American Statistical Association New York City Metropolitan Area Chapter Mailman School of Public Health Columbia University Department of Biostatistics Colloquium

Considerable research has investigated first hitting times as models for survival and other event times. A first hitting time is the earliest time that a stochastic process reaches a fixed threshold or boundary state. In the medical context, the process represents the latent health status of a subject and the threshold represents a critical level of health that triggers an adverse medical event (relapse, disease onset, death). The time scale can be calendar time or some other operational measure of disease progression. Threshold regression refers to first hitting time models with regression structures that accommodate covariate data. The process, threshold parameters and time scale may all depend on the covariates. Threshold regression methodology has already demonstrated its value in studies of infectious disease, cancer and occupational risk. The model generally does not have proportional hazards and thus provides an important alternative to this conventional approach. This talk examines aspects of this topic and discusses fruitful avenues for practical application and future research.