Signature
I_m = P_m / c_d; U_m = I_m - P_m
| Inputs | Definition | Unit |
|---|---|---|
P_m | Amount paid by the valuation date for care given in service month m | currency |
c_d | Cumulative share of a service month's eventual claims paid by the end of d months after that month, from past payment patterns, entered as a decimal | proportion, above 0 and at most 1 |
I_m | Estimated total claims incurred for care given in service month m, paid or not | currency |
|---|---|---|
U_m | Estimated claims for service month m not yet paid at the valuation date, including unreported claims and reported but unpaid claims | currency |
Function
Actuarial claims costing, premium loading and claims reserving function
Maps utilisation rates, unit costs and the size of a covered group to the expected claims cost of a health insurance scheme, turns that expected cost into a gross premium or contribution with loadings, measures how predictable the group's average cost is, and estimates the claims incurred but not yet paid at a reporting date. These are the calculations of the Actuarial Analysis article. The plan generosity measure is covered separately on the Actuarial Value page.
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Implementations
Excel
Incurred and unpaid claims from a completion factor in two cells
The first formula returns estimated incurred claims and the second the unpaid amount, from named cells holding the amount paid to date for the month and its completion factor as a decimal.
=PaidToDate/Completion; =PaidToDate/Completion-PaidToDate
Assumptions
Past payment pattern applies to the current month
Claims for the month are paid at the same pace as in the past experience used to set c_d. Changes in claims processing, provider contracts or benefit mix alter the lag pattern and bias the estimate.
Completion factor matched to the lag of the month
The factor used is the one for the number of months that have passed between the service month and the valuation date, and P_m is the cumulative amount paid over the same period.
Worked examples
Completion factor of 80% after two months
In the article's example 80% of a month's claims are usually paid within two months. With £4 million paid after two months, estimated incurred claims are £5 million and £1 million remains unpaid.
P_m = 4000000; c_d = 0.80; I_m = 5000000; U_m = 1000000
Fully run-off month with completion factor of one
For an old month whose claims are fully paid the completion factor is 1, so incurred claims equal paid claims and nothing remains unpaid, a limiting case that checks the implementation.
P_m = 4000000; c_d = 1; I_m = 4000000; U_m = 0
Common errors
Using unadjusted paid claims for recent months
Counting the £4 million paid so far as the month's cost understates it by £1 million, a fifth of the estimated £5 million. Applied to the latest months of a claims extract, unadjusted totals suggest a spurious fall in spending.
Dividing by the share paid in one month instead of the cumulative share
If 30% of a month's claims are typically paid in the second month alone, dividing £4 million by 0.30 gives about £13.33 million instead of £5 million. The completion factor is the cumulative share paid by the lag, not the increment.
Applying completion factors to paid claims inflated by large claims
When the amount paid to date includes an unusually high number or amount of large claims, dividing by the completion factor scales those claims up as if more were still to come, so incurred claims are overstated. Large claims are reviewed and adjusted before the factor is applied.
Sources
ASOP 5 development method and unpaid claims liability
Actuarial Standards Board. Actuarial Standard of Practice No. 5: Incurred Health and Disability Claims (Doc. No. 186). Washington, DC: ASB; 2017. Sections 2.5 (development or lag method: claims grouped by incurral and payment period to build a payment pattern), 2.17 (unpaid claims liability) and 3.3.4 (completion factors applied to paid claims with unusual large claims may overstate incurred claims).
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