14 - Survival Models

Summary

Chapter Preview. This chapter introduces regression where the dependent variable is the time until an event, such as the time until death, the onset of a disease, or the default on a loan. Event times are often limited by sampling procedures and so ideas of censoring and truncation of data are summarized in this chapter. Event times are nonnegative and their distributions are described in terms of survival and hazard functions. Two types of hazard-based regression are considered, a fully parametric accelerated failure time model and a semiparametric proportional hazards models.

Introduction

In survival models, the dependent variable is the time until an event of interest. The classic example of an event is time until death (the complement of death being survival). Survival models are now widely applied in many scientific disciplines; other examples of events of interest include the onset of Alzheimer's disease (biomedical), time until bankruptcy (economics), and time until divorce (sociology).

Example: Time until Bankruptcy. Shumway (2001) examined the time to bankruptcy for 3,182 firms listed on Compustat Industrial File and the CRSP Daily Stock Return File for the New York Stock Exchange over the period 1962–92. Several explanatory financial variables were examined, including working capital to total assets, retained earnings to total assets, earnings before interest and taxes to total assets, market equity to total liabilities, sales to total assets, net income to total assets, total liabilities to total assets, and current assets to current liabilities. The dataset included 300 bankruptcies from 39,745 firm years.