Regression Modeling of Competing Risks with Applications to Bone Marrow Transplantation Studies and Mortgage Prepayment and Default Analysis

Competing risks frequently arise in medical applications when the subject under study may fail from more than one cause. Typically, regression models for competing risks are based on cause-specific hazards. However, the cause-specific hazard does not have a direct interpretation in terms of survival probability of a particular failure type. In recent years, many researchers have begun using the cumulative incidence function, i.e., the marginal failure probability of a particular cause, to model competing risks. In the literature several methods have been suggested for direct regression modeling of the cumulative incidence function, such as Fine and Gray (1999), Klein and Andersen (2005) and Scheike and Zhang (2008). Fine and Gray's and Scheike and Zhang's methods require estimating the censoring distribution; hence, their performance is highly sensitive to how well the censoring distribution can be estimated. Although Klein and Andersen (2005) avoid estimating the censoring distribution by using pseudo-values, their method suffers from a loss in efficiency. We propose an iterative maximum likelihood method to directly model the cumulative incidence function in the first part of this thesis. It involves iterating between two steps: the first step estimates the baseline subdistribution hazards using the current estimate of the regression coefficients; the second step updates the estimate of the coefficients by maximizing the log-likelihood with the baseline hazards fixed. We derive its asymptotic normality and illustrate the method on a real dataset to compare the risks of relapse and death in remission after bone marrow transplants from different types of donors. Simulation studies show that our method outperforms the methods of Fine and Gray (1999) and Klein and Andersen (2005). Competing risks also arise in mortgage data, which involves two mutually exclusive endpoints, prepayment and default. Many U.S. mortgages issued in recent years were made to subprime borrowers. As the house prices began to decline in mid 2006, subprime mortgage delinquencies soared, which made subprime-mortgage-backed securities almost worthless and led to a global credit crunch. A quantitative model to accurately predict the mortgage prepayment and default rates based on the loan level information and the state of the economy is therefore very important for both risk management and pricing mortgage-backed securities. In the second part of this thesis, we propose a neural network model to model the prepayment and default probabilities. We apply the model to a large dataset consisting of subprime loans originated from 2004 to 2006. Our analysis shows that the neural network model has better performance than the multilogit regression model for predicting mortgage prepayment and default rates.