Demand Forecasting

Demand Forecasting for Health Services, Medicine Uptake and Staffing

Health systems commit money, beds and training places years before patients arrive, so planners and health economists need estimates of how much care will be used and by whom. What planners can observe is recorded use, and recorded use can sit well below or above what people would seek, because supply limits, waiting lists and professional judgement shape the activity data. Forecasts are built with demographic projection, time-series models or causal and econometric models, and their outputs feed budget impact analysis, capacity planning and workforce planning. An illustrative worked example projects hospital admissions for an ageing district.

Need, demand or utilisation as the target of a forecast

The quantity a forecast targets decides which data are suitable and how the result should be read. Need, demand and supply overlap only in part, as the demand page sets out, and most forecasting data record utilisation, such as admissions, dispensed prescriptions or outpatient attendances.

Utilisation is where demand meets supply, so activity counts already reflect the beds, clinics and staff that were available and the gatekeeping rules in force. Wright, Williams and Wilkinson, opening a BMJ series on health needs assessment, note that waiting lists act as a surrogate marker of demand and also influence it. A forecast built on past activity therefore predicts future use under past supply conditions. A question about demand needs waiting lists and other unmet demand added, and a question about need needs epidemiological evidence, because people who need care but do not seek it never appear in activity data.

A forecast is also different from a plan. Hyndman and Athanasopoulos separate forecasting, which predicts the future as accurately as possible, from goals and from planning, which is the response to forecasts and goals.

Demographic projection from population and use rates

The most common starting point in health system planning applies current rates of use to a projected population. Use rates are calculated by age group (often by sex and area too) for a base year, and official population projections supply the future denominators. The forecast is the sum of projected population multiplied by base-year rates.

$$\hat{U}_t = \sum_{a} P_{a,t} \times r_{a,0}$$

where $\hat{U}_t$ is the forecast number of services used in year $t$, $P_{a,t}$ is the projected population in age group $a$ in year $t$, $r_{a,0}$ is the observed utilisation rate per person in age group $a$ in the base year, and the sum runs over all age groups.

The method is transparent and needs little data. Its central assumption is that age-specific rates stay at base-year levels, so only the size and age structure of the population change. In a review of health workforce planning, Lopes, Almeida and Almada-Lobo criticise studies that estimate demand solely from the current level of service and projected demographic profiles, since this leaves out epidemiological need. The assumption can be relaxed by trending each rate forward or adjusting it for changes in the prevalence or incidence of the conditions concerned.

Time-series methods, from exponential smoothing to ARIMA

Time-series methods forecast a series from its own past values. Hyndman and Athanasopoulos state that quantitative forecasting requires numerical information about the past and a reasonable assumption that some aspects of past patterns will continue. These methods suit short-term operational forecasts, such as monthly emergency admissions with stable policy and clear seasonal patterns.

Simple exponential smoothing forecasts the next period as a weighted average of the latest observation and the previous forecast.

$$\hat{y}_{t+1} = \alpha y_t + (1 - \alpha) \hat{y}_t$$

where $\hat{y}_{t+1}$ is the forecast for the next period, $y_t$ is the observed value in period $t$, $\hat{y}_t$ is the forecast that had been made for period $t$, and $\alpha$ is the smoothing parameter between 0 and 1. A value near 1 puts most weight on recent observations. Holt's linear trend method adds a smoothed trend, and seasonal versions add a seasonal component, which matters for winter pressures on hospitals.

ARIMA models instead describe the autocorrelation in a series. A non-seasonal ARIMA($p$, $d$, $q$) model differences the series $d$ times, then models the differenced series with $p$ of its own lagged values and $q$ lagged errors. Both families extrapolate the past and use no other information, so they cannot anticipate a drug launch, a change in eligibility or a new referral pathway unless that is added separately.

Causal and econometric models

Causal or explanatory models forecast use from the factors thought to drive it. A typical model relates use of a service to age structure, disease prevalence, income, insurance cover or out-of-pocket price, and supply, estimated by regression analysis; counts such as admissions are often modelled with Poisson regression, or with negative binomial regression when the counts vary more than a Poisson model allows. Price terms link the forecast to the price elasticity of demand and the demand curve.

Two features matter for forecasting. A genuine forecast made in advance, which Hyndman and Athanasopoulos call an ex-ante forecast, needs forecasts of the predictors themselves, so a model driven by future prevalence is only as good as the prevalence projection. A predictor can also be useful for forecasting without causing the outcome; that is acceptable for predicting next year's activity under unchanged policy, but a scenario such as removing a charge or expanding a service needs coefficients with a causal reading.

A new medicine has no history to extrapolate. Hyndman and Athanasopoulos note that judgemental forecasting is usually the only available method for a new product, and they advise documenting the forecasts and reasoning so that they can be evaluated once data arrive.

Uptake and eligible-population forecasts in budget impact analysis

Budget impact analysis is the main route by which demand forecasting enters health technology assessment. The ISPOR good practice task force led by Sullivan recommends that the design take account of the anticipated uptake of the new intervention, and lists among the key elements the size of the eligible population and the current and expected mix of treatments. Each is a forecast of how many people will be eligible in each year, or of how quickly the new treatment will displace current care.

The task force recommends a simple cost calculator where possible, and states that a cohort or patient-level model may be used when changes in eligible population size, severity mix or treatment patterns over time cannot be captured credibly that way.

Capacity and workforce planning

Capacity planning turns a forecast of arrivals into the beds, sessions, clinic slots or equipment hours needed to serve them. The forecast supplies expected workload by period; capacity planning adds variation, backlog and bottlenecks, which a forecast of average volumes does not address.

Workforce planning needs longer horizons because training takes years. Lopes and colleagues describe three demand-side approaches, namely a needs-based approach that estimates the staff hours required to meet epidemiological need, an effective demand approach that works from the services the population actually uses, and service targets set for each area of care. On the supply side, stock-and-flow models project professional numbers from intakes and exits such as retirement, migration and death. A forecast in service units becomes a staffing requirement when multiplied by staff time per unit of service and compared with projected supply.

Worked example with admissions in an ageing district

The figures in this example are illustrative. A district of 250,000 people records 22,500 emergency medical admissions in the base year and wants a five-year projection to plan bed numbers.

1. Project admissions at constant rates. Base-year rates are applied to the projected population.

$$\hat{U}_5 = 198000 \times 0.05 + 46000 \times 0.20 + 13000 \times 0.45 = 9900 + 9200 + 5850 = 24950$$

where $\hat{U}_5$ is the forecast number of admissions in year 5.

2. Separate population growth from ageing. The population grows by 7,000, or 2.8 per cent, but admissions grow faster.

$$\frac{24950 - 22500}{22500} = \frac{2450}{22500} = 0.109$$

where the result is the proportional growth in admissions, about 10.9 per cent. The growth comes from the two older groups, which gain 9,000 people between them while the youngest group shrinks.

3. Test the constant-rate assumption. Age-specific use in older groups may fall over time, for example because, as survival improves, a smaller share of each older age group is in its last years of life, the mechanism discussed under ageing below. An alternative scenario therefore lowers 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.

$$\hat{U}_5^{alt} = 9900 + 46000 \times 0.19 + 13000 \times 0.405 = 9900 + 8740 + 5265 = 23905$$

where $\hat{U}_5^{alt}$ is the forecast under the alternative scenario. Growth falls to 1,405 admissions, about 6.2 per cent.

4. Convert to beds. In a steady state, where admissions equal discharges, with an illustrative average length of stay of 5 days and planning occupancy of 85 per cent, the bed requirement is as follows.

$$B = \frac{U \times \bar{L}}{365 \times o}$$

where $B$ is the number of beds required, $U$ is annual admissions, $\bar{L}$ is the average length of stay in days and $o$ is the target occupancy as a proportion. The base year needs 22,500 × 5 / (365 × 0.85) = 362.6 beds, the constant-rate forecast 24,950 × 5 / (365 × 0.85) = 402.1 beds and the alternative 23,905 × 5 / (365 × 0.85) = 385.3 beds. Using a single 5-day average for every age group understates bed growth when the case mix ages, because older patients tend to stay longer. For emergency admissions in England in 2022, the Health Foundation reported an average stay of 12.5 days for patients aged 85 and over, against 5.1 days for those aged 16 to 44.

5. Interpret. Constant rates imply about 40 extra beds and the alternative about 23. The gap of 17 beds comes from one assumption about future age-specific rates, so a demographic projection should be reported with scenarios rather than as a single number. The example also forecasts utilisation, not need, so if base-year admissions were held down by a shortage of beds, the base-year rates understate what the population would use with more capacity.

Measuring forecast accuracy

Accuracy can only be judged against data that were not used to build the forecast. Hyndman and Athanasopoulos describe holding back a test set for this purpose. Each forecast error is the observed value minus the forecast, and the errors are summarised with the measures below.

$$e_t = y_t - \hat{y}_t, \qquad MAE = \frac{1}{n} \sum_{t=1}^{n} |e_t|, \qquad MAPE = \frac{100}{n} \sum_{t=1}^{n} \left| \frac{e_t}{y_t} \right|$$

where $e_t$ is the forecast error in period $t$, $y_t$ is the observed value, $\hat{y}_t$ is the forecast, $n$ is the number of test periods, $MAE$ is the mean absolute error and $MAPE$ is the mean absolute percentage error. The MAPE is unit-free but undefined when any observed value is zero and extreme when values are close to zero, a real problem for rare procedures. Prediction intervals usually widen as the horizon lengthens.

Evaluations of real forecasts show the size of the problem. An evaluation of Region Stockholm's forecasts by Linnér and colleagues found that forecasts of annual growth in total drug expenditure, which ranged from 2 to 8 per cent, missed actual growth by 1.9 percentage points on average. Same-year forecasts were more accurate than next-year forecasts, and accuracy was affected by the timing of new medicines and generics, the rate of uptake of new medicines and sudden changes in reimbursement policy. In a retrospective analysis of 12 budget impact models submitted to Ireland's National Centre for Pharmacoeconomics, six underpredicted and six overpredicted realised annual utilisation, and the authors concluded that the models had limited accuracy in predicting it.

Where demand forecasts go wrong

Several errors recur in health service forecasting. Because admission rates vary more with bed supply than with mortality, as Wright and colleagues report, a forecast that extrapolates them to justify more capacity can lock in supplier-induced demand.

Holding age-specific costs constant can overstate the effect of ageing. Zweifel, Felder and Meiers, analysing health care expenditure in the last eight quarters of life of people who had died, found that it depended on remaining lifetime rather than calendar age, at least beyond 65, and suggested that population ageing may add much less to future spending than most observers had claimed. The same reasoning applies to age-specific use rates in a demographic projection.

Structural breaks defeat extrapolation, because a new medicine, a generic entry or a reimbursement change alters the process generating the data, as the Stockholm evaluation found. Uptake forecasts for new technologies rest largely on judgement, so they belong in sensitivity analysis as scenarios and should be updated as close as possible to the decision they inform.

Sources

• 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. Briefing. London: The Health Foundation; 23 June 2023. Section on age. https://www.health.org.uk/reports-and-analysis/briefings/longer-hospital-stays-and-fewer-admissions
• Hyndman RJ, Athanasopoulos G. Forecasting: Principles and Practice. 3rd ed. Melbourne: OTexts; 2021. Sections 1.2, 1.4, 5.5, 5.8, 6.6, 7.6, 7.8, 8.1 to 8.3, chapter 9 introduction and 9.5. https://otexts.com/fpp3/
• Lamrock F, McCullagh L, Tilson L, Barry M. A retrospective analysis of budget impact models submitted to the National Centre for Pharmacoeconomics in Ireland. European Journal of Health Economics. 2020;21(6):895-901. doi:10.1007/s10198-020-01181-0
• Linnér L, Eriksson I, Persson M, Wettermark B. Forecasting drug utilization and expenditure: ten years of experience in Stockholm. BMC Health Services Research. 2020;20:410. doi:10.1186/s12913-020-05170-0
• Lopes MA, Almeida ÁS, Almada-Lobo B. Handling healthcare workforce planning with care: where do we stand? Human Resources for Health. 2015;13:38. doi:10.1186/s12960-015-0028-0
• Sullivan SD, Mauskopf JA, Augustovski F, Jaime Caro J, Lee KM, Minchin M, et al. Budget impact analysis: principles of good practice. Report of the ISPOR 2012 Budget Impact Analysis Good Practice II Task Force. Value in Health. 2014;17(1):5-14. doi:10.1016/j.jval.2013.08.2291
• 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
• Zweifel P, Felder S, Meiers M. Ageing of population and health care expenditure: a red herring? Health Economics. 1999;8(6):485-496. doi:10.1002/(SICI)1099-1050(199909)8:6<485::AID-HEC461>3.0.CO;2-4