5. Modeling Multiple Failure Time Data: A Survey of Variance-Corrected Proportional Hazards Models with Empirical Applications to Arrest Data

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Abstract
Proportional hazards models are powerful methods for the analysis of dynamic social processes and are widely used in sociology to estimate the effects of covariates on event timing (e.g., time to arrest, birth, marriage). The proper statistical modeling of failure time data is an important analytical issue in sociology, but to date the field has largely neglected the application of these models to multiple failure time data in which the conventional assumption of the independence of failure times is not tenable. This paper critically describes a class of models known as variance-corrected proportional hazards models that have been developed by statisticians to take into account a lack of independence among failure times. The purpose is to provide an exposition and comparison for sociologists of several such models and associated methods for handling multiple failure time data that can be readily estimated in commonly available statistical software packages. We pay special attention to the data requirements necessary for estimation of the models. The paper concludes with an illustrative application of the models to analyze the arrest patterns of a sample of California Youth Authority parolees.