Describing and forecasting patient census: Comparing linear and nonlinear analysis results

Traditional analysis and forecasting techniques are based on assumptions of linearity. Yet hospitals are open systems, in continuous interaction with the environment. As such, they are nonlinear phenomena. Chaos theory offers methods for analyzing and modeling nonlinear phenomena.

Scientists applying chaos theory to management agree that nonlinear analysis provides new information, they do not agree, however, on what statistical analysis should be computed or what type of forecasting is possible. This study assessed the applicability of several nonlinear techniques for describing and forecasting patient census.

Chaos theory or nonlinear dynamics provided the theoretical framework for the study. Chaos theory is a collection of mathematical, numerical and geometrical techniques that address nonlinear problems for which no explicit general solutions exist (Cambel, 1993). The techniques of chaos theory allow phenomena to be considered in the natural environment, and require that only one variable be measured. These techniques allow scientists to examine complex problems, even nonchaotic complex problems, that have been beyond the reach of traditional analysis. Nonlinear analysis techniques were developed in the physical sciences but have been used to study a wide range of phenomena, including fluid turbulence, predator/prey systems, epidemics, and language (Gleick, 1987).

This study applied statistical methods derived from chaos theory to analyzing and forecasting patient census in a hospital. Patient census data from 1991 through 1994 for an intensive care unit and a pediatric unit within a single community hospital were analyzed. The results of the nonlinear analysis were compared to time series analysis of the same data.

Traditional analysis revealed strong seasonal variation in the pediatric unit census. Traditional analysis techniques failed to identify pattern in the census of the intensive care unit. Nonlinear analysis identified sensitivity to initial conditions in the census data from both units. The pediatric unit was non-chaotic on most measures. The intensive care unit demonstrated several characteristics of a chaotic process, including a positive Lyapunov exponent, fractal structure, and a distinctly patterned return map.

The findings of this study suggested several strategies for nurse administrators planning and budgeting for patient care services. Nonlinear analysis could be a useful adjunct to strategic planning and business development processes. Nonlinear techniques, such as two-dimensional time series graphs and phase plane plots, could provide useful insights to routine budget monitoring processes.