Developing a Weibull Model Extension to Estimate Cancer Latency

Abstract

The mathematical model discussed in this paper presents a technique to estimate the length of the cancer’s silent growth period. The methodology described utilizes information obtained from observed cancer incidence to reconstruct what is cautiously believed to be the period of time from malignant cancer initiation to diagnosis. Analyses show a decreasing hazard for cancer indicating that the longer a patient survives, the more likely they are to reach the upper limit of their natural lifespan. Based on previous research, the Weibull distribution has been used to describe the mechanisms of cancer development. In contrast to the memoryless exponential distribution which assumes a constant failure rate, the shape of the Weibull distribution is dependent on past events and preserves a memory of prior survival. This provides a simple but powerful way to characterize how the unobserved experience of cancer relates to the observed as a function to estimate the time between onset and diagnosis. The results indicate a window of opportunity for early intervention when cancer is most treatable. The method presented provides useful information to identify cancers with high mortality and prolonged periods of undetected growth to distinguish types of dire public health concern.