Signature
C_net = C_prog + tau * N / 1000 * c_event
| Inputs | Definition | Unit |
|---|---|---|
C_prog | Cost of the payment or service change per year | currency per year |
tau | Estimated change in events per 1,000 people per year, negative for a reduction | events per 1,000 people per year |
N | Number of people in the treated population to whom the rate applies | people |
c_event | Average cost of one event, such as an emergency admission | currency per event |
C_net | Policy cost plus the cost of the change in events; negative values are net savings | currency per year |
|---|
Function
Difference-in-differences estimate of a policy effect from treated and comparison groups
Maps outcomes observed before and after a policy in a group exposed to it and a group that is not to an estimate of the policy's average effect on the exposed: the change in the exposed group minus the change in the comparison group. Fixed differences between the groups and shocks common to both cancel. The estimate is causal only under parallel trends and no anticipation. The notation follows the Difference-in-Differences article.
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Implementations
Excel
Net policy cost from named estimate, population and costs
With ProgrammeCost, DiDEstimate (per 1,000), CoveredPopulation and CostPerEvent named, the formula returns the net cost, held in NetPolicyCost.
=ProgrammeCost+DiDEstimate*CoveredPopulation/1000*CostPerEvent
Assumptions
Difference-in-differences effect applied to the population covered
tau is the average effect on the treated, so N is the treated population; applying it to later adopters assumes they would gain as much.
Difference-in-differences effect persists over the year costed
The rate change holds for the full year; Kristensen and colleagues found the Advancing Quality mortality reduction no longer significant by 42 months, so effect duration is a modelling choice.
Worked examples
Net cost of the care-coordination payment from the unadjusted difference-in-differences estimate
With 200,000 residents aged 75 and over, a cost of 3,000 pounds per admission and a payment costing 1.2 million pounds a year, 600 fewer admissions save 1.8 million pounds, a net saving of 0.6 million, as in the article.
C_prog = 1200000; tau = -3; N = 200000; c_event = 3000; C_net = -600000
Care-coordination payment with the trend-adjusted estimate
With the trend-adjusted estimate of plus 1.0 per 1,000, 200 more admissions cost 0.6 million pounds, and the net cost is about 1.8 million, as in the article.
C_prog = 1200000; tau = 1; N = 200000; c_event = 3000; C_net = 1800000
Common errors
Dropping the per 1,000 scaling of a difference-in-differences rate
Multiplying minus 3.0 by 200,000 instead of 200 claims 600,000 fewer admissions, a thousandfold overstatement.
Ignoring spillovers to other services or payers when costing a difference-in-differences effect
If comparison areas also benefit or patients are displaced into them, the estimate is biased and the cost change misallocated; Meacock and colleagues stress positive and negative spillovers and who receives any savings.
Sources
Pay-for-performance cost-effectiveness built on a difference-in-differences effect
Meacock R, Kristensen SR, Sutton M. The cost-effectiveness of using financial incentives to improve provider quality: a framework and application. Health Economics. 2014;23(1):1-13. doi:10.1002/hec.2978 (abstract read). Abstract: evaluations of pay-for-performance need to consider the residual claimant on savings, positive and negative spillovers and whether improvement is transitory; for Advancing Quality, about 5,200 QALYs and 4.4 million pounds of savings in reduced length of stay against 13 million pounds of total programme costs, cost-effective in its first 18 months.
Advancing Quality difference-in-differences mortality reduction as deaths avoided
Sutton M, Nikolova S, Boaden R, Lester H, McDonald R, Roland M. Reduced mortality with hospital pay for performance in England. New England Journal of Medicine. 2012;367(19):1821-1828. doi:10.1056/NEJMsa1114951 (abstract read). Abstract: difference-in-differences regression comparing 18 months before and after; absolute reduction of 1.3 percentage points in risk-adjusted mortality, equivalent to 890 fewer deaths during the 18-month period.
Advancing Quality mortality effect no longer significant at 42 months
Kristensen SR, Meacock R, Turner AJ, Boaden R, McDonald R, Roland M, Sutton M. Long-term effect of hospital pay for performance on mortality in England. New England Journal of Medicine. 2014;371(6):540-548. doi:10.1056/NEJMoa1400962 (abstract read). Difference-in-differences regression of 30-day in-hospital mortality: by the end of the 42-month follow-up the reduced mortality in participating hospitals was no longer significant (minus 0.1 percentage points), and mortality for conditions outside the programme fell more in participating hospitals, raising the possibility of a positive spillover.
Canonical Identity
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