  Malcolm E. Turner,et al.  Parametric Survival Analysis Combining Longitudinal and Cross-Sectional-Censored and Interval-Censored Data with Concomitant Information , 1982 .

[24]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[25]  M D Schluchter,et al.  Methods for the analysis of informatively censored longitudinal data. , 1992, Statistics in medicine.

[26]  E. Tuzcu,et al.  Do bisphosphonates slow the progression of aortic stenosis? , 2010, Journal of the American College of Cardiology.

[27]  D. Farrar,et al.  Importance of preoperative liver function as a predictor of survival in patients supported with Thoratec ventricular assist devices as a bridge to transplantation. , 1998, The Journal of thoracic and cardiovascular surgery.

[28]  Jeevanantham Rajeswaran,et al.  A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation , 2017, Statistical methods in medical research.

[29]  Jeevanantham Rajeswaran,et al.  Spirometry after transplantation: how much better are two lungs than one? , 2008, The Annals of thoracic surgery.

[30]  M. Wulfsohn,et al.  A joint model for survival and longitudinal data measured with error. , 1997, Biometrics.

[31]  Virginie Rondeau,et al.  Tutorial in Joint Modeling and Prediction: a Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event , 2017, 1701.03675.

[32]  Dimitris Rizopoulos,et al.  The R Package JMbayes for Fitting Joint Models for Longitudinal and Time-to-Event Data using MCMC , 2014, 1404.7625.

[33]  Jeevanantham Rajeswaran,et al.  Surgery for permanent atrial fibrillation: impact of patient factors and lesion set. , 2006, The Annals of thoracic surgery.

[34]  Malcolm E. Turner,et al.  The Decomposition of Time-Varying Hazard into Phases, Each Incorporating a Separate Stream of Concomitant Information , 1986 .

[35]  L. Skovgaard.  NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[36]  Lang Wu,et al.  A Joint Model for Nonlinear Mixed-Effects Models With Censoring and Covariates Measured With Error, With Application to AIDS Studies , 2002 .

[37]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[38]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[39]  J. M. Taylor,et al.  A comparison of smoothing techniques for CD4 data measured with error in a time-dependent Cox proportional hazards model. , 1998, Statistics in medicine.

[40]  Amanda G Chetwynd,et al.  Joint modelling of repeated measurements and time-to-event outcomes: the fourth Armitage lecture. , 2008, Statistics in medicine.

[41]  E. Vonesh,et al.  Linear and Nonlinear Models for the Analysis of Repeated Measurements , 1996 .

[42]  Marie Davidian,et al.  A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time‐to‐Event Data , 2002, Biometrics.

[43]  Martin Schumacher,et al.  Competing Risks and Multistate Models , 2012, Clinical Cancer Research.

[44]  Eleni-Rosalina Andrinopoulou,et al.  Joint modeling of two longitudinal outcomes and competing risk data , 2014, Statistics in medicine.

[45]  Geert Molenberghs,et al.  The analysis of multivariate longitudinal data: A review , 2014, Statistical methods in medical research.

[46]  Joseph G Ibrahim,et al.  Sample size and power determination in joint modeling of longitudinal and survival data , 2011, Statistics in medicine.

[47]  Liang Li,et al.  Boosted multivariate trees for longitudinal data , 2016, Machine Learning.

[48]  M. Crowder.  Classical Competing Risks , 2001 .