Progressive multi-state models for informatively incomplete longitudinal data

Abstract Progressive multi-state models provide a convenient framework for characterizing chronic disease processes where the states represent the degree of damage resulting from the disease. Incomplete data often arise in studies of such processes, and standard methods of analysis can lead to biased parameter estimates when observation of data is response-dependent. This paper describes a joint analysis useful for fitting progressive multi-state models to data arising in longitudinal studies in such settings. Likelihood based methods are described and parameters are shown to be identifiable. An EM algorithm is described for parameter estimation, and variance estimation is carried out using the Louis’ method. Simulation studies demonstrate that the proposed method works well in practice under a variety of settings. An application to data from a smoking prevention study illustrates the utility of the method.

[1]  L. Zhao,et al.  Correlated binary regression using a quadratic exponential model , 1990 .

[2]  G. Molenberghs,et al.  Linear Mixed Models for Longitudinal Data , 2001 .

[3]  Andrea Rotnitzky,et al.  Regression Models for Discrete Longitudinal Responses , 1993 .

[4]  P. Diggle,et al.  Analysis of Longitudinal Data , 2003 .

[5]  R D Gill,et al.  Non-response models for the analysis of non-monotone ignorable missing data. , 1997, Statistics in medicine.

[6]  Nan M. Laird,et al.  Multivariate Logistic Models for Incomplete Binary Responses , 1996 .

[7]  P. Albert,et al.  A two-state Markov chain for heterogeneous transitional data: a quasi-likelihood approach. , 1998, Statistics in medicine.

[8]  K. Brown,et al.  Effectiveness of a social influences smoking prevention program as a function of provider type, training method, and school risk. , 1999, American journal of public health.

[9]  N M Laird,et al.  Maximum likelihood analysis of generalized linear models with missing covariates , 1999, Statistical methods in medical research.

[10]  D. Berry,et al.  Statistical models in epidemiology, the environment, and clinical trials , 2000 .

[11]  Scott L. Zeger,et al.  Feedback Models for Discrete and Continuous Time Series , 1991 .

[12]  J. Robins,et al.  Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models , 1999 .

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

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[16]  R. Prentice,et al.  Correlated binary regression with covariates specific to each binary observation. , 1988, Biometrics.

[17]  Richard J. Cook,et al.  Transition Models for Multivariate Longitudinal Binary Data , 2007 .

[18]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[19]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .

[20]  J M Neuhaus,et al.  Statistical methods for longitudinal and clustered designs with binary responses , 1992, Statistical methods in medical research.

[21]  Geert Verbeke,et al.  Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles , 2006, Biometrics.

[22]  J. Robins,et al.  Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models , 2000 .

[23]  P S Albert,et al.  A Transitional Model for Longitudinal Binary Data Subject to Nonignorable Missing Data , 2000, Biometrics.

[24]  R. Cook,et al.  A logistic-bivariate normal model for overdispersed two-state Markov processes. , 1997, Biometrics.

[25]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[26]  Paul J Rathouz,et al.  Performance of weighted estimating equations for longitudinal binary data with drop‐outs missing at random , 2002, Statistics in medicine.

[27]  James M. Robins,et al.  Semiparametric Regression for Repeated Outcomes With Nonignorable Nonresponse , 1998 .

[28]  Nan M. Laird,et al.  Regression Analysis for Categorical Variables with Outcome Subject to Nonignorable Nonresponse , 1988 .