A First Passage Time Model for Long-Term Survivors with Competing Risks

Abstract

We investigate a competing risks model, using the specification of the Gompertz distribution for failure times from competing causes and the inverse Gaussian distribution for failure times from the cause of interest. The expectation-maximization algorithm is used for parameter estimation and the model is applied to real data on breast cancer and melanoma. In these applications, our models compare favourably with existing techniques. The proposed method provides a useful technique that may be more broadly applicable than existing alternatives.

A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding

“…Finding the very first such time, τ ¼ infft j W ðtÞ ¼ 1g; known as the "first passage" of the process through the boundary B = 1, is easier said than done, one of those classical problems whose concise statements conceal their difficulty (1-4). For general fluctuating random processes, the first-passage time problem is both extremely difficult (5-9) and highly relevant, due to its manifold practical applications: it models phenomena as diverse as the onset of chemical reactions (10)(11)(12)(13)(14), transitions of macromolecular assemblies (15)(16)(17)(18)(19), time-to-failure of a device (20)(21)(22), accumulation of evidence in neural decision-making circuits (23), the "gambler's ruin" problem in game theory (24), species extinction probabilities in ecology (25), survival probabilities of patients and disease progression (26)(27)(28), triggering of orders in the stock market (29)(30)(31), and firing of neural action potentials (32)(33)(34)(35)(36)(37).…”

An Evidence of Link between Default and Loss of Bank Loans from the Modeling of Competing Risks

“…We suggest the reader to references in texts Maller and Zhou (1996) and Ibrahim et al (2005). The modeling of competing risks is widespread in literature in articles such as Cooner et al (2006), Cooner et al (2007), Xu et al (2011). Among a wide number of papers, this subject have been aware due important in articles as Chen et al (1999), Tsodikov et al (2003) and Tournoud and Ecochard (2007).…”

An Evidence of Link between Default and Losses of Bank Loans from the Modeling Risks

“…We suggest the reader to references in texts Maller and Zhou (1996) and Ibrahim et al (2005). The modeling of competing risks is widespread in literature in articles such as Cooner et al (2006), Cooner et al (2007), Xu et al (2011). Among a wide number of papers, this subject have been aware due important in articles as Chen et al (1999), Tsodikov et al (2003) and Tournoud and Ecochard (2007).…”