Robust inference for mixed censored and binary response models with missing covariates

In biomedical and epidemiological studies, often outcomes obtained are of mixed discrete and continuous in nature. Furthermore, due to some technical inconvenience or else, continuous responses are censored and also a few covariates cease to be observed completely. In this paper, we develop a model to tackle these complex situations. Our methodology is developed in a more general framework and provides a full-scale robust analysis of such complex models. The proposed robust maximum likelihood estimators of the model parameters are resistant to potential outliers in the data. We discuss the asymptotic properties of the robust estimators. To avoid computational difficulties involving irreducibly high-dimensional integrals, we propose a Monte Carlo method based on the Metropolis algorithm for approximating the robust maximum likelihood estimators. We study the empirical properties of these estimators in simulations. We also illustrate the proposed robust method using clustered data on blood sugar content from a clinical trial of individuals who were investigated for diabetes.

[1]  C H Brown,et al.  Protecting against nonrandomly missing data in longitudinal studies. , 1990, Biometrics.

[2]  M. Kenward,et al.  Informative Drop‐Out in Longitudinal Data Analysis , 1994 .

[3]  D. Pregibon.  Resistant fits for some commonly used logistic models with medical application. , 1982, Biometrics.

[4]  John S. Preisser,et al.  Analysis of Smoking Trends with Incomplete Longitudinal Binary Responses , 2000 .

[5]  S. P. Pederson,et al.  On Robustness in the Logistic Regression Model , 1993 .

[6]  D. Ruppert,et al.  Optimally bounded score functions for generalized linear models with applications to logistic regression , 1986 .

[7]  Chris Robinson,et al.  Cautionary Tails about Arbitrary Deletion of Observations; or, Throwing the Variance Out with the Bathwater , 1985, Journal of Labor Economics.

[8]  Geert Molenberghs,et al.  A review on linear mixed models for longitudinal data, possibly subject to dropout , 2001 .

[9]  R. Little,et al.  Editing and Imputation for Quantitative Survey Data , 1987 .

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

[11]  S. Lipsitz,et al.  Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable , 2001 .

[12]  Weiren Wang,et al.  A model with mixed binary responses and censored observations , 1997 .

[13]  Hui Xie.  A local sensitivity analysis approach to longitudinal non-Gaussian data with non-ignorable dropout. , 2008, Statistics in medicine.

[14]  Wei Liu,et al.  A longitudinal study of children's aggressive behaviours based on multivariate mixed models with incomplete data , 2009 .

[15]  Russell V. Lenth,et al.  Statistical Analysis With Missing Data (2nd ed.) (Book) , 2004 .

[16]  S. Hosseinian,et al.  Robust inference for generalized linear models , 2009 .

[17]  S. Morgenthaler.  Least-Absolute-Deviations Fits for Generalized Linear Models , 1992 .

[18]  Richard J. Cook,et al.  Marginal Methods for Incomplete Longitudinal Data Arising in Clusters , 2002 .

[19]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data , 1988 .

[20]  C. McCulloch.  Maximum Likelihood Variance Components Estimation for Binary Data , 1994 .

[21]  C. McCulloch.  Maximum Likelihood Algorithms for Generalized Linear Mixed Models , 1997 .

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

[23]  Geert Molenberghs,et al.  Longitudinal and incomplete clinical studies , 2005 .

[24]  Sanjoy K. Sinha,et al.  Robust Analysis of Generalized Linear Mixed Models , 2004 .

[25]  S. Sinha.  Robust methods for generalized linear models with nonignorable missing covariates , 2008 .

[26]  J S Preisser,et al.  Robust Regression for Clustered Data with Application to Binary Responses , 1999, Biometrics.

[27]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[28]  Joseph G. Ibrahim,et al.  Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable , 1999 .

[29]  Cécile Proust-Lima,et al.  Pattern Mixture Models and Latent Class Models for the Analysis of Multivariate Longitudinal Data with Informative Dropouts , 2008, The international journal of biostatistics.

[30]  R. Carroll,et al.  Conditionally Unbiased Bounded-Influence Estimation in General Regression Models, with Applications to Generalized Linear Models , 1989 .