Master of Science, The Ohio State University, 2024, Public Health
Threshold regression, also known as the first hitting time regression model, offers a robust alternative when the proportional hazard assumption of the Cox proportional hazard model is invalid for time-to-event or survival data. This model defines the event time as the first time a latent stochastic process enters a boundary set. When the underlying process follows a Wiener diffusion process, the event time has an inverse Gaussian distribution. Two essential parameters that determine the behavior of the stochastic process are the level at time zero and its mean rate of change. In medical contexts, this models health trajectory with separate functions for initial health status and the mean rate of change for a patient's health trajectory. This flexibility can provide deeper insights for patients' health process. For example, by separately analyzing initial health status and the rate of health degradation, we can identify specific factors or interventions that significantly impact either the baseline health or its rate of change. However, this led to challenges in variable selection, as we must determine which parameters should be included in the regression function for either the initial health status, the degradation rate, or both.
This thesis evaluated various variable selection methods under different conditions through both simulation studies and empirical data analysis. The approaches included frequentist methods such as forward selection, backward selection, and broken adaptive ridge threshold regression estimator (ThregBAR), as well as Bayesian methods including the Bayesian Horseshoe and Bayesian LASSO. The scenarios considered were the event time follows an inverse Gaussian Distribution, as the assumptions stated, and where the number of covariates exceeds the number of observations. The methods were compared based on several criteria, including the false positive rate, false negative rate, and true model rate. In general, we found that Bayesian methods h (open full item for complete abstract)
Committee: Kellie Archer (Committee Member); Michael Pennell (Advisor)
Subjects: Biostatistics