An episode-based framework for analyzing health care expenditures: an application of reward renewal models

Health Services Research, Dec, 2005 by E. Michael Foster, Fengjuan Xuan

Many questions in health services research revolve around the issue of timing. This issue arises in research on treatment onset or termination as well as transitions between treatment settings. Measures of treatment timing are frequently used as indicators of quality or as part of treatment guidelines. For example, several elements of the Health Plan Employer Data and Information Set (HEDIS) involve timing. For example, one indicator tracks whether or not individuals with mental illness discharged from hospitals receive follow-up care within 30 days. HEDIS also tracks whether individuals being treated with antidepressants remain on those medications continuously during the acute phase of their illness (Druss and Rosenheck 1997; Druss et al. 2002; Busch, Leslie, and Rosenheck 2004). Treatment guidelines also refer to timing issues. For example, the American Academy of Pediatrics recommends treatment plans for children with attention problems so that they receive timely medication management and monitoring (Bauchner 2000; Herrerias, Perrin, and Stein 200 I; Stein and Perrin 2003; Leslie et al. 2004; Rushton, Fant, and Clark 2004).

The issue of timing is central to analysis of treatment episodes--"a series of temporally contiguous health care services related to treatment of a given spell of illness or provided in response to a specific request by the patient or other relevant entity" (Hornbrook, Hurtado, and Johnson 1985). Researchers have long been interested in the dynamics of treatment episodes. This research involves their length and the factors that influence their beginning and end (e.g., Foster 1998; Goldman et al. 1998).

In contrast, analyses of costs or expenditures (1) often focus on a fixed time period, such as a calendar or fiscal year. (2) This strategy makes sense for many budgetary or accounting purposes, such as predicting expenditures during a given budget period. However, analyzing the data in this way discards a great deal of information about the dynamics of expenditures. Two individuals with the same total expenditures in a period may differ significantly in the timing of those expenditures. One individual may have large expenditures in a single treatment episode occurring early in the year. For another expenditures may be spread throughout the year across a series of treatment episodes (Bondy et al. 2000). As noted above, these patterns may have a variety of implications for the quality of care and long-term patient outcomes.

This variation in the timing of expenditures--and service use--may have a variety of implications concerning access to and quality of care as well as treatment outcomes. An episodic perspective highlights that expenditures are shaped by several processes. These include the timing with which episodes start and stop as well as the magnitude of expenditures while in treatment. All three may be shaped by different forces. Whether an individual begins treatment may depend on system-level factors, such as the availability of services. How long he or she remains in treatment may depend on other characteristics, such as transportation. Expenditures per day while in treatment may depend on treatment setting and the efficiency of the particular facility or provider delivering services. As discussed below, this multitude of processes has important implications for predicting expenditures as well. In particular, a model that predicts expenditures in a period assuming a single process will often perform poorly. (This possibility is quite striking in light of the difficulties health economists have had in predicting expenditures on mental health services for risk-adjustment purposes [Ettner et al. 1998, 2001; Kaput, Young, and Murata 2000].) Furthermore, the estimated parameters of that model will be difficult to interpret--they will capture a blend of the parameters of the underlying models.

In this paper, we use a class of stochastic processes known as reward renewal models as a means of understanding the dynamics of service use underlying expenditures in a given period. These models are frequently used in engineering to describe any process that cycles on and off. When the process cycles off, a cost occurs, or an expenditure is made. Engineers use these models to understand the cost implications of various strategies for machine maintenance.

While the terms "broken," "repaired," and "costs of repairs" are regrettable in the context of illness, the reward renewal model has many potential benefits for health services research. Like the two-part model (Duan et al. 1983, 1984), these models can be used to decompose expenditure differences into underlying choices or behaviors. The reward renewal model takes the two-part model one step further: it allows one to decompose the likelihood of being in treatment into the choices to enter and leave treatment. These behaviors may be well worth distinguishing as they may have different determinants and may be sensitive to alternative interventions to influence them.