%0 Journal Article
%T Developing a Weibull Model Extension to Estimate Cancer Latency
%A Diana L. Nadler
%A Igor G. Zurbenko
%J ISRN Epidemiology
%D 2013
%R 10.5402/2013/750857
%X 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. 1. Introduction Survival analysis statistics in cancer research are often reported in terms of individual survival from the time of diagnosis. When utilizing cancer registry data, the true time in which malignant cancer cells developed in the body is unknown because there is often no indication. The telltale signs and symptoms characteristic of cancer could be months, if not years, away. Causal factors may act in sequence to initiate or promote carcinogenesis, and ten or more years often pass between exposure to external factors and detectable cancer [1]. More than one-third of all Americans will be diagnosed with cancer sometime in their lives. Though their illness may be invisible now, it presents a great, and largely unexamined, opportunity to find and treat their cancers early [2]. Early detection represents one of the most promising approaches to reduce the growing cancer burden by identifying cancer while it is localized and curable, preventing not only mortality, but also reducing morbidity and costs [3]. The two-parameter Weibull distribution is a popular lifetime model frequently used in biomedical sciences survival analysis to describe age-specific mortality and failure rates [4]. Because the Weibull distribution makes no assumptions about the form of the underlying hazard
%U http://www.hindawi.com/journals/isrn.epidemiology/2013/750857/