An exploratory analysis of variance and volatility in epileptic electroencephalograms

The electroencephalogram (EEG) is a physiological time series that measures electrical activity at different locations in the brain, and plays an important role in epilepsy research. Exploring the variance and/or volatility may yield insights for seizure prediction, seizure detection and seizure propagation/dynamics.^ Maximal Overlap Discrete Wavelet Transforms (MODWTs) and ARMA-GARCH models were used to determine variance and volatility characteristics of 66 channels for different states of an epileptic EEG – sleep, awake, sleep-to-awake and seizure. The wavelet variances, changes in wavelet variances and volatility half-lives for the four states were compared for possible differences between seizure and non-seizure channels.^ The half-lives of two of the three seizure channels were found to be shorter than all of the non-seizure channels, based on 95% CIs for the pre-seizure and awake signals. No discernible patterns were found the wavelet variances of the change points for the different signals. ^

Patients' preferences for a prostate cancer consultation, a discrete choice experiment

Four basic medical decision making models are commonly discussed in the literature in reference to physician-patient interactions. All fall short in their attempt to capture the nuances of physician-patient interactions, and none satisfactorily address patients' preferences for communication and other attributes of care. Prostate cancer consultations are one setting where preferences matter and are likely to vary among patients. Fortunately, discrete choice experiments are capable of casting light on patients' preferences for communication and other attributes of value that make up a consultation before the consultation occurs, which is crucial if patients are to derive the most utility from the process of reaching a decision as well as the decision itself. The results of my dissertation provide strong support to the notion that patients, at least in the hypothetical setting of a DCE, have identifiable preferences for the attributes of a prostate cancer consultation and that those preferences are capable of being elicited before a consultation takes place. Further, patients' willingness-to-pay for the non-cost attributes of the consultation is surprisingly robust to a variety of individual level variables of interest. ^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^