Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: A Bayesian approach

Joint modeling of longitudinal data and survival data has been used widely for analyzing AIDS clinical trials, where a biological marker such as CD4 count measurement can be an important predictor of survival. In most of these studies, a normal distribution is used for modeling longitudinal responses, which leads to vulnerable inference in the presence of outliers in longitudinal measurements. Powerful distributions for robust analysis are normal/independent distributions, which include univariate and multivariate versions of the Student's t, the slash and the contaminated normal distributions in addition to the normal. In this paper, a linear-mixed effects model with normal/independent distribution for both random effects and residuals and Cox's model for survival time are used. For estimation, a Bayesian approach using Markov Chain Monte Carlo is adopted. Some simulation studies are performed for illustration of the proposed method. Also, the method is illustrated on a real AIDS data set and the best model is selected using some criteria.

[1]  Samuel Kotz,et al.  Multivariate T-Distributions and Their Applications , 2004 .

[2]  B. Efron.  THE GEOMETRY OF EXPONENTIAL FAMILIES , 1978 .

[3]  D J Spiegelhalter,et al.  Flexible random‐effects models using Bayesian semi‐parametric models: applications to institutional comparisons , 2007, Statistics in medicine.

[4]  B P Carlin,et al.  Response of CD4 lymphocytes and clinical consequences of treatment using ddI or ddC in patients with advanced HIV infection. , 1996, Journal of acquired immune deficiency syndromes and human retrovirology : official publication of the International Retrovirology Association.

[5]  F. Hsieh,et al.  Joint modelling of accelerated failure time and longitudinal data , 2005 .

[6]  J. Geweke,et al.  Bayesian Treatment of the Independent Student- t Linear Model , 1993 .

[7]  K. Lange,et al.  Normal/Independent Distributions and Their Applications in Robust Regression , 1993 .

[8]  Lang Wu,et al.  Mixed Effects Models for Complex Data , 2019 .

[9]  N. L. Johnson,et al.  Continuous Multivariate Distributions: Models and Applications , 2005 .

[10]  Joseph G. Ibrahim,et al.  A new joint model for longitudinal and survival data with a cure fraction , 2004 .

[11]  Brian J. Smith,et al.  boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference , 2007 .

[12]  M. Genton,et al.  The multivariate skew-slash distribution , 2006 .

[13]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[14]  R. Hashemi,et al.  A Latent Process Model for Joint Modeling of Events and Marker , 2003, Lifetime data analysis.

[15]  Joseph G Ibrahim,et al.  Joint Models for Multivariate Longitudinal and Multivariate Survival Data , 2006, Biometrics.

[16]  R Henderson,et al.  Joint modelling of longitudinal measurements and event time data. , 2000, Biostatistics.

[17]  M. Kenward,et al.  Informative dropout in longitudinal data analysis (with discussion) , 1994 .

[18]  Jeremy MG Taylor,et al.  Robust Statistical Modeling Using the t Distribution , 1989 .

[19]  C. Kendziorski,et al.  The efficiency of pooling mRNA in microarray experiments. , 2003, Biostatistics.

[20]  R. Little.  Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values , 1988 .

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

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

[23]  Xin Huang,et al.  A joint model of longitudinal and competing risks survival data with heterogeneous random effects and outlying longitudinal measurements. , 2010, Statistics and its interface.

[24]  W. R. Buckland,et al.  Contributions to Probability and Statistics , 1960 .

[25]  D. F. Andrews,et al.  Scale Mixtures of Normal Distributions , 1974 .

[26]  Yongseok Park,et al.  Real‐Time Individual Predictions of Prostate Cancer Recurrence Using Joint Models , 2013, Biometrics.

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

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

[29]  Ronald Christensen,et al.  Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians , 2010 .

[30]  Ying Nian Wu,et al.  Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution , 2001 .

[31]  Daniel Gianola,et al.  Robust Linear Mixed Models with Normal/Independent Distributions and Bayesian MCMC Implementation , 2003 .

[32]  Ludwig Fahrmeir,et al.  Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection , 2010, Stat. Comput..

[33]  J. Tukey.  A survey of sampling from contaminated distributions , 1960 .

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

[35]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[36]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[37]  Boris Iglewicz,et al.  Outlier detection using robust measures of scale , 1982 .

[38]  Philip Heidelberger,et al.  Simulation Run Length Control in the Presence of an Initial Transient , 1983, Oper. Res..

[39]  Daniel Commenges,et al.  Correction of the p-Value after Multiple Tests in a Cox Proportional Hazard Model , 2002, Lifetime data analysis.

[40]  Anastasios A. Tsiatis,et al.  A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error , 2001 .

[41]  W. R. Buckland,et al.  Contributions to Probability and Statistics , 1960 .

[42]  Joseph G. Ibrahim,et al.  BAYESIAN METHODS FOR JOINT MODELING OF LONGITUDINAL AND SURVIVAL DATA WITH APPLICATIONS TO CANCER VACCINE TRIALS , 2004 .

[43]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .