Pattern-mixture models

Geert Molenberghs; Herbert Thijs; Bart Michiels; Geert Verbeke; Michael G. Kenward

Journal de la société française de statistique (2004)

  • Volume: 145, Issue: 2, page 49-77
  • ISSN: 1962-5197

How to cite


Molenberghs, Geert, et al. "Pattern-mixture models." Journal de la société française de statistique 145.2 (2004): 49-77. <>.

author = {Molenberghs, Geert, Thijs, Herbert, Michiels, Bart, Verbeke, Geert, Kenward, Michael G.},
journal = {Journal de la société française de statistique},
keywords = {Delta method; Linear mixed model; Missing data; Repeated measures; Sensitivity analysis},
language = {eng},
number = {2},
pages = {49-77},
publisher = {Société française de statistique},
title = {Pattern-mixture models},
url = {},
volume = {145},
year = {2004},

AU - Molenberghs, Geert
AU - Thijs, Herbert
AU - Michiels, Bart
AU - Verbeke, Geert
AU - Kenward, Michael G.
TI - Pattern-mixture models
JO - Journal de la société française de statistique
PY - 2004
PB - Société française de statistique
VL - 145
IS - 2
SP - 49
EP - 77
LA - eng
KW - Delta method; Linear mixed model; Missing data; Repeated measures; Sensitivity analysis
UR -
ER -


  1. ALLISON P.D. (1987). Estimation of linear models with incomplete data. Sociology Methodology, 71-103. 
  2. COHEN J. and COHEN P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences. (2nd ed.). Hillsdale, NJ: Erlbaum. 
  3. DIGGLE P.J. and KENWARD M.G. (1994). Informative drop-out in longitudinal data analysis (with discussion). Applied Statistics, 4 3 , 49-93. Zbl0825.62010
  4. DRAPER D. (1995). Assessment and propagation of model uncertainty (with discussion). Journal of the Royal Statistical Society, Séries B, 57, 45-97. Zbl0812.62001MR1325378
  5. EKHOLM A. and SKINNER C. (1998). The muscatine children's obesity data reanalysed using pattern mixture models. Applied Statistics, 4 7 , 251-263. 
  6. GLYNN R.J., LAIRD N.M. and RUBIN D.B. (1986). Selection Modelling versus mixture modelling with nonignorable nonresponse. In Drawing Inferences from Self-Selected Samples, Ed. H. Wainer, pp. 115-142. New York: Springer Verlag. 
  7. GOSS P.E., WINER E.P., TANNOCK I.F., SCHWARTZ L.H. and KREMER A.B. (1999). A randomized phase III trial comparing the new potent and selective third-generation aromatase inhibitor vorozole with megestrol acetate in post-menopausal advanced breast cancer patients. Journal of Clinical Oncology, 17, 52-63. 
  8. HEDEKER D. and GIBBONS R.D. (1997). Application of random-effects pattern-mixture models for missing data in longitudinal studies. Psychological Methods, 2, 64-78. 
  9. HOGAN J.W. and LAIRD N.M. (1997). Mixture models for the joint distribution of repeated measures and event times. Statistics in Medicine, 16, 239-258. 
  10. KENWARD M.G. and MOLENBERGHS G. (1999). Parametric models for incomplete continuous and categorical longitudinal studies data. Statistical Methods in Medical Research, 8, 51-83. 
  11. KENWARD M.G., MOLENBERGHS G. and THIJS H. (2003). Pattern-mixture models with proper time dependence. Biometrika, 90, 53-71. Zbl1035.62112MR1966550
  12. LAIRD N.M. (1994). Discussion to Diggle P.J. and Kenward M.G.: Informative dropout in longitudinal data analysis. Applied Statistics, 43, 84. 
  13. LITTLE R.J.A. (1993). Pattern-mixture models for multivariate incomplete data. Journal of the American Statistical Association, 8 8 , 125-134. Zbl0775.62134
  14. LITTLE R.J.A. ( 1994a). A class of pattern-mixture models for normal incomplete data. Biometrika, 8 1 , 471-483. Zbl0816.62023MR1311091
  15. LITTLE R.J.A. ( 1994b). Discussion to Diggle P.J. and Kenward M.G.: Informative dropout in longitudinal data analysis. Applied Statistics, 43, 78. 
  16. LITTLE R.J.A. (1995). Modelling the dropout mechanism in repeated-measures studies. Journal of the American Statistical Association, 90, 1112-1121. Zbl0841.62099MR1354029
  17. LITTLE R.J.A. and RUBIN D.B. (1987). Statistical Analysis with Missing Data. New York: Wiley. Zbl1011.62004MR890519
  18. LITTLE R.J.A. and WANG Y. (1996). Pattern-mixture models for multivariate incomplete data with covariates. Biometrics, 52, 98-111. Zbl0875.62273
  19. MCARDLE J.J. and HAMAGAMI F. (1992). modelling incomplete longitudinal and cross-sectional data using latent growth structural models. Experimental Aging Research, 18, 145-166. 
  20. MININI P. and CHAVANCE M. ( 2004a). Observations longitudinales incomplètes : de la modélisation des observations disponibles à l'analyse de sensibilité. Journal de la Société française de Statistique, 145, 2, 5-18. 
  21. MININI P. and CHAVANCE M. ( 2004b). Sensitivity analysis of longitudinal binary data with non-monotone missing values. Biostatistics, 5, 531-544. Zbl1069.62101
  22. MOLENBERGHS G., KENWARD M. G. and LESAFFRE E. (1997). The analysis of longitudinal ordinal data with non-random dropout. Biometrika, 84, 33-44. Zbl0883.62120
  23. MOLENBERGHS G., MICHIELS B. and KENWARD M.G. (1998). Pseudo-likelihood for combined selection and pattern-mixture models for missing data problems. Biometrical Journal, 40, 557-572. Zbl0911.62020
  24. MOLENBERGHS G., MICHIELS B., KENWARD M.G. and DIGGLE P.J. (1998). Missing data mechanisms and pattern-mixture models. Statistica Neerlandica, 52, 153-161. Zbl0946.62034MR1649081
  25. MOLENBERGHS G., MICHIELS B. and LIPSITZ S.R. (1999). Selection models and pattern-mixture models for incomplete categorical data with covariates. Biometrics, 55, 978-983. Zbl1059.62677
  26. MUTHÉN B., KAPLAN D. and HOLLIS M. (1987). On structural equation modelling with data that are not missing completely at random. Psychometrika, 52, 431-462. Zbl0627.62066
  27. NELDER J.A. and MEAD R. (1965). A simplex method for function minimisation. The Computer Journal, 7, 303-313. Zbl0229.65053
  28. REISBERG B., BORENSTEIN J., SALOB S.P., FERRIS S.H., FRANSSEN E. and GEORGOTAS A. (1987). Behavioral symptoms in Alzheimer's disease: phenomenology and treatment. Journal of Clinical Psychiatry, 48, 9-13. 
  29. RUBIN D.B. (1976). Inference and missing data. Biometrika, 6 3 , 581-592. Zbl0344.62034MR455196
  30. RUBIN D.B. (1987). Multiple Imputation for Nonresponse in Surveys. John Wiley and Sons, New York. Zbl1070.62007MR899519
  31. RUBIN D.B. (1994). Discussion to Diggle, P.J. and Kenward, M.G.: Informative dropout in longitudinal data analysis. Applied Statistics, 43, 80-82. 
  32. SCHAFER J.L. (1997). Analysis of incomplete multivariate data. London: Chapman and Hall. and Hall. Zbl0997.62510MR1692799
  33. SCHIPPER H., CLINCH J. and MCMURRAY A. (1984). Measuring the quality of life of cancer patients: the Functional-Living Index-Cancer: development and validation. Journal of Clinical Oncology, 2, 472-483. 
  34. SHEINER L.B., BEAL S.L. and DUNNE A. (1997). Analysis of nonrandomly censored ordered categorical longitudinal data from analgesie trials. Journal of the American Statistical Association, 92, 1235-1244. Zbl0914.62102
  35. SHIH W.J. and QUAN H. (1997). Testing for treatment differences with dropouts present in clinical trials - A composite approach. Statistics in Medicine, 16, 1225-1239. 
  36. THIJS H., MOLENBERGHS G., MICHIELS B., VERBEKE G. and CURRAN D. (2002). Strategies to fit pattern-mixture models. Biostatistics, 3, 245-265. Zbl1133.62371
  37. VERBEKE G. and MOLENBERGHS G. (2000). Linear Mixed Models for Longitudinal Data. New York: Springer-Verlag. Zbl0956.62055MR1880596
  38. WU M.C. and BAILEY K.R. (1989). Estimation and comparison of changes in the presence of informative right censoring: conditional linear model. Biometrics 45, 939-55. Zbl0715.62123MR1029611

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.