Signature
U_t = P_1 * r_1 + P_2 * r_2 + P_3 * r_3
| Inputs | Definition | Unit |
|---|---|---|
P_1 | Projected population of age group 1 in year t | persons |
r_1 | Services used per person per year in age group 1 in the base year | services per person per year |
P_2 | Projected population of age group 2 in year t | persons |
r_2 | Services used per person per year in age group 2 in the base year | services per person per year |
P_3 | Projected population of age group 3 in year t | persons |
r_3 | Services used per person per year in age group 3 in the base year | services per person per year |
U_t | Forecast annual use, such as emergency admissions, in year t | services per year |
|---|
Function
Forecasting health service use and measuring forecast accuracy
Maps past use and projected populations to forecasts of future service use, by applying age-specific use rates to a projected population or by smoothing a time series of activity, and compares forecasts with data held back from fitting to measure their accuracy. The notation follows the Demand Forecasting article and its ageing district.
Try this function
Implementations
Excel
Demographic projection from named population and admission ranges
With base-year populations and admissions by age group in BasePop and BaseUse and projected populations in ProjPop, the first formula returns the base-year rates, held in UseRates, and the second the forecast, held in Forecast.
=BaseUse/BasePop; =SUMPRODUCT(ProjPop,UseRates)
Assumptions
Age-specific use rates held at base-year levels
Rates do not change between the base year and year t, so the forecast moves only with the size and age mix of the population; scenarios relax this by trending the rates or adjusting them for changes in prevalence or incidence.
Base-year activity measures use under base-year supply
The rates come from recorded utilisation, which reflects the beds, clinics and gatekeeping of the base year; the forecast is of use under similar supply, not of need.
Age groups cover the whole population once
The groups do not overlap and together make up the population whose use is forecast.
Worked examples
Base-year admissions in the ageing district
200,000 people aged 0 to 64 at 0.05, 40,000 aged 65 to 79 at 0.20 and 10,000 aged 80 and over at 0.45 give 10,000, 8,000 and 4,500, a total of 22,500 emergency admissions, as in the article.
P_1 = 200000; P_2 = 40000; P_3 = 10000; r_1 = 0.05; r_2 = 0.2; r_3 = 0.45; U_t = 22500
Year 5 admissions at constant rates in the ageing district
The projected populations of 198,000, 46,000 and 13,000 give 9,900, 9,200 and 5,850, or 24,950 admissions, 10.9 per cent more while the population grows 2.8 per cent, as in the article.
P_1 = 198000; P_2 = 46000; P_3 = 13000; r_1 = 0.05; r_2 = 0.2; r_3 = 0.45; U_t = 24950
Year 5 admissions with lower rates in the older groups
Lowering the 65 to 79 rate by 5 per cent to 0.19 and the 80 and over rate by 10 per cent to 0.405 gives 23,905 admissions, growth of about 6.2 per cent, as in the article.
P_1 = 198000; P_2 = 46000; P_3 = 13000; r_1 = 0.05; r_2 = 0.19; r_3 = 0.405; U_t = 23905
Common errors
Holding age-specific rates fixed as survival improves
Zweifel, Felder and Meiers found that health care expenditure in the last eight quarters of life depended on remaining lifetime rather than calendar age beyond 65, so constant age-specific rates can overstate the effect of ageing; in the example a modest fall in older-group rates cuts the forecast from 24,950 to 23,905.
Projecting with one crude rate for the whole population
Base-year use of 22,500 over 250,000 people is 0.09 per person; applied to 257,000 people it gives 23,130 admissions and misses the 1,820 that come from the shift towards older groups (computed here for illustration).
Reading a utilisation forecast as a forecast of need
Wright and colleagues report that geographical variation in hospital admission rates is explained more by the supply of beds than by mortality, so rates extrapolated from activity data carry past supply forward and can lock in supplier-induced demand.
Converting the forecast to beds with one average length of stay
Beds follow from admissions times average stay over 365 times occupancy (HE-FM-ALOS-002 solved for beds), but older patients stay longer: for emergency admissions in England in 2022 the Health Foundation reported 12.5 days for those aged 85 and over against 5.1 days at 16 to 44, so one average understates bed growth when the case mix ages.
Sources
Demand estimated from current service levels and demographic projections
Lopes MA, Almeida ÁS, Almada-Lobo B. Human Resources for Health. 2015;13:38. doi:10.1186/s12960-015-0028-0. Background, methodologies for modelling demand: some studies estimate demand solely based on the current level of service in relation to future projections of demographic profiles, thereby leaving out an important determinant of demand, the epidemiological needs.
Expenditure depends on remaining lifetime rather than calendar age
Zweifel P, Felder S, Meiers M. Ageing of population and health care expenditure: a red herring? Health Economics. 1999;8(6):485-496 (abstract read). Abstract: health care expenditure in the last eight quarters of life of individuals who died during 1983 to 1992 depends on remaining lifetime but not on calendar age, at least beyond 65; population ageing may contribute much less to future growth of the health care sector than claimed by most observers.
Hospital admission rates explained more by bed supply than by mortality
Wright J, Williams R, Wilkinson JR. Development and importance of health needs assessment. BMJ. 1998;316(7140):1310-1313. doi:10.1136/bmj.316.7140.1310. Section on needs: geographical variation in hospital admission rates is explained more by the supply of hospital beds than by indicators of mortality; waiting lists become a surrogate marker and an influence on demand.
Average length of stay of emergency admissions by age in England
Cavallaro F, Ewbank L, Marszalek K, Grimm F, Tallack C. Longer hospital stays and fewer admissions: how NHS hospital care changed in England between 2019 and 2022. London: The Health Foundation; 23 June 2023. Section on age: for patients aged 85 years and older average length of stay for emergency admissions increased from 10.8 to 12.5 days between 2019 and 2022, compared with an increase from 4.7 to 5.1 days among patients aged 16 to 44 years.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0