Browsing by Subject "treatment regime"

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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.
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    Statistical Methods for Organ Transplant
    (2021-07) McKearnan, Shannon
    In this dissertation, we propose novel statistical methods to improve clinical decision support for organ transplant donors and recipients, using data from the United Network for Organ Sharing national registry. In our first project, we develop a feature selection method for support vector regression in order to benefit from the method’s flexibility while combating overfitting. Support vector regression is advantageous due to its use of a kernel for flexibility and computational efficiency; penalized methods for feature selection limit the choice in kernel to finite dimensional transformations and are thus insufficient. We propose a novel feature selection method for support vector regression based on a genetic algorithm that iteratively searches across potential subsets of covariates to find those that yield the best performance according to a user-defined fitness function. We apply our method to predict donor kidney function one year after transplant. In our second project, we develop an estimator for marginal survival under a dynamic treatment regime for organ transplant, where treatment is defined as the patient’s decision to accept or decline an organ when it is offered to them. We apply our method to kidney transplant patients to recommend thresholds of the quality of organ for acceptance. In our third project, we again utilize the genetic algorithm’s flexible optimization, this time to identify optimal treatment regimes. We define the treatment regime as a decision list in order to develop our method. We apply our method to identify treatment regimes for liver transplant patients who may wish to undergo a simultaneous kidney transplant. Overall, we develop novel methods in diverse fields of statistics tailored for the organ transplantation context, and we demonstrate their performance and meaningful clinical implications via simulations and real data examples.