Browsing by Subject "censored data"

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    An Approach to Nonparametric Bayesian Analysis for High Dimensional Longitudinal Data Sets
    (2016-06) Shang, Kan
    The goal of this thesis is to develop a more powerful and flexible nonparametric method for the analysis of longitudinal data arising from high throughput biological assays, such as arise in next generation sequence analysis, proteomics and metabolomics, by expanding on an existing approach. The method compared 2 groups by testing for differences in the time to upcrossings and downcrossings for all possible levels using standard nonparametric statistical methods for testing for differences between event times that are subject to censoring. The main problem with nonparametric approaches is their lack of power relative to parametric alternatives, hence methods that aim to redress the shortcomings of nonparametric methods would provide researchers with an approach that greatly enhances their ability to analyze data sets that have a potential impact on human health. Hence in this thesis, we first develop a Bayesian counterpart to rank based tests using the Dirichlet process mixture (DPM) prior. Then we expand this approach to tie sets of distinct level crossing problems together via a hierarchical model to develop a more powerful test. While focusing on the first passage time is useful, such an approach ignores data beyond the first passage time. Hence, we also explore the analysis of recurrent event data from a Bayesian semi-parametric perspective and examine under what conditions the consideration of recurrent events leads to a more powerful procedure. There are not universally agreed upon methods for nonparametric longitudinal analysis, especially in a high dimensional context. As such the thesis research could help fill this gap in the field.
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    Optimal Treatment Regimes Estimation with Censored Data and Related Topics
    (2021-06) Sengupta, Sanhita
    The thesis is divided in three sections of interconnected topics. Motivated by applications from precision medicine, we consider the problem of estimating an optimal treatment regime (or individual optimal decision rule) based on right-censored survival data. We consider a non-parametric approach that maximizes the expected mean restricted survival time of the potential outcome distribution. Comparing with existing methods, our approach does not need to assume the decision rule belongs to a restricted class (e.g., class of index rules) and can accommodate high-dimensional covariates. We investigate the theory of the estimated optimal treatment regime. Monte Carlo studies and a real data example are used to demonstrate the performance of our proposed method. Random forests are widely used today for various purposes such as regression classification, survival analysis however its theoretical properties are not yet explored completely. We propose a quantile random forest estimator which considers sub-sampling instead of complete bootstrap samples as in Meinshausen[2006]. We study the point wise asymptotics of quantile random forest estimator proposed by rendering it in the framework of U-statistics. We prove point-wise weak convergence to normality and also propose a consistent estimator of the variance. We further explore the asymptotic behavior of the proposed estimator via a simulation study. Measuring the efficacy of a treatment or policy can involve data heterogeneity. In such cases, the entire conditional distributional impact of the treatment is important rather than just a discrete metric such as the average treatment effect. Quantiles inform more about the distribution than an average and multiple quantiles can be used together to get an idea about the entire distribution. In the context of survival analysis with censored data, we propose a quantile regression model estimated using survival random forest. We further extend this to estimate quantile treatment effects under censoring. We show the efficacy of the proposed method via simulations. We also demonstrate using this method and interpreting quantile effect by analysing a colon cancer dataset.