Reducing Nursing Home Use Through Community Long-Term Care: An Optimization Analysis Using Data from the National Channeling Demonstration. OPTIMIZING SERVICE ASSIGNMENTS


The optimization problem solved is this: subject to spending no more on community services than was estimated to have been actually spent during the period of the NLTCCD demonstration among the observed population, assign hours of these services to individuals in such a manner that the proportion of total sample exposure expected to be spent in nursing home care is as small as possible. Since this overall proportion is itself a function of the proportion of time that each individual may expect to spend in nursing home care, which in turn is a function of the individual transition probabilities, which are finally themselves in turn a function of community services received and baseline individual characteristics, it follows that the proportion of sample exposure expected to be spent in nursing home residence is itself in part a function of services used by individuals.

The resulting objective function, detailed below, relates the optimization criterion (expected proportion of total exposure time spent in nursing home residence by the sample) to the set of "control variables" whose values (the types and levels of services assigned to each individual) may be set by decision makers, subject to a constraint on total expenditures. This latter is set equal to the estimated actual expenditures for these services within the optimization study sample, since the question of interest is whether this same "budget" could in principle have been used to greater overall effect in reducing nursing home use.

One should bear in mind that nursing home use in the sample is determined not only by admissions to nursing home care, but by exits from it as well. Hence, the optimization assigns services to two distinct groups. The first group consists of frail, elderly persons observed in the community but who are at risk of nursing home entry. The second group consists of people observed during the demonstration to be in nursing homes but who, if appropriate packages of services were available to them, might be able to return to the community. A given individual may be in a different group at different times. In this way, the optimization is designed to minimize nursing home use among the complete eligible population.

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