Forecasting client transitions in British Columbia's Long-Term Care Program

This article presents a model for the annual transitions of clients through various home and facility placements in a long-term care program. The model, an application of Markov chain analysis, is developed, tested, and applied to over 9,000 clients (N = 9,483) in British Columbia's Long Term Care Program (LTC) over the period 1978-1983. Results show that the model gives accurate forecasts of the progress of groups of clients from state to state in the long-term care system from time of admission until eventual death. Statistical methods are used to test the modeling hypothesis that clients' year-over-year transitions occur in constant proportions from state to state within the long-term care system. Tests are carried out by examining actual year-over-year transitions of each year's new admission cohort (1978-1983). Various subsets of the available data are analyzed and, after accounting for clear differences among annual cohorts, the most acceptable model of the actual client transition data occurred when clients were separated into male and female groups, i.e., the transition behavior of each group is describable by a different Markov model. To validate the model, we develop model estimates for the numbers of existing clients in each state of the long-term care system for the period (1981-1983) for which actual data are available. When these estimates are compared with the actual data, total weighted absolute deviations do not exceed 10 percent of actuals. Finally, we use the properties of the Markov chain probability transition matrix and simulation methods to develop three-year forecasts with prediction intervals for the distribution of the existing total clients into each state of the system. The tests, forecasts, and Markov model supplemental information are contained in a mechanized procedure suitable for a microcomputer. The procedure provides a powerful, efficient tool for decision makers planning facilities and services in response to the needs of long-term care clients.