{"title":"Jointly modeling means and variances for nonlinear mixed effects models with measurement errors and outliers.","authors":"Qian Ye, Lang Wu, Viviane Dias Lima","doi":"10.1093/biomtc/ujaf018","DOIUrl":null,"url":null,"abstract":"<p><p>In longitudinal data analyses, the within-individual repeated measurements often exhibit large variations and these variations appear to change over time. Understanding the nature of the within-individual systematic and random variations allows us to conduct more efficient statistical inferences. Motivated by human immunodeficiency virus (HIV) viral dynamic studies, we considered a nonlinear mixed effects model for modeling the longitudinal means, together with a model for the within-individual variances which also allows us to address outliers in the repeated measurements. Statistical inference was then based on a joint model for the mean and variance, implemented by a computationally efficient approximate method. Extensive simulations evaluated the proposed method. We found that the proposed method produces more efficient estimates than the corresponding method without modeling the variances. Moreover, the proposed method provides robust inference against outliers. The proposed method was applied to a recent HIV-related dataset, with interesting new findings.</p>","PeriodicalId":8930,"journal":{"name":"Biometrics","volume":"81 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biometrics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/biomtc/ujaf018","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
In longitudinal data analyses, the within-individual repeated measurements often exhibit large variations and these variations appear to change over time. Understanding the nature of the within-individual systematic and random variations allows us to conduct more efficient statistical inferences. Motivated by human immunodeficiency virus (HIV) viral dynamic studies, we considered a nonlinear mixed effects model for modeling the longitudinal means, together with a model for the within-individual variances which also allows us to address outliers in the repeated measurements. Statistical inference was then based on a joint model for the mean and variance, implemented by a computationally efficient approximate method. Extensive simulations evaluated the proposed method. We found that the proposed method produces more efficient estimates than the corresponding method without modeling the variances. Moreover, the proposed method provides robust inference against outliers. The proposed method was applied to a recent HIV-related dataset, with interesting new findings.
期刊介绍:
The International Biometric Society is an international society promoting the development and application of statistical and mathematical theory and methods in the biosciences, including agriculture, biomedical science and public health, ecology, environmental sciences, forestry, and allied disciplines. The Society welcomes as members statisticians, mathematicians, biological scientists, and others devoted to interdisciplinary efforts in advancing the collection and interpretation of information in the biosciences. The Society sponsors the biennial International Biometric Conference, held in sites throughout the world; through its National Groups and Regions, it also Society sponsors regional and local meetings.