Description
An individual who is susceptible to a chronic disease naturally progresses from being disease free to being asymptomatic (preclinical) [1].
This progression is modeled [2] by assuming that the time spent in the disease free and the asymptomatic states are random variables following specified distributions. Early detection may occur if screening takes place before the development of symptoms. The parameters to be estimated are those regarding sensitivity of screening, the preclinical intensity (the probability of the disease to onset in given short time interval) and the time spent in the preclinical state.
To get data is hard and costly in such medical scenarios, so we built a simulator to check the proposed estimation methods, based on given distributions. We also gave confidence intervals for estimators and have analyzed the effects of misspecified distributions.
[1] Zelen, M., & Feinleib, M. (1969). On the Theory of Screening for Chronic Diseases. Biometrika, 56(3), 601-614. doi:10.2307/2334668
[2] Wu, D., Rosner, G. L. and Broemeling, L. (2005), MLE and Bayesian Inference of Age-Dependent Sensitivity and Transition Probability in Periodic Screening. Biometrics, 61: 1056–1063. doi:10.1111/j.1541-0420.2005.00361.x