Cox regression methods are well-known. It has, however, a strong proportional hazards assumption. In many medical contexts, a disease progresses until a failure event (such as death) is triggered when the health level first reaches a failure threshold. I’ll present the Threshold Regression (TR) model for patient’s latent health process that requires few assumptions and, hence, is quite general in its potential application. We use TR to analyze data from a randomized clinical trial of treatment for multiple myeloma. A comparison is made with a Cox proportional hazards regression analysis of the same data.