11.8 Population-utilization projections

Suppose an organization observed \(E_{g,t}\) events for group \(g\) in period \(t\), and the corresponding population was \(P_{g,t}\). The utilization rate per 1,000 people is

\[ R_{g,t}=\frac{E_{g,t}}{P_{g,t}}\times1000. \]

If the projected future population is \(P_{g,f}\), a constant-rate projection is

\[ \widehat{E}_{g,f}=R_g\times\frac{P_{g,f}}{1000}. \]

The rate may use the latest complete year, a selected comparable year, an average of recent years, a recent minimum or maximum for scenarios, or a modelled rate. The choice should reflect data quality, stability, horizon, and decision purpose.

Worked Example: Projecting Aquatics Demand

NVRW records 3,600 annual aquatics visits among 24,000 residents in one age group.

\[ R=\frac{3600}{24000}\times1000=150\text{ visits per 1,000 residents}. \]

If the projected population is 27,200, the constant-rate projection is

\[ \widehat{E}=150\times\frac{27200}{1000}=4,080\text{ visits}. \]

The result is conditional on the rate remaining constant. It does not account for pricing, capacity, program changes, competition, weather, or the facility expansion.

Client and population data must share compatible age, location, or other grouping variables. Details available only in the organizational data can be allocated after the population projection only when a defensible rule exists.

Unknown locations should not be silently deleted. They may be reported separately, assigned a broader valid denominator, or carried forward as a stable share. Each treatment changes interpretation.