Modeling based on progressively type-i interval censored sample

Progressively type-I interval censored data occurs very often in public health study. For example, 112 patients with plasma cell myeloma were admitted to be treated at the National Cancer Institute and all patients were under examination at time schedules (in terms of months), 5.5, 10.5, 15.5, 20.5, 25.5, 30.5, 40.5, 50.5, 60.5, respectively. The data reported by Carbone et al. (Am J Med 42:937-948, 1967) shows the number of patients at risk in each time interval and the number of withdrawn at each examination time schedule which is the most right end point of each time interval. After 60.5 months, the study was terminated. The patients withdrawn at the right end point of time interval have no follow-up study. This table did not provide any patient's exact lifetime. The data structure presented in the table is called progressively type-I interval censored data. In this chapter, many parametric modeling procedures will be discussed via maximum likelihood estimate, moment method estimate, probability plot estimate, and Bayesian estimation. Finally, model selection based on Bayesian concept will be addressed. The entire chapter will also include the model presentation of general data structure and simulation procedure for getting progressively type-I interval censored sample. Basically, this chapter will provide the techniques published by Ng and Wang (J Stat Comput Simul 79: 145-159, 2009), Chen and Lio (Comput Stat Data Anal 54:1581-1591, 2010), and Lin and Lio (2012). R and WinBUGS implementation for the techniques will be included.