Browsing by Subject "Errors-in-variables models"

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    Flexible models of time-varying exposures
    (2015-05) Wang, Chenkun; Gao, Sujuan; Liu, Hai; Yu, Zhangsheng; Callahan, Christopher M.
    With the availability of electronic medical records, medication dispensing data offers an unprecedented opportunity for researchers to explore complex relationships among longterm medication use, disease progression and potential side-effects in large patient populations. However, these data also pose challenges to existing statistical models because both medication exposure status and its intensity vary over time. This dissertation focused on flexible models to investigate the association between time-varying exposures and different types of outcomes. First, a penalized functional regression model was developed to estimate the effect of time-varying exposures on multivariate longitudinal outcomes. Second, for survival outcomes, a regression spline based model was proposed in the Cox proportional hazards (PH) framework to compare disease risk among different types of time-varying exposures. Finally, a penalized spline based Cox PH model with functional interaction terms was developed to estimate interaction effect between multiple medication classes. Data from a primary care patient cohort are used to illustrate the proposed approaches in determining the association between antidepressant use and various outcomes.
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    Single-index regression models
    (2015-05) Wu, Jingwei; Tu, Wanzhu
    Useful medical indices pose important roles in predicting medical outcomes. Medical indices, such as the well-known Body Mass Index (BMI), Charleson Comorbidity Index, etc., have been used extensively in research and clinical practice, for the quantification of risks in individual patients. However, the development of these indices is challenged; and primarily based on heuristic arguments. Statistically, most medical indices can be expressed as a function of a linear combination of individual variables and fitted by single-index model. Single-index model represents a way to retain latent nonlinear features of the data without the usual complications that come with increased dimensionality. In my dissertation, I propose a single-index model approach to analytically derive indices from observed data; the resulted index inherently correlates with specific health outcomes of interest. The first part of this dissertation discusses the derivation of an index function for the prediction of one outcome using longitudinal data. A cubic-spline estimation scheme for partially linear single-index mixed effect model is proposed to incorporate the within-subject correlations among outcome measures contributed by the same subject. A recursive algorithm based on the optimization of penalized least square estimation equation is derived and is shown to work well in both simulated data and derivation of a new body mass measure for the assessment of hypertension risk in children. The second part of this dissertation extends the single-index model to a multivariate setting. Specifically, a multivariate version of single-index model for longitudinal data is presented. An important feature of the proposed model is the accommodation of both correlations among multivariate outcomes and among the repeated measurements from the same subject via random effects that link the outcomes in a unified modeling structure. A new body mass index measure that simultaneously predicts systolic and diastolic blood pressure in children is illustrated. The final part of this dissertation shows existence, root-n strong consistency and asymptotic normality of the estimators in multivariate single-index model under suitable conditions. These asymptotic results are assessed in finite sample simulation and permit joint inference for all parameters.