MSc (Statistics) / Department of Statistics / Selection of variables is vital in high dimensional statistical modelling as it aims to identify the right subset model. However, variable selection for discrete survival analysis poses many challenges due to a complicated data structure. Survival data might have unobserved heterogeneity leading to biased estimates when not taken into account. Conventional variable selection methods have stability problems. A simulation approach was used to assess and compare the performance of Least Absolute Shrinkage and Selection Operator (Lasso) and gradient boosting on discrete survival data. Parameter related mean squared errors (MSEs) and false positive rates suggest Lasso performs better than gradient boosting. Frailty models outperform discrete survival models that do not account for unobserved heterogeneity. The two methods were also applied on Zimbabwe Demographic Health Survey (ZDHS) 2016 data on age at first marriage and did not select exactly the same variables. Gradient boosting retained more variables into the model. Place of residence, highest educational level attained and age cohort are the major influential factors of age at first marriage in Zimbabwe based on Lasso. / NRF

Indiana University-Purdue University Indianapolis (IUPUI) / Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects, as well as their functional forms is essential for practical data analysis. However, no existing methods have been developed to meet this need in a joint model setting. In this dissertation, I describe a penalized likelihood-based method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for model selection. By reparameterizing variance components through a Cholesky decomposition, I introduce a penalty function of group shrinkage; the penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. The functional forms of the independent effects are determined through a procedure for structural discovery. Specifically, I first construct the model by penalized cubic B-spline and then decompose the B-spline to linear and nonlinear elements by spectral decomposition. The decomposition represents the model in a mixed-effects model format, and I then use the mixed-effects variable selection method to perform structural discovery. Simulation studies show excellent performance. A clinical application is described to illustrate the use of the proposed methods, and the analytical results demonstrate the usefulness of the methods.

In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data. Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion.

Indiana University-Purdue University Indianapolis (IUPUI) / In medical research, data analysis often requires complex statistical methods where no closed-form solutions are available. Under such circumstances, Monte Carlo (MC) methods have found many applications. In this dissertation, we proposed several novel statistical models where MC methods are utilized. For the first part, we focused on semicompeting risks data in which a non-terminal event was subject to dependent censoring by a terminal event. Based on an illness-death multistate survival model, we proposed flexible random effects models. Further, we extended our model to the setting of joint modeling where both semicompeting risks data and repeated marker data are simultaneously analyzed. Since the proposed methods involve high-dimensional integrations, Bayesian Monte Carlo Markov Chain (MCMC) methods were utilized for estimation. The use of Bayesian methods also facilitates the prediction of individual patient outcomes. The proposed methods were demonstrated in both simulation and case studies. For the second part, we focused on re-randomization test, which is a nonparametric method that makes inferences solely based on the randomization procedure used in clinical trials. With this type of inference, Monte Carlo method is often used for generating null distributions on the treatment difference. However, an issue was recently discovered when subjects in a clinical trial were randomized with unbalanced treatment allocation to two treatments according to the minimization algorithm, a randomization procedure frequently used in practice. The null distribution of the re-randomization test statistics was found not to be centered at zero, which comprised power of the test. In this dissertation, we investigated the property of the re-randomization test and proposed a weighted re-randomization method to overcome this issue. The proposed method was demonstrated through extensive simulation studies.

Indiana University-Purdue University Indianapolis (IUPUI) / Epidemiologic and clinical studies routinely collect longitudinal measures of multiple outcomes. These longitudinal outcomes can be used to establish the temporal order of relevant biological processes and their association with the onset of clinical symptoms. In the first part of this thesis, we proposed to use bivariate change point models for two longitudinal outcomes with a focus on estimating the correlation between the two change points. We adopted a Bayesian approach for parameter estimation and inference. In the second part, we considered the situation when time-to-event outcome is also collected along with multiple longitudinal biomarkers measured until the occurrence of the event or censoring. Joint models for longitudinal and time-to-event data can be used to estimate the association between the characteristics of the longitudinal measures over time and survival time. We developed a maximum-likelihood method to joint model multiple longitudinal biomarkers and a time-to-event outcome. In addition, we focused on predicting conditional survival probabilities and evaluating the predictive accuracy of multiple longitudinal biomarkers in the joint modeling framework. We assessed the performance of the proposed methods in simulation studies and applied the new methods to data sets from two cohort studies. / National Institutes of Health (NIH) Grants R01 AG019181, R24 MH080827, P30 AG10133, R01 AG09956.

Indiana University-Purdue University Indianapolis (IUPUI) / Phytoestrogens that abound in soy products, legumes, and chickpeas can induce biologic responses in animals and humans due to structural similarity to 17β-estradiol. Although experimental studies suggest that phytoestrogen intake may alter the risk of cancer and cardiovascular disease, few epidemiologic studies have investigated this research question. This dissertation investigated the associations of intake of total and individual phytoestrogens and their urinary biomarkers with these chronic conditions using data previously collected from two US national cohort studies (NHANES and PLCO). Utilizing NHANES data with urinary phytoestrogen concentrations and follow-up mortality, Cox proportional hazards regression (HR; 95% CI) were performed to evaluate the association between total cancer, cardiovascular disease, and all-cause mortality and urinary phytoestrogens. After adjustment for confounders, it was found that higher concentrations of lignans were associated with a reduced risk of death from cardiovascular disease (0.48; 0.24-0.97), whereas higher concentrations of isoflavones (2.14; 1.03-4.47) and daidzein (2.05; 1.02-4.11) were associated with an increased risk. A reduction in all-cause mortality was observed for elevated concentrations of lignans (0.65; 0.43-0.96) and enterolactone (0.65; 0.44-0.97). Utilizing PLCO data and dietary phytoestrogens, Cox proportional hazards regression examined the associations between dietary phytoestrogens and the risk of prostate cancer incidence. After adjustment for confounders, a positive association was found between dietary intake of isoflavones (1.58; 1.11-2.24), genistein (1.42; 1.02-1.98), daidzein (1.62; 1.13-2.32), and glycitein (1.53; 1.09-2.15) and the risk of advanced prostate cancer. Conversely, an inverse association existed between dietary intake of genistein and the risk of non-advanced prostate cancer (0.88; 0.78-0.99) and total prostate cancer (0.90; 0.81-1.00). C-reactive protein (CRP) concentration levels rise in response to inflammation and higher levels are a risk factor for some cancers and cardiovascular disease reported in epidemiologic studies. Logistic regression performed on NHANES data evaluated the association between CRP and urinary phytoestrogen concentrations. Higher concentrations of total and individual phytoestrogens were associated with lower concentrations of CRP. In summary, dietary intake of some phytoestrogens significantly modulates prostate cancer risk and cardiovascular disease mortality. It is possible that these associations may be in part mediated through the influence of phytoestrogen intake on circulating levels of C-reactive protein.