Expected long-run nursing home use in the study sample fell dramatically under optimum service distribution as compared to the distribution actually observed (Table 3). The proportion of total person-months expected to be spent in nursing home care fell from nearly 12 percent to just over 3 percent, a 75 percent reduction. This is equivalent to a reduction in expected nursing home use by the 3,446 individuals in the full study sample on an annual basis from 4,383 person-days to 1,282 person-days. Bear in mind that this reduction was achieved without increasing total expenditures, indicating that the observed service distribution was extremely inefficient from the standpoint of mitigating nursing home use. It indicates also that, optimally used to this end, community services can in principle have a very much more substantial impact on nursing home use.
As seen also in Table 3, the aggregate service distributions changed substantially under optimum assignment. Hours per month of nursing services increased from the observed 0.77 to 1.24 at optimum, a 61 percent increase, while the incidence of nursing services (the percent receiving at least some service) remained virtually unchanged (14 and 15 percent respectively). Thus the optimization increases the intensity of nursing service use relative to the use actually observed in the sample, but not its incidence.
Changes for lower level services are more dramatic. Home health aide hours fell from an observed average of 5.26 hours per month to 1.2 hours, and service incidence fell from 7 percent to 2. Personal care aide services, which was by far the dominant service in terms of volume in observed use, was eliminated alto ether under the optimization. Conversely, use of housekeeping services was dramatically increased by the optimization, from a mean of 5.9 hours per month to a mean of 47 hours at optimum. The shift in overall service use by the sample is shown in Table 4.
The detailed basis for reallocation of services to individuals by the optimization algorithm is a complex reflection of individual client and service characteristics involved in the objective function. But the dominating factors driving the aggregate results just considered are clearly the services effectiveness (indicated by the magnitude of their TPM coefficients) and their prices (because of the budget constraint). Other things equal, the optimization favors services whose effect is large relative to their cost. That is, it favors services with a high "bang for the buck." An inspection of the coefficients in Table 2 and the costs reported in Appendix A makes it clear that nursing and housekeeping indeed have high impact coefficients relative to their unit cost when compared to home health and personal care aide services.
These aggregate changes, of course, merely summarize the underlying changes that are occurring as services are reallocated across individuals by the optimization. Shifts in nursing hours for individuals ranged from a reduction in services of 98 hours per month at one extreme to an increase of 32 hours per month at the other. Overall, 14 percent (331 of 2,406) of the sample were allocated increased nursing services by the optimization, 12 percent saw reductions in their nursing services, while 74 percent saw their service levels unchanged--these last being nearly all individuals using no nursing services to begin with.
As would be expected given the data in Table 3, the trend for change in home health aide services is negative, the average reduction being 4.1 hours per week. The extremes ranged from a reduction of 722 hours per month (a case of round-the-clock service being reduced to zero) to an increase of 144 hours per month. Personal care aide services, as noted, were eliminated for everyone by the optimization, with their costs being used for other services.
Housekeeping services saw an increase of 41 hours on average, the extremes ranging from a decrease of 370 hours per month to an increase of 187 hours per month. Since these figures seem unreasonably large for housekeeping activities as such, it is clear that other services are being provided under this rubric as well.
Of most general interest is the question of the basis for the resource reallocations generated by the optimization. That is, who is getting more resources (hence reducing their expected nursing home use) at optimum and who is getting less? To descriptively summarize an answer to this question, the difference between the expected nursing home use for each individual [the coefficient given in expression (2)] at its observed value and at optimum was computed. Those getting more services, other things equal, will show a reduction in this risk, while those whose services were reduced will show an increase in risk. The average change in was -0.086, reflecting the strong tendency toward reduction in risk under optimum conditions. Overall, 78 percent of the sample (1,887 of 2,406) were put at reduced risk through the optimization, while 13 percent (305) were actually put at increased risk. These latter are individuals who were among those consuming resources that the optimization determined could be better used elsewhere. About 9 percent of the sample saw their risk unaffected by the optimization.
As a summary analysis of characteristics associated with change in risk under optimization, results of a linear regression of the change in risk () on a variety of individual characteristics are given in Table 5. Change is coded so that a positive coefficient indicates that predicted risk increases (indicating a decrease in effective community services) for individuals with the characteristic indicated. (While significance levels are reported, the simulated data are not a sample, and results should be considered descriptive only.)
Referring to the regressions, immediately noteworthy is the fact that the optimization has moved resources away from African- and Hispanic-Americans, leaving them, on average, at considerably higher risk. This reflects the fact that many in these groups were at much lower initial risk (see Table 2), making them relatively unproductive targets for additional resources, and indeed often presenting the opportunity to transfer resources from them to others where risk levels are higher and are more responsive at the margin to additional resources.
There was no significant difference by gender--on average men and women were treated similarly by the optimization. Older persons on average saw their risks decline, but homeowners saw theirs increase very substantially as their relatively low prior risk made them relatively unattractive as a target for resources.
Note that the optimization shifts considerable additional resources to persons with the classic risk factors for nursing home use--those living alone, those severely impaired in ADL, IADL, or cognition, and those with fewer children or lower income. Those in better health and (unexpectedly) those in wheelchairs saw their services decline somewhat.