Problems in the Estimation of the Key Parameters using MLE in Lung Cancer Screening

Abstract

We have been working in the area of cancer screening modeling for many years. A well-known and frequently used model in cancer screening is the progressive three-state model [1], where all cancer patients are assumed to go through three states: the disease-free state when one is cancer-free or the cancer is in an early stage that no technology can find; the preclinical state when one without symptom but cancer could be detected by screening, and the clinical state when cancer related symptoms show up. There are three key parameters in the model: a) the screening sensitivity, the probability of a positive screening result given that one is in the preclinical state; b) the distribution of sojourn time, which measures the time duration in the preclinical state; and c) the transition density, which measures the time duration in the disease-free state, or the onset age of the preclinical state. These three parameters are called the key parameters since they determines the screening processes and all other terms, for example, lead time (diagnosis time advanced by screening), probability of over-diagnosis, etc., are functions of these three. Therefore accurate estimation of these three key parameters is critical and lays a foundation for all other estimations.