A semi-parametric shared parameter model to handle nonmonotone nonignorable missingness. (English) Zbl 1159.62083

Summary: Longitudinal studies often generate incomplete response patterns according to a missing not at random mechanism. Shared parameter models provide an appealing framework for the joint modelling of the measurement and missingness processes, especially in the nonmonotone missingness case, and assume a set of random effects to induce the interdependence. Parametric assumptions are typically made for the random effects distribution, violation of which leads to model misspecification with a potential effect on the parameter estimates and standard errors.
We avoid any parametric assumption for the random effects distribution and leave it completely unspecified. The estimation of the model is then made using a semi-parametric maximum likelihood method. Our proposal is illustrated on a randomized longitudinal study on patients with rheumatoid arthritis exhibiting nonmonotone missingness.


62P10 Applications of statistics to biology and medical sciences; meta analysis
62G05 Nonparametric estimation
62N02 Estimation in survival analysis and censored data
Full Text: DOI


[1] Beunckens, A latent-class mixture model for incomplete longitudinal gaussian data, Biometrics 64 pp 96– (2008) · Zbl 1274.62721
[2] Böhning, Numerical estimation of a probability measure, Journal of Statistical Planning and Inference 11 pp 57– (1985) · Zbl 0574.62046
[3] Böhning, Computer-Assisted Analysis of Mixtures and Applications. Monographs on Statistics and Applied Probability (1999)
[4] De Gruttola, Modelling progression of CD-4 lymphocyte count and its relationship to survival time, Biometrics 50 pp 1003– (1994) · Zbl 0825.62792
[5] Diggle, Informative dropout in longitudinal data analysis (with discussion), Applied Statistics 43 pp 33– (1994) · Zbl 0825.62010
[6] Follmann, An approximate generalized linear model with random effects for informative missing data, Biometrics 51 pp 151– (1995) · Zbl 0825.62607
[7] Furst, Dose response and safety study of meloxicam up to 22.5 mg daily in RA: A 12 week multicenter, double blind, dose response study versus placebo and diclofenac, Journal of Rheumatology 29 pp 436– (2002)
[8] Hsieh, Joint modeling of survival and longitudinal data: Likelihood approach revisited, Biometrics 62 pp 1037– (2006) · Zbl 1116.62105
[9] Kiefer, Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters, Annals of Mathematical Statistics 27 pp 886– (1956) · Zbl 0073.14701
[10] Laird, Nonparametric maximum likelihood estimation of a mixing distribution, Journal of the American Statistical Association 73 pp 805– (1978) · Zbl 0391.62029
[11] Lin, A latent class mixed model for analysing biomarker trajectories with irregularly scheduled observations, Statistics in Medicine 19 pp 1303– (2000)
[12] Lindsay, The geometry of mixture likelihoods: A general theory, The Annals of Statistics 11 pp 86– (1983) · Zbl 0512.62005
[13] Little, Modeling the drop-out mechanism in repeated-measures studies, Journal of the American Statistical Association 90 pp 1112– (1995) · Zbl 0841.62099
[14] Molenberghs, Models for Discrete Longitudinal Data (2005) · Zbl 1093.62002
[15] Pulkstenis, Model for the analysis of binary longitudinal pain data subject to informative dropout through remedication, Journal of the American Statistical Association 93 pp 438– (1998) · Zbl 0926.62110
[16] Rizopoulos, Shared parameter models under random effects misspecification, Biometrika 95 pp 63– (2008) · Zbl 1437.62592
[17] Roeder, Application of maximum likelihood methods to population genetic data for the estimation of individual fertilities, Biometrics 45 pp 363– (1989) · Zbl 0707.62233
[18] Rubin, Inference and missing data (with discussion), Biometrika 63 pp 581– (1976) · Zbl 0344.62034
[19] Song, A semiparametric likelihood approach to joint modelling of longitudinal and time to event data, Biometrics 58 pp 742– (2002) · Zbl 1210.62132
[20] Ten Have, Mixed effects logistic regression models for longitudinal binary response data with informative dropout, Biometrics 54 pp 367– (1998) · Zbl 1058.62660
[21] van der Vaart, Efficient estimation in semiparametric models, Annals of Statistics 24 pp 862– (1996) · Zbl 0860.62029
[22] Verbeke, Linear Mixed Models for Longitudinal Data (2000)
[23] Wu, Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process, Biometrics 44 pp 175– (1988) · Zbl 0707.62210
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.