Estimating Cancer Latency Times Using a Weibull Model

Abstract

Mathematical models can be useful tools in exploring population disease trends over time and can be used to gain insight into the fundamental mechanisms of cancer development. In this paper, we provide a systematic comparison between the exact and the approximate solutions for estimating the length of time between the biological initiation of cancer and diagnosis through the development of a Weibull-like survival model. A total of 1,608,484 malignant primary cancers were used in the analysis using cancer incidence data obtained from the National Cancer Institute’s Surveillance, Epidemiology, and End Results (SEER) program. We find that the approximate solution provides a reliable comparison of the latency periods for different types of cancer and has no significant effect on the estimation accuracy, which differs from the exact solution by 0% to 11.3%. Thirty-five of the 44 cancers in this analysis were found to progress silently for 10 years or longer prior to detection representing 89% of the patients in this analysis. The results of this analysis differentiate cancer types that progress undetected over a period of years to identify new opportunities for early detection which increases the likelihood of successful treatment and alleviates the ever-growing cancer burden.