State’s Statewide Planning and Research Cooperative System (SPARCS) 2013 is a system initially created to collect information on discharges from hospitals within New York State. SPARCS currently collects patient level detail on patient characteristics, diagnoses and treatments, services, and charges for each hospital inpatient stay and outpatient visit; and each ambulatory surgery and outpatient services visit to a hospital extension clinic and diagnostic and treatment center licensed to provide ambulatory surgery services. In 2013, the SPARCS contains nearly 2.5 million inpatient discharges from 218 facilities and 58 counties in New York State. Patient demographics in the SPARCS include age group at admission, gender, race, source of payment and zip code. Patient clinical characteristics include type of admission, diagnosis codes (MDC code, DRG code, CCS diagnosis code etc.) and treatment procedures undergone (CCS Procedure Code).

An important property of the SPARCS data is that there is not any other longitudinal observation available for time-dependent variables, like the cumulative charge, than the observation at the discharge time. Therefore, neither the traditional maximum partial likelihood method nor the estimation procedures designed for the joint models as discussed in [@kim2013joint; @zeng2007maximum] can be well applied to the SPARCS data. In contrast, the approach proposed 