Discriminant analysis for longitudinal data with application in medical diagnostics. Classification methods for longitudinal data bear the potential to identify classifiers that are superior to those based on cross-sectional data. Recently, the univariate longitudinal quadratic discriminant analysis (longQDA) was proposed for such purposes. Its key idea is to use marginal means and covariance matrices of linear mixed models as group-specific plug-in estimators for the discriminant rule. This dissertation investigates some of the unaddressed issues as model selection and several multivariate extensions. A complementary software implementation in R is presented which fulfills state-of-the-art design and user requirements. Longitudinal biomarker data from diagnostic studies that are assessed for their potential to classify patients as therapy-resistant or not serve as motivating applications. First, we compare two model selection criteria for determining the most appropriate univariate linear mixed model structures for each group and quantify the corresponding bias of an incorrect decision. The first criterion selects the model structure that yields the best classification performance. The second selects the model with the minimal Bayesian information criterion and performs better in our simulation study. The bias of an incorrect decision turns out to be higher for longer data profiles and more complex longitudinal models with random effects. Subsequently, we present multivariate extensions of long QDA.Two multivariate mixed model classes with a parsimonious parametrization are proposed: multivariate random effects models and covariance pattern models with a Kronecker product structure. With a special set-up of the data, estimation algorithms implemented for the univariate case are used for the first model class. The restricted maximum likelihood estimation of Kronecker product models is accomplished by a numerical constraint optimization algorithm. Finally, we introduce the R package long QDA for executing quadratic discriminant analysis with longitudinal data. Beyond the statistical methodology presented in this dissertation, the entire process of data analysis up to the reporting of the results is supported. The software implementation follows the modern object-orientated concept with S4 classes and fulfills conceptual requirements such as a user-friendly handling, a good run-time performance and easy extensibility. The latter quality criterion is demonstrated for two features: the functionalities for multivariate data settings and its use in simulation studies.
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- Kohlman, Mareike: Discriminant analysis for longitudinal data with application in medical diagnostics. (2010)