HA535 Unit 7 Medical-Surgical Census Forecast Example

January at 355.8 Patients Against 356 Staffed Beds: A Trend Forecast of Medical-Surgical Census for a Composite Regional System, Testing Three Methods on the Most Recent Year and Turning the Winner Into a Planning Band

[Student Name]

Purdue University Global

HA535: Data Analytics for Health Care Managers

Unit 7 Trend Forecast

[Instructor Name]

[Date]

The system, the census series and every forecast value are composite and bracketed; figures are described in words for this page.

The Series

Forty-eight months of average daily census on the system's medical-surgical units. The series rises by about half a patient a month and has a clear seasonal pattern: a January peak and a June trough every year. Both trend and seasonality must be captured for a forecast to be useful.

The Test

Each method is fitted on the first [36] months and used to forecast the last [12], which it has not seen. Accuracy is scored with the mean absolute percentage error: each month's miss is taken as a share of actual census, and the shares are averaged. Holding out recent data is the standard way to compare forecasting methods fairly (Hyndman & Athanasopoulos, 2021).

Three Methods

1. Seasonal naive: each month's forecast equals the same month last year. Error: [2.24] percent.

2. Seasonal naive with growth: the same, plus the average yearly increase. Error: [2.04] percent.

3. Holt-Winters exponential smoothing: a method that updates level, trend and seasonal components with weights that favor recent data, developed for seasonal sales forecasting (Winters, 1960). Error: [1.82] percent.

Holt-Winters wins, though the margin over the simpler methods is modest. The best method beat the simplest by less than half a percentage point, which is a reminder that a simple, explainable forecast is often nearly as good as a sophisticated one.

The Forecast

The winning model is refit on all four years and projects the next twelve months, each with a point estimate and an 80 percent range: January: [355.8], range [347.9] to [363.8]. February: [350.4]. December: [343.0]. The summer trough falls to about [318].

Against Capacity

A final figure sets the forecast band against a staffed-bed line at [356]. In January the point forecast nearly equals staffed beds, and the upper end of the range exceeds them. Because occupancy above about [85] to [90] percent brings longer waits for beds, as daily flow varies around the monthly average, the system will feel full well before the average census reaches capacity.

Why an 80 Percent Range

A point forecast alone suggests false precision. An 80 percent range shows the spread of likely outcomes and lets managers plan for the upper end without assuming the worst. Research on short-term hospital occupancy prediction similarly stresses forecasting ranges rather than single values for capacity planning (Littig & Isken, 2007).

Reading the Seasonal Pattern

The January peak reflects respiratory illness and elective surgery scheduled after the holidays; the June trough reflects fewer respiratory admissions and staff vacations that limit elective cases. The pattern repeats closely enough that even the simplest method captures much of it. What changes from year to year is the level, which has risen by about six patients a year.

How Wrong Could January Be?

If January census reached the top of the 80 percent range, [363.8], the system would need about eight more staffed beds than it has, before allowing for daily peaks. If it reached the bottom, [347.9], it would still run at nearly [98] percent of staffed capacity. Either way, January will be tight.

Communicating the Forecast

Leaders should see the band, not only the point. The presentation will show the shaded range against the capacity line and say plainly: in January, the system is likely to be full and could be over capacity.

What the Forecast Does Not Include

A severe influenza season, a nearby hospital closing or a new service line would shift the census beyond the model's range. These are risks to monitor, not inputs to the model.

Checking the Model's Assumptions

The residuals, the gaps between fitted and actual values, show no remaining seasonal pattern and no trend, which suggests the model has captured the main structure of the series. Two months stand out: a January three years ago with an unusually severe influenza season and a June with a temporary unit closure. Neither was removed, because similar events could recur.

Implications

1. Plan for January and February at or above staffed capacity.

2. Decide by September whether to reopen closed beds, add temporary staff or reduce avoidable days, since staffing takes months to arrange.

3. Update the forecast monthly as new data arrive, and widen the range if early winter admissions run high.

Limits

Four years of history is short for estimating seasonality with confidence. Monthly averages hide daily peaks, which run several patients higher on busy days. The model assumes past patterns continue.

Conclusion

The forecast puts January census at the edge of staffed capacity, with a real chance of exceeding it. That finding, not the method, is what leaders need, and it sets up the winter staffing decision in Unit 9.

References

Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and practice (3rd ed.). OTexts.

Littig, S. J., & Isken, M. W. (2007). Short term hospital occupancy prediction. Health Care Management Science, 10(1), 47-66. https://doi.org/10.1007/s10729-006-9000-9

Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages. Management Science, 6(3), 324-342. https://doi.org/10.1287/mnsc.6.3.324