Use of medicare services before and after introduction of the prospective payment system

Health Services Research, August, 1993 by Kenneth G. Manton, Max A. Woodbury, James C. Vertrees, Eric Stallard

If each of |L.sub.j~ responses to variable j is coded as a binary variable, |x.sub.ijl~, the model is

Prob (|x.sub.ijl~ = 1.0) = |g.sub.i1~ |center dot~ ||Lambda~.sub.1jl~ |g.sub.i2~ |center dot~ ||Lambda~.sub.2jl~ . . . |g.sub.iK~ |center dot~ ||Lambda~.sub.Kjl~ (1)

a linear function where the |g.sub.ik~ and ||Lambda~.sub.kjl~ are simultaneously estimated using maximum likelihood. A number of algorithms are used to implement the model (e.g., Shah, 1990; Proceedings of the First International Conference on Fuzzy Sets 1993). To test if the K 1 group improves the model, this statistic (minus twice the difference of the log likelihood with K and K 1 groups) is calculated, which is ||Chi~.sup.2~ distributed with degrees of freedom equal to the number of additional |g.sub.ik~s and ||Lambda~.sub.kjl~s estimated (Manton, Woodbury, and Tolley 1993). ||Lambda~.sub.kjl~s are "consistently" estimated (i.e., converge to "true" values as sample size increases), as are up to J moments of the |g.sub.ik~ distribution (Woodbury, Manton, and Tolley 1993).

LIFE TABLES

Life tables describe service duration and mortality. They are calculated from the probability of a change of state (e.g., alive to dead; to hospital admission from the community) in a time period. These are calculated from variables where the number of categories (|L.sub.j~) is the number of time intervals (e.g., |L.sub.t~) multiplied by the number of states a person can move to (e.g., |L.sub.s~). The |L.sub.t~ x |L.sub.s~ probabilities define life tables describing the length of time that (|l.sub.t~) a person stays in a state (say, |l.sub.s~ = 1 = hospital) before changing (e.g., going to, say, |l.sub.s~ = 2 = community residence). To adjust for health, life tables are estimated for each of K groups defined from the NLTCS health variables. Thus, if a group has few medical problems, its life tables represent service use by "healthy" persons. If a group has multiple impairments, its life tables represent service use by the frail. Persons intermediate in health are represented by combining life tables for two (or more) groups using |g.sub.ik~ as weights. ||Lambda~.sub.kj(lt, ls)~ are estimated in a separate maximum likelihood procedure with |g.sub.ik~s "fixed," that is, ||Lambda~.sub.kj(lt, ls)~ are estimated for case-mix groups.

Service episodes are the unit of analysis (Manton and Stallard 1988). The time line in Figure 1 illustrates how the NLTCS health data relate to Medicare data on the dates and types of service used in the 12 (or 24) months after a survey. Persons are followed from October 1, 1982 to September 30, 1986.

Vertical lines indicate dates on which services used changed. For example, 24 months after the 1982 NLTCS there are three (|e.sub.1~, |e.sub.2~, |e.sub.3~) episodes; the person is home for three months (|e.sub.1~); enters a hospital for a month (|e.sub.2~), and returns home for 20 months (|e.sub.3~). In a 12-month analysis, only episodes up to Time 2 are used, that is, only the first eight months of the second community episode (|e.sub.3~) is counted. Episodes, and associated life tables, are assumed to be independent conditional upon |g.sub.ik~. This is tested by recalculating |g.sub.ik~s for 1982 and 1984 adding prior service use to health variables to describe the dependency remaining between pre- and post-PPS episodes after conditioning on the |g.sub.ik~ calculated only from the NLTCS health measures. The type, duration, and disposition of episodes in pre- and post-PPS periods is calculated for each health group. From Medicare data four types of "service episodes" are defined: "community" (where Medicare services are not used); HHA use; hospital stays; and SNF stays. A community episode ends in one of five ways (|L.sub.s~ = 5): admission to a hospital, a SNF, or a HHA; or death; or end of follow-up. Thus, a life table is calculated for the "service" currently used (4) and for the way in which the service terminates (5): 20 life tables represent the duration of each episode and identify the service termination for each health group. Life tables are important if episode duration varies, or if episodes are censored.