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Joint Analysis of Longitudinal Data with Informative Right Censoring

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Longitudinal data arise when subjects are followed over a period of time. A commonly encountered complication in the analysis of such data is the variable length of follow-up due to right censorship. This can be further exacerbated by the possible dependency between the censoring time and the longitudinal measurements. This article proposes a combination of a semiparametric transformation model for the censoring time and a linear mixed effects model for the longitudinal measurements. The dependency is handled via latent variables which are naturally incorporated. We show that the likelihood function has an explicit form and develops a two-stage estimation procedure to avoid direct maximization over a high-dimensional parameter space. The resulting estimators are shown to be consistent and asymptotically normal, with a closed form for the variance–covariance matrix that can be used to obtain a plug-in estimator. Finite sample performance of the proposed approach is assessed through extensive simulations. The method is applied to renal disease data.

Keywords: Counting process; Loss to follow-up; Maximum likelihood estimation; Mixed effects; Normal transformation model

Document Type: Research Article


Affiliations: 1: Division of Biostatistics, School of Medicine, New York University, 650 First Avenue, New York, New York 10016, U.S.A., Email: 2: Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, New York 10027, U.S.A.

Publication date: June 1, 2007

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