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It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter\u2010subject heterogeneity. Even though it is common for biological processes to entail non\u2010linear relationships, examples of multivariate non\u2010linear 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\u2010linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non\u2010linear longitudinal profiles subject to censoring, by combining multivariate random effects, non\u2010linear growth and Tobit regression. We explore the hypothesis of a common infant\u2010specific mechanism underlying maternal immunity using a pairwise correlated random\u2010effects 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 \u00a9 2015 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.6518","type":"journal-article","created":{"date-parts":[[2015,4,24]],"date-time":"2015-04-24T05:18:16Z","timestamp":1429852696000},"page":"2858-2871","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi\u2010disease analysis of maternal antibody decay using non\u2010linear mixed models accounting for censoring"],"prefix":"10.1002","volume":"34","author":[{"given":"Nele","family":"Goeyvaerts","sequence":"first","affiliation":[{"name":"Interuniversity Institute for Biostatistics and Statistical Bioinformatics Hasselt University  Agoralaan 1 Building D 3590 Diepenbeek Belgium"},{"name":"Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination Vaccine &amp; Infectious Disease Institute University of Antwerp  Universiteitsplein 1 2610 Antwerp Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elke","family":"Leuridan","sequence":"additional","affiliation":[{"name":"Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination Vaccine &amp; Infectious Disease Institute University of Antwerp  Universiteitsplein 1 2610 Antwerp Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christel","family":"Faes","sequence":"additional","affiliation":[{"name":"Interuniversity Institute for Biostatistics and Statistical Bioinformatics Hasselt University  Agoralaan 1 Building D 3590 Diepenbeek Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre","family":"Van Damme","sequence":"additional","affiliation":[{"name":"Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination Vaccine &amp; Infectious Disease Institute University of Antwerp  Universiteitsplein 1 2610 Antwerp Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Niel","family":"Hens","sequence":"additional","affiliation":[{"name":"Interuniversity Institute for Biostatistics and Statistical Bioinformatics Hasselt University  Agoralaan 1 Building D 3590 Diepenbeek Belgium"},{"name":"Centre for Health Economics Research and Modelling Infectious Diseases and Centre for the Evaluation of Vaccination Vaccine &amp; Infectious Disease Institute University of Antwerp  Universiteitsplein 1 2610 Antwerp Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2015,4,24]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280209340191"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280212445834"},{"volume-title":"Nonlinear Models for Repeated Measurement Data","year":"1995","author":"Davidian M","key":"e_1_2_8_4_1"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.9.3.334"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0264-410X(03)00341-4"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1086\/313926"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.c1626"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.vaccine.2010.06.004"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2003.08.004"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.2307\/1907382"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2006.00507.x"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/2532914"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1885"},{"key":"e_1_2_8_15_1","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1080\/01621459.1982.10477785","article-title":"Multivariate repeated\u2010measurement or growth curve models with multivariate random\u2010effects covariance structure","volume":"77","author":"Reinsel G","year":"1982","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10474030"},{"volume-title":"Encyclopedia of Biostatistics, chap. 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