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Multi‐disease analysis of maternal antibody decay using non‐linear mixed models accounting for censoring
Author(s) -
Goeyvaerts Nele,
Leuridan Elke,
Faes Christel,
Van Damme Pierre,
Hens Niel
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6518
Subject(s) - censoring (clinical trials) , multivariate statistics , rubella , correlation , generalized linear mixed model , statistics , mixed model , linear model , random effects model , pairwise comparison , measles , tobit model , econometrics , disease , mathematics , medicine , immunology , meta analysis , geometry , vaccination
Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter‐subject heterogeneity. Even though it is common for biological processes to entail non‐linear relationships, examples of multivariate non‐linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non‐linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non‐linear longitudinal profiles subject to censoring, by combining multivariate random effects, non‐linear growth and Tobit regression. We explore the hypothesis of a common infant‐specific mechanism underlying maternal immunity using a pairwise correlated random‐effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.