Period Prevalence

Period Prevalence in Cost-of-Illness and Budget Impact Work

Period prevalence counts everyone who had a condition at some time within a stated interval, usually a year, and divides that count by the population over the same interval. In health economics it is the natural count behind an annual cost-of-illness estimate and behind the number of people a service will see during a budget year. The measure sits between point prevalence, which takes a snapshot on one date, and incidence, which counts only people whose condition begins during the interval. Its value depends on the length of the window and on how an episode is defined, and a period prevalence figure is a count of people, not of time spent ill, which matters whenever it is multiplied by a unit cost.

Counting everyone affected within a window

Prevalence in general includes all cases, new and pre-existing, and the CDC teaching text Principles of Epidemiology in Public Health Practice separates two forms. Point prevalence is the proportion with the condition on a particular date. Period prevalence is the proportion with the condition at any time during an interval, and the CDC table of morbidity measures gives its numerator as current cases, new and pre-existing, over the period and its denominator as the average or mid-interval population.

$$PP_L = \frac{C_0 + A_L}{N} \times 10^n$$

Here $PP_L$ is the period prevalence over a window of length $L$, $C_0$ is the number of people who already have the condition at the start of the window, $A_L$ is the number of people free of the condition at the start who develop it during the window, $N$ is the denominator population and multiplying by ten to the power $n$ scales the result, for example per 1,000 people. Each person enters the numerator once, however many episodes they have in the window.

When $N$ is the population at the start of the window and nobody enters or leaves, the formula splits into a prevalence part and an incidence part.

$$PP_L = P_0 + \frac{A_L}{N}$$

Here $P_0$ is $C_0 / N$, the point prevalence at the start, and $A_L / N$ is the number of new cases per head of the population during the window. Period prevalence then equals or exceeds the starting point prevalence, by more as the window lengthens or onsets quicken.

The CDC worked example shows the parts in a population of 20 people followed for a year. Six people were already ill at the start and four more fell ill during the year, so ten were ill at some time, a period prevalence of 10 out of 20, or 50.0%. The point prevalence on the mid-year date was 7 out of 18, or 38.89%, because by then two people had died and not every case was ill on that date.

Choices that change the number

A period prevalence is only interpretable alongside the analytic choices behind it. None of them is a property of the disease.

The denominator

The CDC table names the average or mid-interval population, yet its worked example divides by all 20 people present during the year, and the two people who died before mid-year were among the ten cases. With the mid-year population of 18 the result would be 10 out of 18, or 55.6%, with two people in the numerator who are missing from the denominator. Spronk and colleagues, working with Dutch general practice records, used person-years instead. In a mobile or high-mortality population these options diverge.

The length of the window

Spronk and colleagues report that one-year period prevalence is the form most often used in general practice research. They compared three definitions on the same Dutch data for 2012, a point prevalence on 31 December, a one-year period prevalence and a contact prevalence (people with at least one GP encounter for the condition during the year). For long-lasting non-chronic diseases, one-year period prevalence was between 58.3% and 206.6% higher than point prevalence. They attribute the gap to people whose episode ended during the year. For chronic diseases, which by their definition do not end, point prevalence came out slightly higher (by 3.5%), because the person-year denominator of the period measure was larger than the year-end population.

The case definition and look-back

In routine data, deciding when an episode starts and stops is itself an analytic choice. Spronk and colleagues closed a non-chronic episode 26 weeks after the last GP encounter, and they found one-year period prevalence between 26.2% and 79.7% higher than contact prevalence for long-lasting diseases, because many people with an open episode had no encounter that year. They conclude that the choice of prevalence type has a high impact and that sources should describe their methods.

Look-back windows stretch the idea further. Vestergaard and colleagues, costing 25 brain disorders from Danish registries, counted as prevalent any person alive on 1 January 2015 with a hospital diagnosis recorded between 1995 and 2014, which gave 18.9% of the population. They note that some of these disorders may be reversible and chose the window because severe disease may affect future income and service use. Such a count measures people ever diagnosed and still alive, not the number currently ill.

Where period prevalence enters health economic work

Period prevalence answers questions about heads, such as how many different people a service will see during the year or how many patients a new pathway must reach. The measure says nothing about how long those people spend ill, and costs that accrue per day or per month of illness depend on time.

Prevalence-based cost-of-illness studies

Jo describes two ways a cost-of-illness study can use epidemiological data. The prevalence-based approach, the more common one, estimates the economic burden of a condition over a specific period, usually a year, while the incidence-based approach estimates the lifetime costs of new cases. Jo notes that for long-lasting conditions the prevalence-based approach is the only practicable one, though it may not quantify long-term consequences. The case count that matches a one-year costing window is a one-year period prevalence, and the cost per person must be measured on the same basis. The result describes burden of illness in that year, not the lifetime cost of the cases.

Urwin and colleagues show the stakes in a UK cost-of-illness study of venous leg ulcers treated by the NHS. Their survey of nine community care locales over two-week periods gave a point prevalence of 3.2 per 10,000 population. Unable to observe annual prevalence directly, they took the point prevalence as a floor and estimated the annual figure in two ways. Adding a published incidence rate of 10 per 10,000 gave an annual period prevalence of 13.2 per 10,000, while assuming a completely new set of patients in every two-week period of the year gave a theoretical maximum of 82.4 per 10,000, roughly 26 fortnights times the point prevalence. The two annual figures differ by a factor of 6.2, yet the national annual cost came from scaling the two-week snapshot of costs and cases, so the total did not depend on which annual prevalence was chosen. The annual figure served only as the denominator of a cost per person.

Budget impact and service planning

The ISPOR good practice report on budget impact analysis by Sullivan and colleagues lists estimating the size of the eligible population as a key element, and where a simple calculator cannot capture changes in that population it allows a cohort or patient-level model that accounts for those entering and leaving. Over a budget year, the people treated at some point form a period prevalence, while drug and staff costs accrue to the person-time on treatment. A cohort model that tracks entries and exits by cycle yields both, whereas multiplying the period-prevalent count by a full year of treatment cost overstates the budget whenever people are treated for less than the whole year.

Inputs to decision models

In a screening or diagnostic model the share of the starting cohort with the condition at the decision point is a point prevalence question, and movements between states come from incidence rates or probabilities, as under cumulative incidence. A period prevalence blends the two, so it serves as neither.

Worked example of an annual costing for an episodic condition

All figures in this example are illustrative. A health authority covers a population of 500,000 adults, assumed closed for the year, and wants the annual cost of community treatment for an episodic skin condition, together with the budget impact of a new dressing.

1. Count the people affected in the year. On 1 April, 650 people have an open episode. During the year, 900 people who had no open episode on 1 April start one, and nobody has a second episode within the year.

$$PP_{1} = \frac{650 + 900}{500{,}000} = 0.0031$$

Here $PP_{1}$ is the one-year period prevalence, 650 is the number with an open episode at the start, 900 is the number of new onsets and 500,000 is the population. The result is 3.1 per 1,000, while the point prevalence on 1 April is 650 out of 500,000, or 1.3 per 1,000. Period prevalence is 3.1 / 1.3 = 2.38 times the snapshot.

2. Measure time with the condition. Daily counts show that, on average, 650 people have an open episode on any given day, so the year contains 650 case-years of treatment. Each person affected spends 650 / 1,550 = 0.419 years, or about 5.0 months, with an open episode within the year.

3. Check the steady state. The disease-free person-time is about 500,000 minus 650, or 499,350 person-years, so the incidence rate is 900 / 499,350 = 0.0018 per person-year. Under the steady-state relation that Pearce gives, prevalence odds equal incidence rate times mean duration, so the mean episode length is

$$D = \frac{650 / 499{,}350}{900 / 499{,}350} = \frac{650}{900} = 0.722$$

where $D$ is the mean duration of an episode in years, the numerator is the prevalence odds and the denominator is the incidence rate per person-year. An average episode lasts about 8.7 months, longer than the 5.0 months spent ill inside the window, because the window edges cut the episodes open at the start and at the end.

4. Cost the year correctly. Treatment costs GBP 400 per case-month, or GBP 4,800 per case-year. The annual cost is 650 × 4,800 = GBP 3,120,000, and the cost per person affected is 3,120,000 / 1,550 = GBP 2,012.90.

5. See the two common errors. Multiplying the period-prevalent count by the cost per case-year gives 1,550 × 4,800 = GBP 7,440,000, an overstatement by a factor of 2.38. Multiplying the point-prevalent count by the cost per person affected gives 650 × 2,012.90 = GBP 1,308,385, an understatement. Both errors pair a count on one basis with a unit cost on another.

6. Budget impact of the new dressing. The dressing adds GBP 50 per case-month. The correct extra spend is 650 case-years × 12 months × GBP 50 = GBP 390,000. Applying a full year of the extra cost to every person in the period prevalence gives 1,550 × 12 × 50 = GBP 930,000, more than double.

7. Interpretation. The authority should expect about 1,550 different patients during the year, which sizes clinic lists, but its spending follows the 650 case-years.

Period prevalence beside its neighbours

The neighbouring measures differ mainly in what the numerator counts and over what time. Each suits a different input.

A prevalence ratio can be computed from point or period prevalence, but both groups must share the same window and case definition. Electronic health record and claims data record contacts over time, so they lend themselves to period measures, with the contact-prevalence caveat above.

Common misreadings

Most errors with period prevalence come from forgetting that the window and the episode rule are part of the number. The rest come from pairing a count of people with a cost or probability defined on another basis.

1. Comparing across windows. A one-year period prevalence set against the point prevalence of another study can show a large difference that is purely definitional.
2. Pairing heads with time. Period-prevalent persons multiplied by a cost per case-year overstate the cost of short episodes, as in step 5.
3. Reading contacts as disease. Contact counts understate period prevalence of chronic conditions whose patients are not seen every year.
4. Treating a long look-back as current illness. People ever diagnosed include people who have recovered.
5. Ignoring the denominator. A mid-interval denominator can leave people who died or moved away in the numerator only.

Sources

• Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, 3rd ed. Lesson 3: Measures of Risk, Section 2 (Morbidity frequency measures). Atlanta: CDC; 2006, page last reviewed 2012. https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html
• Jo C. Cost-of-illness studies: concepts, scopes, and methods. Clinical and Molecular Hepatology. 2014;20(4):327-337. https://doi.org/10.3350/cmh.2014.20.4.327
• Pearce N. Effect measures in prevalence studies. Environmental Health Perspectives. 2004;112(10):1047-1050. https://doi.org/10.1289/ehp.6927
• Spronk I, Korevaar JC, Poos R, et al. Calculating incidence rates and prevalence proportions: not as simple as it seems. BMC Public Health. 2019;19:512. https://doi.org/10.1186/s12889-019-6820-3
• Sullivan SD, Mauskopf JA, Augustovski F, 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. https://doi.org/10.1016/j.jval.2013.08.2291
• Urwin S, Dumville JC, Sutton M, Cullum N. Health service costs of treating venous leg ulcers in the UK: evidence from a cross-sectional survey based in the north west of England. BMJ Open. 2022;12(1):e056790. https://doi.org/10.1136/bmjopen-2021-056790
• Vestergaard SV, Rasmussen TB, Stallknecht S, et al. Occurrence, mortality and cost of brain disorders in Denmark: a population-based cohort study. BMJ Open. 2020;10(11):e037564. https://doi.org/10.1136/bmjopen-2020-037564