A local influence approach to sensitivity analysis of incomplete longitudinal ordinal data

One of the major concerns when analysing incomplete longitudinal data is the fact that models necessarily rest on strong assumptions, unverifiable from the data. In response to these concerns, there is growing awareness of the usefulness of sensitivity analysis. In this paper we will focus on repeated ordinal data. Specifically, we implement a formal approach to such a sensitivity assessment, based on local influence, in the presence of multivariate categorical data. We explore the influence of perturbing a MAR dropout model in the direction of non-random dropout, and apply the proposed method to data from a longitudinal multicentre psychiatric study.

[1]  E Lesaffre,et al.  Local influence in linear mixed models. , 1998, Biometrics.

[2]  Roderick J. A. Little,et al.  A Class of Pattern-Mixture Models for Normal Incomplete Data , 1994 .

[3]  Missing data perspectives of the fluvoxamine data set: a review. , 1999, Statistics in medicine.

[4]  M. Kenward,et al.  The analysis of longitudinal ordinal data with nonrandom drop-out , 1997 .

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

[6]  G Molenberghs,et al.  An application of maximum likelihood and generalized estimating equations to the analysis of ordinal data from a longitudinal study with cases missing at random. , 1994, Biometrics.

[7]  J. Ware,et al.  Random-effects models for serial observations with binary response. , 1984, Biometrics.

[8]  Geert Molenberghs,et al.  Pseudo-likelihood inference for clustered binary data , 1997 .

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

[10]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

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

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

[13]  R. Wolfinger,et al.  Generalized linear mixed models a pseudo-likelihood approach , 1993 .

[14]  P. Albert,et al.  Models for longitudinal data: a generalized estimating equation approach. , 1988, Biometrics.

[15]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

[16]  J. Ashford,et al.  Multi-variate probit analysis. , 1970, Biometrics.

[17]  N. Laird,et al.  A likelihood-based method for analysing longitudinal binary responses , 1993 .

[18]  D. Cox.  The Analysis of Multivariate Binary Data , 1972 .

[19]  G. Molenberghs,et al.  Marginal Modeling of Correlated Ordinal Data Using a Multivariate Plackett Distribution , 1994 .

[20]  R. Little.  Pattern-Mixture Models for Multivariate Incomplete Data , 1993 .

[21]  G. Molenberghs,et al.  Marginal modelling of multivariate categorical data. , 1999, Statistics in medicine.

[22]  Charles E. Brown.  Multivariate Probit Analysis , 1998 .

[23]  Donald B. Rubin,et al.  Selection modelling versus mixture modelling with nonignorable nonresponse , 1986 .

[24]  M. Lindstrom,et al.  A survey of methods for analyzing clustered binary response data , 1996 .

[25]  J. Dale.  Global cross-ratio models for bivariate, discrete, ordered responses. , 1986, Biometrics.

[26]  Donald B. Rubin,et al.  Selection Modeling Versus Mixture Modeling with Nonignorable Nonresponse , 1986 .

[27]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[28]  R. Cook.  Assessment of Local Influence , 1986 .

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

[30]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[31]  G. Molenberghs,et al.  An exponential family model for clustered multivariate binary data , 1999 .

[32]  B Rosner,et al.  Multivariate methods in ophthalmology with application to other paired-data situations. , 1984, Biometrics.

[33]  Christopher J. Nachtsheim,et al.  Diagnostics for mixed-model analysis of variance , 1987 .

[34]  N M Laird,et al.  Mixture models for the joint distribution of repeated measures and event times. , 1997, Statistics in medicine.

[35]  Geert Molenberghs,et al.  Strategies to fit pattern-mixture models. , 2002, Biostatistics.

[36]  G Molenberghs,et al.  Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach , 2001, Biometrics.

[37]  Eric R. Ziegel,et al.  Multivariate Statistical Modelling Based on Generalized Linear Models , 2002, Technometrics.

[38]  R. Plackett.  A Class of Bivariate Distributions , 1965 .

[39]  G. Molenberghs,et al.  Pseudolikelihood Modeling of Multivariate Outcomes in Developmental Toxicology , 1999 .

[40]  G Molenberghs,et al.  Statistical Methods for Developmental Toxicity: Analysis of Clustered Multivariate Binary Data , 1999, Annals of the New York Academy of Sciences.

[41]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[42]  Geert Molenberghs,et al.  Sensitivity analysis for incomplete contingency tables: the Slovenian plebiscite case , 2001 .

[43]  Robin Thompson,et al.  Composite Link Functions in Generalized Linear Models , 1981 .

[44]  P. Diggle.  Analysis of Longitudinal Data , 1995 .