Date on Master's Thesis/Doctoral Dissertation
Bioinformatics and Biostatistics
Survival regression; MALDI-TOF mass spectrometry; Multistate models; Non-parametric regression; High-dimensional data
Survival analysis (Biometry); Regression analysis
A common research interest in medical, biological, and engineering research is determining whether certain independent variables are correlated with the survival or failure times. Standard statistical techniques cannot usually be applied for failure-time data due to the lack of complete data or in other word, due to censoring. From a statistical perspective, the study of time to event data is even more challenging when further complexities such as high dimensionality or multivariablity is added to the model. In this dissertation, we consider the predicating patient survival from proteomic profile of patient serum using matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) data of non-small cell lung cancer patients. Due to much larger dimension of features in a mass spectrum compared to the study sample size, traditional linear regression modeling of survival times with high number of proteomic features is not feasible. Hence, we consider latent factor and regularized/penalized methods for fitting such models in order to predict patient survival from the mass spectrometry features. Extensive numerical studies involving both simulated as well as real mass spectrometry data are used to compare four popular regression methods, namely, partial least squares (PLS), sparse partial least square (SPLS), least absolute shrinkage and selection operator (LASSO) and elastic net regularization, on processed spectra. Right censoring is handled through a residual based multiple imputation. Overall, more complex methods such as the elastic net and SPLS result in better performances provided the operational parameters are chosen carefully via cross validation. For survival time prediction, we recommend using the elastic net based on a selected set of features. As a type of multivariate survival data, multistate models have a wide range of applications. Most of the existing regression approaches to analyze such data are based on parametric and semi-parametric procedures in which one should rely on specific model structures. In this dissertation, we construct non-parametric regression estimators of a number of temporal functions in a multistate system based on a univariate continuous baseline covariate. These estimators include state occupation probabilities, state entry, exit and waiting (sojourn) times distribution functions of a general progressive (e.g. acyclic) multistate model. The data are subject to right censoring and the censoring mechanism is explainable by observable covariates that could be time dependent. The resulting estimators are valid even if the multistate process is non-Markov. The performance of the estimators is studied using a detailed simulation. We illustrate our estimators using a data set on bone marrow transplant patients. Finally, some extension of the proposed methods to more general case with multivariate covariates are presented along with plans for future developments.
Mostajabi, Farida, "Regression methods for survival and multistate models." (2011). Electronic Theses and Dissertations. Paper 1014.