Throughput

Throughput in Health Services and Economic Evaluation

Throughput is the realised rate of completed care in a health service, for example discharges per day from a ward, scans per week from a scanner or assessments per session in a clinic. Health economists treat it as the observable output of a service, so it feeds unit costs, efficiency comparisons and the capacity assumptions inside decision models. The figure means something only once the unit of care, the exit point and the time window are fixed, because a ward that counts admissions and one that counts discharges describe different flows. A higher throughput is not the same as more health produced, and most misuse of the measure starts from treating the two as one.

Counting completions at a defined exit

Throughput is a flow, measured where patients leave a defined part of a pathway. Referrals, arrivals and bookings count entries and can run ahead of completions for long periods, while the number of patients currently inside the pathway is a stock measured at a point in time. Capacity is the most a service could complete under stated staffing and opening hours, so throughput is the realised rate and capacity its ceiling.

$$TH = \frac{Q}{T}$$

where $TH$ is observed throughput, $Q$ is the number of completed units of care crossing the chosen exit during the observation window, and $T$ is the length of that window in a stated time unit, such as clinic days or staffed hours.

The unit chosen changes the figure. Outpatient attendances, consultant episodes and hospital spells are all legitimate units, and one admission can generate several episodes. Calendar and staffed time give different rates for a weekday clinic. Patients who leave without completing care are not throughput either. Green notes that some arrivals see a long queue and decline to join it, and that others leave the queue before being served, as with emergency department patients who leave without being seen.

Little's law linking flow, stock and time

Little's law ties throughput to the two other quantities a service can observe. In its queueing form it states that the average number of items in a system equals their average arrival rate multiplied by the average time each spends in the system. Operations management usually writes the same relation in terms of output, the form most useful for throughput, and Little cites Hopp and Spearman's definition of throughput as the average output of a production process per unit time.

$$TH = \frac{WIP}{CT}$$

where $TH$ is throughput in completed units per unit time, $WIP$ (work in process) is the average number of patients inside the pathway boundary, and $CT$ (cycle time) is the average time a patient spends inside that boundary. On a ward, $WIP$ is the average number of occupied beds and $CT$ is the average length of stay.

Little's 2011 review shows that the relation holds exactly over a finite observation period that starts and ends with the system empty, such as a single clinic session, when all three quantities are measured on the same record of arrivals and departures. The proof needs no stationary arrival process and holds whatever the order of service. A second version covers a system that is never empty, provided the arrival rate also counts the patients already present at the start of the period and time in the system counts only time spent inside the period, so a ward census and the average length of stay of discharged patients match only approximately. The practical condition is consistency of boundary and period, so a length of stay from one year cannot be paired with a bed census from another. Forecasting is a separate matter, because queueing theory deals mainly with long-run averages of a stable system, which the queuing model page sets out.

Little adds that in operations management any increase in output requires more work in process, a shorter cycle time or both, unless the process itself changes. For a hospital, more discharges per day need more occupied beds or shorter stays, or a redesign. He reports a flow analysis by Lovejoy and Desmond that sized an observation unit for short-stay patients who were occupying inpatient beds. Observation patients stayed 1.14 days on average, so the expected number in the unit followed from the flow rate, and dividing that number by a target utilisation suggested how many beds to install. The bed turnover and occupancy rate pages apply the same identity to bed statistics.

Throughput between demand and the bottleneck

Over a long period a service cannot complete more patients than arrive or more than its capacity allows, so sustained throughput is bounded by the smaller of demand and capacity. When arrivals exceed completions, the waiting list grows by the difference, an accounting identity from the stock and flow model.

$$B_{1}=B_{0}+A-Q$$

where $B_0$ is the number waiting at the start of a period, $B_1$ is the number waiting at its end, $A$ is the number added to the list during the period and $Q$ is the number completed, all counted at the same boundary. Patients removed for other reasons, such as transfers or deaths, need a separate term.

A pathway completes no more patients than its tightest stage allows. Little describes Harris's emergency department staffing method, in which the minimum number of doctors is the arrival rate divided by the patients per hour one doctor can treat, so 10 arrivals per hour and 2.5 patients per doctor per hour imply at least 4 doctors. Variability in arrivals and service times means more are needed, and Harris suggested 10% to 20% above the minimum as a rule of thumb. Adding doctors when nurses are short does not help, because the nurses become the bottleneck and patients queue in front of them while the extra doctors stand idle. Capacity management deals with the day-to-day levers, while this measure records what they achieve.

Throughput as hospital output in costing and efficiency studies

The final output of a hospital is improvement in patients' health, which cannot be observed directly. Wang and colleagues note that researchers have used throughputs, or intermediate outputs, such as cases treated, patient days and outpatient consultations as proxies, and that this raises problems because outputs differ in case mix and quality. Citing Ellis, they add that hospitals with higher mortality and readmission rates ought not to be regarded as producing the same output as hospitals with lower rates, and that using throughput alone misses information on the effectiveness of treatment.

Throughput therefore enters cost function and data envelopment analysis studies as a measured output, and a provider can look efficient because it treats easier patients or does less for each one. A rise in throughput is evidence of better technical efficiency only when inputs, case mix and quality are held constant, and readmission rates are one check that faster flow has not moved work into later episodes.

Throughput in economic evaluation and HTA

Throughput enters economic evaluation first through unit cost. A service with fixed annual costs has an average cost per use that falls as throughput rises, so the throughput assumed in a model sets the cost per patient. The NICE manual (PMG36, section 4.4.20) bases the initial average cost of a technology with several NHS uses on its expected use or throughput for the uses being evaluated, with a marginal cost analysis allowed in addition where the technology is already recommended for another purpose and spare capacity exists.

The second route is access. Karnon and colleagues, in the ISPOR-SMDM task force report on discrete event simulation, describe the common assumption in health economic models that all required resources are available as needed, with no capacity limitations. They list throughput with flow times, wait times and resource utilisation among the usual outcomes of constrained-resource models. The report recommends that such models consider effects on health-related outcomes and not focus solely on resource use and system capacity, and that constraints be modelled when levels of access change and time to access has significant effects on costs or outcomes.

Thokala and colleagues name patient throughput constraints, such as a fixed number of appointments per day, as one of their categories of resource constraint, using throughput as a proxy for the combined effect of several constrained resources. When every patient receives either the intervention or the comparator, such a constraint leaves per-patient costs, QALYs and the ICER unchanged. It reduces the number who receive the intervention, which changes the population-level net monetary benefit or net health benefit, and they call this an access-limiting capacity constraint. PMG36 (section 4.2.16) asks for net health benefits at values of GBP 25,000 and GBP 35,000 per QALY gained.

Worked example of a capped diagnostic clinic

All numbers in this example are illustrative. A one-stop diagnostic clinic for a new referral pathway runs 7.5 hours a day on 240 days a year, and a commissioner wants to know what the pathway is worth at the clinic's current throughput.

1. Observed throughput. The clinic completed 300 assessments over 20 clinic days, so throughput is 300 / 20 = 15 completed assessments per day, or 15 / 7.5 = 2 per hour.

2. Little's law check. Time stamps give a mean of 3 hours between arrival and completed assessment, so the average number in the clinic should be 2 × 3 = 6. The clinic's own hourly census averages 9, which would imply a mean time of 9 / 2 = 4.5 hours. The two records use different boundaries, perhaps because the census includes patients waiting for transport, and the analysis has to settle on one before using either.

3. Annual throughput and unit cost. Annual throughput is 15 × 240 = 3,600 assessments. With fixed annual costs of GBP 270,000 and a variable cost of GBP 45 per assessment, the fixed cost per assessment is 270,000 / 3,600 = 75, so the average cost is GBP 120 once the GBP 45 is added. A model that assumed a design throughput of 4,500, which the clinic has not achieved, would give 270,000 / 4,500 = 60 and an average cost of GBP 105, understating the cost by GBP 15 per patient.

4. Demand above throughput. Eligible referrals are 5,000 a year. If the unserved patients wait, the list grows by 1,400 patients a year, the gap between 5,000 referrals and 3,600 completions.

5. Per-patient value. The new pathway costs GBP 800 more per patient than usual care and gains 0.08 QALYs. The ICER is 800 / 0.08 = GBP 10,000 per QALY, and at GBP 25,000 per QALY the health gain is valued at 0.08 × 25,000 = GBP 2,000, so net monetary benefit is GBP 1,200 per patient after the GBP 800 cost.

6. Population value with and without the cap. If all 5,000 were assessed, population net monetary benefit would be 5,000 × 1,200 = GBP 6,000,000 a year. At the throughput of 3,600 it is 3,600 × 1,200 = GBP 4,320,000, a shortfall of GBP 1,680,000, equal to 1,680,000 / 25,000 = 67.2 QALYs of net health benefit. At GBP 35,000 per QALY the gain is valued at 0.08 × 35,000 = GBP 2,800, net monetary benefit is GBP 2,000 per patient, and the shortfall is 1,400 × 2,000 = GBP 2,800,000.

7. Interpretation. The ICER is the same with or without the cap, yet the pathway delivers only 3,600 / 5,000 = 0.72, or 72%, of its potential value. Step 6 assumes the patients who are not assessed receive usual care. If they wait instead, Thokala and colleagues note that delay caused by a resource constraint can be valued as reduced life expectancy or lost utility, so the loss can be larger.

Where throughput figures mislead

Most errors come from reading the count as more than a count of completions. The figure shows how many patients left a stage, not how well they were treated.

1. Counting activity as health. More completed episodes can reflect shorter or less appropriate care, or repeat visits caused by poor quality of care.
2. Mixing units or boundaries. Episodes, spells and attendances give different totals for the same patients, and a census and a length of stay taken at different boundaries break Little's law.
3. Reading throughput as capacity. Low throughput can mean low demand, not a shortage, and throughput divided by capacity is capacity utilisation, not capacity.
4. Adding resources off the bottleneck. Extra staff or beds at a stage that is not binding leave throughput unchanged.
5. Planning on averages. A daily mean hides peaks, and capacity planning has to size services for variability as well as the mean.

Sources

• Green L. Queueing analysis in healthcare. In: Hall RW, editor. Patient Flow: Reducing Delay in Healthcare Delivery. New York: Springer; 2006. p. 281-307. https://doi.org/10.1007/978-0-387-33636-7_10
• Karnon J, Stahl J, Brennan A, Caro JJ, Mar J, Möller J. Modeling using discrete event simulation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-4. Value in Health. 2012;15(6):821-827. https://doi.org/10.1016/j.jval.2012.04.013
• Little JDC. Little's Law as viewed on its 50th anniversary. Operations Research. 2011;59(3):536-549. https://doi.org/10.1287/opre.1110.0940
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; published 31 January 2022, last updated 13 October 2026. Sections 4.2.16 and 4.4.20. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• Thokala P, Duarte H, Wright S, Husereau D, Durand-Zaleski I, Lindgren P, Postema R, Machnicki G, Garrison L. Incorporating resource constraints in health economic evaluations: overview and methodological considerations. PharmacoEconomics Open. 2025;9(2):161-178. https://doi.org/10.1007/s41669-024-00537-z
• Wang J, Zhao Z, Mahmood A. Relative efficiency, scale effect, and scope effect of public hospitals: evidence from Australia. IZA Discussion Paper No. 2520. Bonn: Institute for the Study of Labor; December 2006. https://docs.iza.org/dp2520.pdf