A local influence approach applied to binary data from a psychiatric study.

Antidepressive Agents, Tricyclic/therapeutic use; Depression/drug therapy; Fluvoxamine/therapeutic use; Humans; Longitudinal Studies; Models, Psychological; Models, Statistical; Multivariate Analysis; Randomized Controlled Trials as Topic/methods

Abstract :

[en] Recently, a lot of concern has been raised about assumptions needed in order to fit statistical models to incomplete multivariate and longitudinal data. In response, research efforts are being devoted to the development of tools that assess the sensitivity of such models to often strong but always, at least in part, unverifiable assumptions. Many efforts have been devoted to longitudinal data, primarily in the selection model context, although some researchers have expressed interest in the pattern-mixture setting as well. A promising tool, proposed by Verbeke et al. (2001, Biometrics 57, 43-50), is based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B 48, 133-169). These authors considered the Diggle and Kenward (1994, Applied Statistics 43, 49-93) model, which is based on a selection model, integrating a linear mixed model for continuous outcomes with logistic regression for dropout. In this article, we show that a similar idea can be developed for multivariate and longitudinal binary data, subject to nonmonotone missingness. We focus on the model proposed by Baker, Rosenberger, and DerSimonian (1992, Statistics in Medicine 11, 643-657). The original model is first extended to allow for (possibly continuous) covariates, whereafter a local influence strategy is developed to support the model-building process. The model is able to deal with nonmonotone missingness but has some limitations as well, stemming from the conditional nature of the model parameters. Some analytical insight is provided into the behavior of the local influence graphs.

Disciplines :

Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others

Author, co-author :

Jansen, Ivy

Molenberghs, Geert

Aerts, Marc

Thijs, Herbert

Van Steen, Kristel ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Bioinformatique

Language :

English

Title :

A local influence approach applied to binary data from a psychiatric study.

Publication date :

2003

Journal title :

Biometrics

ISSN :

0006-341X

eISSN :

1541-0420

Publisher :

Biometric Society, Alexandria, United States - Virginia

Volume :

Issue :

Pages :

410-9

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 24 May 2010

Statistics

Number of views

61 (3 by ULiège)

Number of downloads

0 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

Agresti, A. (1990). Categorical Data Analysis. New York: Wiley.
Albert, A. and Lesaffre, E. (1986). Multiple group logistic discrimination. Computers and Mathematics, with Applications 2, 209-224.
Ashford, J. R. and Sowden, R. R. (1970). Multivariate probit analysis. Biometrics 26, 535-546.
Bahadur, R. R. (1961). A representation of the joint distribution of responses to n dichotomous items. In Studies in Item Analysis and Prediction, H. Solomon (ed). Stanford Mathematical Studies in the Social Sciences VI. Stanford, California: Stanford University Press.
Baker, S. G. (1996). The analysis of categorical case-control data subject to nonignorable nonresponse. Biometrics 52, 362-369.
Baker, S. G. (2000). Analyzing a randomized cancer prevention trial with a missing binary outcome, an auxiliary variable, and all-or-none compliance. Journal of the American Statistical Association 95, 43-50.
Baker, S. G., Rosenberger, W. F., and DerSimonian, R. (1992). Closed-form estimates for missing counts in two-way contingency tables. Statistics in Medicine 11, 643-657.
Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9-25.
Burton, S. W. (1991). Review of fluvoxamine and its uses in depression. International Clinical Psychopharmacology 6 (Suppl. 3), 1-17.
Cook, R. D. (1986). Assessment of local influence. Journal of the Royal Statistical Society, Series B 48, 133-169.
Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regression. London: Chapman and Hall.
Cox, D. R. (1972). The analysis of multivariate binary data. Applied Statistics 21, 113-120.
Diggle, P. D. and Kenward, M. G. (1994). Informative dropout in longitudinal data analysis (with discussion). Applied Statistics 43, 49-93.
Draper, D. (1995). Assessment and propagation of model uncertainty (with discussion). Journal of the Royal Statistical Society, Series B 57, 45-97.
Fahrmeir, L. and Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. Heidelberg: Springer-Verlag.
Glynn, R. J., Laird, N. M., and Rubin, D. B. (1986). Selection modeling versus mixture modeling with non-ignorable nonresponse. In Drawing Inferences from Self-Selected Samples, H. Wainer (ed), 115-142. New York: Springer-Verlag.
Kenward, M. G. (1998). Selection models for repeated measurements with nonrandom dropout: An illustration of sensitivity. Statistics in Medicine 17, 2723-2732.
Kenward, M. G. and Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statistical Science 12, 236-247.
Kenward, M. G., Lesaffre, E., and Molenberghs, G. (1994). An application of maximum likelihood and estimating equations to the analysis of ordinal data from a longitudinal study with cases missing at random. Biometrics 50, 945-953.
Lesaffre, E., Molenberghs, G., and Dewulf, L. (1996). Effect of dropouts in a longitudinal study: An application of a repeated ordinal model. Statistics in Medicine 15, 1123-1141.
Liang, K.-Y. and Zeger, S. L. (1989). A class of logistic regression models for multivariate binary time series. Journal of the American Statistical Association 84, 447-451.
Little, R. J. A. (1995). Modeling the drop-out mechanism in repeated-measures studies. Journal of the American Statistical Association 90, 1112-1121.
Little, R. J. A. and Rubin, D. B. (1987). Statistical Analysis with Missing Data. New York: Wiley.
Michiels, B. and Molenberghs, G. (1997). Protective estimation of longitudinal categorical data with nonrandom dropout. Communications in Statistics - Theory and Methods 26, 65-94.
Molenberghs, G. and Lesaffre, E. (1994). Marginal modelling of correlated ordinal data using a multivariate Plackett distribution. Journal of the American Statistical Association 89, 633-644.
Molenberghs, G. and Lesaffre, E. (1999). Marginal modelling of multivariate categorical data. Statistics in Medicine 18, 2237-2255.
Molenberghs, G., Kenward, M. G., and Lesaffre, E. (1997). The analysis of longitudinal ordinal data with nonrandom dropout. Biometrika 84, 33-44.
Molenberghs, G., Kenward, M. G., and Goetghebeur, E. (2001). Sensitivity analysis for incomplete contingency tables: The Slovenian plebiscite case. Applied Statistics 50, 15-29.
Molenberghs, G., Goetghebeur, E., Lipsitz, S. R., and Kenward, M. G. (1999). Non-random missingness in categorical data: Strengths and limitations. The American Statistician 53, 110-118.
Molenberghs, G., Goetghebeur, E., Lipsitz, S. R., Kenward, M. G., Lesaffre, E., and Michiels, B. (1999). Missing data perspectives of the fluvoxamine data set: A review. Statistics in Medicine 18, 2449-2464.
Molenberghs, G., Verbeke, G., Thijs, H., Lesaffre, E., and Kenward, M. G. (2001). Mastitis in dairy cattle: Local influence to assess sensitivity of the dropout process. Computational Statistics and Data Analysis 37, 93-113.
Pendergast, J. F., Gange, S. J., Newton, M. A., Lindstrom, M. J., Palta, M., and Fisher, M. R. (1996). A survey of methods for analyzing clustered binary response data. International Statistical Review 64, 89-118.
Rosner, B. (1984). Multivariate methods in ophtalmology with applications to other paired-data situations. Biometrics 40, 1025-1035.
Rubin, D. B. (1977). Formalizing subjective notions about the effect of nonresponse in sample surveys. Journal of the American Statistical Association 72, 538-543.
Rubin, D. B. (1996). Multiple imputation after 18+ years. Journal of the American Statistical Association 91, 473-489.
Scharfstein, D. O., Rotnitzky, A., and Robins, J. M. (1999). Adjusting for non-ignorable drop-out using semi-parametric nonresponse models (with discussion). Journal of the American Statistical Association 94, 1096-1146.
Stiratelli, R., Laird, N., and Ware, J. (1984). Random effects models for serial observations with dichotomous response. Biometrics 40, 961-972.
Thijs, H., Molenberghs, G., and Verbeke, G. (2000). The milk protein trial: Influence analysis of the dropout process. Biometrical Journal 42, 617-646.
Van Steen, K., Molenberghs, G., Verbeke, G., and Thijs, H. (2001). A local influence approach to sensitivity analysis of incomplete longitudinal ordinal data. Statistical Modelling: An International Journal 1, 125-142.
Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer-Verlag.
Verbeke, G., Molenberghs, G., Thijs, H., Lesaffre, E., and Kenward, M. G. (2001). Sensitivity analysis for nonrandom dropout: A local influence approach. Biometrics 57, 43-50.
Wolfinger, R. and O'Connell, M. (1993). Generalized linear mixed models: A pseudo-likelihood approach. Journal of Statistical Computation and Simulation 48, 233-243.