1,721,405 research outputs found
The analysis of multivariate longitudinal data: A review
No full textLongitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this article, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.sponsorship: Geert Verbeke, Geert Molenberghs and Steffen Fieuws gratefully acknowledge support from IAP research Network P6/03 of the Belgian Government (Belgian Science Policy). The work of Marie Davidian was supported in part by NIH grants P01 CA142538, R37AI031789 and R01 CA085848. (IAP research Network of the Belgian Government (Belgian Science Policy)|P6/03, NIH|P01 CA142538, NIH|R37AI031789, NIH|R01 CA085848)status: Publishe
A copula-based approach to joint modelling of multiple longitudinal responses with multimodal structures
No full textsponsorship: Authors are grateful to the Editor and anonymous reviewers for positive comments. The first author is also grateful to the Graduate Office of the University of Isfahan for the support. (Graduate Office of the University of Isfahan)status: Publishe
A joint transition model for evaluating eGFR as biomarker for rejection after kidney transplantation
No full textThe estimated glomerular filtration rate (eGFR) quantifies kidney graft function and is measured repeatedly after transplantation. Kidney graft rejection is diagnosed by performing biopsies on a regular basis (protocol biopsies at time of stable eGFR) or by performing biopsies due to clinical cause (indication biopsies at time of declining eGFR). The diagnostic value of the eGFR evolution as biomarker for rejection is not well established. To this end, we built a joint model which combines characteristics of transition models and shared parameter models to carry over information from one biopsy to the next, taking into account the longitudinal information of eGFR collected in between. From our model, applied to data of University Hospitals Leuven (870 transplantations, 2 635 biopsies), we conclude that a negative deviation from the mean eGFR slope increases the probability of rejection in indication biopsies, but that, on top of the biopsy history, there is little benefit in using the eGFR profile for diagnosing rejection. Methodologically, our model fills a gap in the biomarker literature by relating a frequently (repeatedly) measured continuous outcome with a less frequently (repeatedly) measured binary indicator. The developed joint transition model is flexible and applicable to multiple other research settings
Mixed models approaches for joint modeling of different types of responses
No full textIn many biomedical studies, one jointly collects longitudinal continuous, binary, and survival outcomes, possibly with some observations missing. Random-effects models, sometimes called shared-parameter models or frailty models, received a lot of attention. In such models, the corresponding variance components can be employed to capture the association between the various sequences. In some cases, random effects are considered common to various sequences, perhaps up to a scaling factor; in others, there are different but correlated random effects. Even though a variety of data types has been considered in the literature, less attention has been devoted to ordinal data. For univariate longitudinal or hierarchical data, the proportional odds mixed model (POMM) is an instance of the generalized linear mixed model (GLMM; Breslow and Clayton, 1993). Ordinal data are conveniently replaced by a parsimonious set of dummies, which in the longitudinal setting leads to a repeated set of dummies. When ordinal longitudinal data are part of a joint model, the complexity increases further. This is the setting considered in this paper. We formulate a random-effects based model that, in addition, allows for overdispersion. Using two case studies, it is shown that the combination of random effects to capture association with further correction for overdispersion can improve the model's fit considerably and that the resulting models allow to answer research questions that could not be addressed otherwise. Parameters can be estimated in a fairly straightforward way, using the SAS procedure NLMIXED.sponsorship: The authors gratefully acknowledge the financial support from the IAP research network #P7/06 of the Belgain Government (Belgrain Science Policy) and the Flemish Supercomputer Project. (IAP research network of the Belgain Government (Belgrain Science Policy)|P7/06, Flemish Supercomputer Project)status: Publishe
A Model for Overdispersed Hierarchical Ordinal Data
No full text© 2014 SAGE Publications. Non-Gaussian outcomes are frequently modelled using members of the exponential family. In particular, the Bernoulli model for binary data and the Poisson model for count data are well-known. Two reasons for extending this family are (1) the occurrence of overdispersion, implying that the variability in the data is not adequately described by the models, and (2) the incorporation of hierarchical structure in the data. These issues are routinely addressed separately, the first one through overdispersion models, the second one, for example, by means of random effects within the generalized linear mixed models framework. Molenberghs et al. (2007, 2010) introduced a so-called ‘combined model’ that simultaneously addresses both. In these and subsequent papers, a lot of attention was given to binary outcomes, counts, and time-to-event responses. While common in practice, ordinal data have not been studied from this angle. In this article, a model for ordinal repeated measures, subject to overdispersion, is formulated. It can be fitted without difficulty using standard statistical software. The model is exemplified using data from an epidemiological study in diabetic patients and using data from a clinical trial in psychiatric patients.sponsorship: Financial support from the IAP research network #P7/06 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged. (IAP research network of the Belgian Government (Belgian Science Policy)|P7/06)status: Publishe
A framework for analysing longitudinal data involving time-varying covariates
Full text linkStandard models for longitudinal data ignore the stochastic nature of time-varying covariates and their stochastic evolution over time by treating them as fixed variables. There have been recent methods for modelling time-varying covariates; however, those methods cannot be applied to analyse longitudinal data when the longitudinal response and the time-varying covariates for each subject are measured at different time points. Moreover, it is difficult to study the temporal effects of a time-varying covariate on the longitudinal response and the temporal correlation between them. Motivated by data from an AIDS cohort study conducted over 26 years at the University Hospitals Leuven in which the measurements on the CD4 cell count and viral load for patients are not taken at the same time point, we present a framework to address those challenges by using joint multivariate mixed models to jointly model time-varying covariates and a longitudinal response, instead of including time-varying covariates in the response model. This approach also has the advantage that one can study the association between the covariate at any time point and the response at any other time point without having to explicitly model the conditional distribution of the response given the covariate. We use penalised spline functions of time to capture the evolutions of both the response and time-varying covariates over time
Random-effects models for multivariate repeated measures
No full textMixed models are widely used for the analysis of one repeatedly measured outcome. If more than one outcome is present, a mixed model can be used for each one. These separate models can be tied together into a multivariate mixed model by specifying a joint distribution for their random effects. This strategy has been used for joining multivariate longitudinal profiles or other types of multivariate repeated data. However, computational problems are likely to occur when the number of outcomes increases. A pairwise modeling approach, in which all possible bivariate mixed models are fitted and where inference follows from pseudo-likelihood arguments, has been proposed to circumvent the dimensional limitations in multivariate mixed models. An analysis on 22-variate longitudinal measurements of hearing thresholds illustrates the performance of the pairwise approach in the context of multivariate linear mixed models. For generalized linear mixed models, a data set containing repeated measurements of seven aspects of psycho-cognitive functioning will be analyzed.status: Publishe
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