Incidence

Incidence in Health Economic Models and Costing

Incidence measures the onset of disease, counting the people who develop a condition during a period rather than the people already living with it. Health economists treat it as the flow that fills a model, because it sets how many patients become eligible for a new treatment each year, how quickly events occur under standard care and how many cases a prevention programme could avoid. Epidemiologists report it in two main forms, as a proportion of an initially disease-free group and as a rate per unit of person-time at risk, and the two forms suit different modelling tasks. Mixing incidence with prevalence, or a rate with a probability, distorts budget impact and cost-of-illness estimates. In public finance the word has an unrelated meaning, as in benefit incidence, which concerns who gains from public spending.

Counting new cases against a population at risk

The CDC teaching text Principles of Epidemiology in Public Health Practice describes incidence as the occurrence of new cases of disease or injury in a population over a specified period, and names two common types, the incidence proportion and the incidence rate. Both share a numerator, the new cases arising during the period, and differ in the denominator.

$$CI = \frac{A}{N_0} \qquad IR = \frac{A}{PT}$$

Here $CI$ is the incidence proportion, also called cumulative incidence or risk, and $IR$ is the incidence rate. $A$ is the number of new cases during the period, $N_0$ is the number of people at risk at the start of the period and $PT$ is the total person-time at risk, the sum of the time each person was observed until onset, death, loss to follow-up or the end of the study.

The CDC text stresses that the denominator should be limited to the population at risk, people who could become a case. Person-time has the advantage of handling people who enter and leave observation at different times. When incidence is compared between two groups as a ratio of rates, the result is an incidence rate ratio.

Denominator choices appear to matter less for incidence than definitional choices do for prevalence. Spronk and colleagues computed incidence rates from Dutch general practice records with three denominators, person-years at risk, all person-years and the mid-year population. They found that switching denominators changed incidence rates only slightly (between minus 1.3% and 14.8%), whereas the choice of prevalence definition had a much larger effect.

Incidence as a flow and prevalence as a stock

Prevalence includes every case present at or during a period, new and pre-existing, while incidence is limited to new cases. The CDC text explains that prevalence depends on both incidence and the duration of illness, so a high prevalence may reflect high incidence, prolonged survival without cure or both, and a low prevalence may indicate low incidence, a rapidly fatal course or rapid recovery.

Pearce gives the formal link for a population in a steady state.

$$\frac{P}{1-P} = I \times D$$

Here $P$ is the prevalence, so $P/(1-P)$ is the prevalence odds. $I$ is the incidence rate among people free of the disease and $D$ is the average duration of the disease. The relation holds when the population is stationary, when incidence and disease status are unrelated to migration and population size, and when average duration does not change over time. Pearce adds that such a population rarely exists, but it is approximated when incidence and the relevant exposures are not changing markedly.

The economic consequences follow directly. A treatment that prolongs life without curing the disease raises prevalence while leaving incidence unchanged, which can increase treatment spending even as each patient does better. A prevention programme works on incidence, and prevalence responds only as the existing cases leave the pool through recovery or death.

Where incidence enters an economic evaluation

Incidence appears in three distinct places in health economic work. Each needs a different form of the measure, and errors arise when one form is used where another belongs.

Baseline event rates in decision models

The NICE Decision Support Unit's Technical Support Document 5 (NICE DSU TSD 5) notes that most cost-effectiveness analyses have two separate components, a baseline model of the absolute natural history under standard treatment and a model of relative treatment effects. The baseline may come from trial or cohort evidence, while relative effects generally come from randomised controlled trials. The incidence of events under standard care is therefore part of the baseline risk, and TSD 5 asks that it be as specific as possible to the population of interest, asking whether trials carried out many years ago or with very restrictive inclusion criteria represent the target population.

A Markov model needs a transition probability per cycle, not a rate. Gidwani and Russell note that probabilities and rates for the same event differ in their denominators, since a rate accounts for time at risk and a probability does not, and give the standard rate-to-probability conversion for a node with two possible transitions.

$$p = 1 - e^{-r t}$$

Here $p$ is the probability of the event over the period, $r$ is the incidence rate per unit of time and $t$ is the length of the period in the same units.

Where people can leave the population at risk through another event, such as death from an unrelated cause, the risk of the event of interest has to allow for those competing risks. Austin, Lee and Fine show that estimating incidence as one minus the Kaplan-Meier estimator biases it upwards when competing risks are present, and recommend the cumulative incidence function instead.

Eligible populations in budget impact analysis

The ISPOR good practice report on budget impact analysis by Sullivan and colleagues lists estimating the size of the eligible population among its key elements. Where changes in eligible population size cannot be captured by a simple cost calculator, it says a cohort or patient-level model may be used, accounting for those entering and leaving the eligible population over time, using data from the decision maker's own population where possible. For a treatment started at diagnosis, the people entering each year are the incident cases, while the people already eligible on day one are the prevalent pool, so a budget impact model usually needs both figures.

Incidence-based and prevalence-based cost of illness

Jo describes two ways a cost-of-illness study can use epidemiological data. A prevalence-based study estimates the economic burden of a condition over a specific period, usually a year, while an incidence-based study estimates the lifetime costs of the new cases arising in a period, from onset until cure or death. Jo, drawing on Tarricone, describes the incidence-based approach as particularly useful for considering preventive measures, because it estimates the savings that could accrue if prevention is implemented. For emerging problems such as an epidemic of hepatitis infection, incidence-based estimates are generally higher than prevalence-based ones because many infected people may still be in the latent phase.

Worked example of a prevention programme seen through incidence and prevalence

All figures in this example are illustrative. A chronic condition is followed in a regional register, and the health authority is considering a prevention programme for the 200,000 adults at risk.

1. Estimate the incidence rate. The register records 750 new cases over 150,000 person-years at risk.

$$IR = \frac{750}{150{,}000} = 0.005$$

Here 750 is the number of new cases ($A$) and 150,000 is the person-time at risk ($PT$), so the rate is 5 new cases per 1,000 person-years.

2. Expected new cases each year. If the at-risk population stays at about 200,000 people, it contributes about 200,000 person-years a year, so the expected number of new cases is 0.005 × 200,000 = 1,000 a year.

3. Steady-state prevalence. The average duration of the condition is 12 years. The prevalence odds is 0.005 × 12 = 0.06, so the number of prevalent cases is 0.06 × 200,000 = 12,000 and the prevalence is 12,000 / 212,000 = 0.0566, or about 5.7%.

4. Two cost-of-illness figures. Each prevalent case costs GBP 2,500 a year. The prevalence-based annual cost is 12,000 × 2,500 = GBP 30.0 million. The undiscounted lifetime cost of a new case is 12 × 2,500 = GBP 30,000, so the incidence-based cost of one year's new cases is 1,000 × 30,000 = GBP 30.0 million. The two agree here only because the population is in a steady state and no discounting has been applied.

5. Effect of prevention. The programme lowers the incidence rate with an incidence rate ratio of 0.80, to 0.004, so new cases fall to 0.004 × 200,000 = 800 a year and 200 cases are avoided each year. On the incidence-based view, each year of the programme avoids 200 × 30,000 = GBP 6.0 million of lifetime cost. On the prevalence-based view, if each new case incurs a full year of cost in its first year, spending in year one falls by only 200 × 2,500 = GBP 0.5 million. Once the programme has run well beyond the average duration of the condition, the steady-state prevalence odds is 0.004 × 12 = 0.048, giving 0.048 × 200,000 = 9,600 prevalent cases and an annual cost of 9,600 × 2,500 = GBP 24.0 million, which is GBP 6.0 million below the starting figure.

6. Inputs for a closed-cohort model. A Markov model with annual cycles that follows a fixed cohort needs a probability. Without the programme the annual probability is $p = 1 - e^{-0.005} = 0.004988$, and with it $p = 1 - e^{-0.004} = 0.003992$.

7. Interpretation. Both views reach the same long-run saving of GBP 6.0 million a year, but they arrive at it on different timetables. The incidence-based figure shows the lifetime cost avoided by each year of prevention at once, while an annual prevalence-based estimate shows only GBP 0.5 million in the first year and takes more than a decade to reflect the full effect. A full economic evaluation would also discount future costs, count health gains in QALYs and include the cost of the programme, none of which this illustration attempts.

Choices that change an incidence estimate

Two incidence figures for the same disease can differ for reasons unrelated to the underlying risk. Each is worth checking when incidence is taken from a published source.

1. Case definition and timing. Records usually capture diagnosis rather than biological onset, so recorded incidence reflects testing and coding practice as well as disease.
2. First or recurrent events. A rate of first myocardial infarctions and a rate of all myocardial infarctions answer different questions, and a post-event state in a model needs the rate of recurrent events.
3. The denominator. Person-years at risk, all person-years and the mid-year population give slightly different rates, as Spronk and colleagues found.
4. Competing events. Treating deaths from other causes as censoring overstates the risk of the event of interest.

Common misreadings

Most errors with incidence come from using the wrong one of its forms, or from using prevalence in its place. Each of them changes the number of patients or events that a model carries forward.

1. Sizing a budget impact model from prevalence alone. This misses the stream of new patients who become eligible in later years.
2. Reading falling prevalence as falling incidence. Prevalence also falls when patients die sooner, so a drop in prevalence can mean worse outcomes rather than fewer new cases.
3. Taking baseline incidence from an old or highly selected trial arm. TSD 5 asks that the baseline match the target population under current circumstances.
4. Expecting prevention to cut spending at once. Prevention lowers incidence first, and the stock of prevalent cases, with its costs, shrinks only over the duration of the disease.

Sources

• Austin PC, Lee DS, Fine JP. Introduction to the analysis of survival data in the presence of competing risks. Circulation. 2016;133(6):601-609. https://doi.org/10.1161/CIRCULATIONAHA.115.017719
• 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
• Dias S, Welton NJ, Sutton AJ, Ades AE. NICE DSU Technical Support Document 5: Evidence synthesis in the baseline natural history model. Decision Support Unit, ScHARR, University of Sheffield; 2011, last updated April 2012. https://doi.org/10.15131/shef.data.33737536
• Gidwani R, Russell LB. Estimating transition probabilities from published evidence: a tutorial for decision modelers. PharmacoEconomics. 2020;38(11):1153-1164. https://doi.org/10.1007/s40273-020-00937-z
• 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