An Accelerated Life Model Analog for Discrete Survival and Count Data

Background and Objective: Our goal is to provide an overall strategy for utilizing continuous accelerated life models in the discrete setting that provides a unique and flexible modeling approach across a variety of hazard shapes. Methods: We convert well-known continuous accelerated life distributions into their discrete counterpart and show theoretically that the existing software that currently exists to accommodate, left, right and interval censoring in the continuous case is re-usable in the discrete setting due to the structure of the likelihood equations. Results: We demonstrate across a variety of simulated and real-world data that our modeling approach can accommodate discrete data that may either be approximately symmetric, left-skewed or right skewed, overcoming the limitations of more traditional modeling approaches. Conclusions: We illustrate both theoretically and through simulations that our approach for accommodating discrete failure time and count data is quite flexible. We demonstrate that the special case of the discrete Weibull model readily can accommodate truly Poisson distributed data and has a great degree of flexibility for non-Poisson distributed data.