title: Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.
abstract: 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 4 months 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.
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Agoralaan 1 Building D, 3590, Diepenbeek, Belgium.|Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination, Vaccine & Infectious Disease Institute, University of Antwerp, Universiteitsplein 1, 2610, Antwerp, Belgium.
authors.forename: Nele
authors.initials: N
authors.lastname: Goeyvaerts
authors.affiliation: Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination, Vaccine & Infectious Disease Institute, University of Antwerp, Universiteitsplein 1, 2610, Antwerp, Belgium.
authors.forename: Elke
authors.initials: E
authors.lastname: Leuridan
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Agoralaan 1 Building D, 3590, Diepenbeek, Belgium.
authors.forename: Christel
authors.initials: C
authors.lastname: Faes
authors.affiliation: Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination, Vaccine & Infectious Disease Institute, University of Antwerp, Universiteitsplein 1, 2610, Antwerp, Belgium.
authors.forename: Pierre
authors.initials: P
authors.lastname: Van Damme
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Agoralaan 1 Building D, 3590, Diepenbeek, Belgium.|Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination, Vaccine & Infectious Disease Institute, University of Antwerp, Universiteitsplein 1, 2610, Antwerp, Belgium.
authors.forename: Niel
authors.initials: N
authors.lastname: Hens
mesh_terms: D000293:Adolescent; D000328:Adult; D000914:Antibodies, Viral / Q000276:immunology*; D001530:Belgium; D002644:Chickenpox / Q000276:immunology; D005260:Female; D006801:Humans; D007116:Immunization, Passive; D008457:Measles / Q000276:immunology; D008954:Models, Biological; D015233:Models, Statistical; D009035:Mothers; D009107:Mumps / Q000276:immunology; D011247:Pregnancy / Q000276:immunology*; D011446:Prospective Studies; D012409:Rubella / Q000276:immunology; D014777:Virus Diseases / Q000276:immunology*; D055815:Young Adult
chemical_list: D000914:Antibodies, Viral
keywords: censored data; correlated random effects; heterogeneity; maternal antibodies; multivariate longitudinal data; non-linear growth model