Math of Readmit Penalties-Globe1234.com

Formulas for Readmission Adjustment Factor

Summary: The average penalty per excess readmission at a hospital (i.e. above the national readmission rate) is the average base payment for the patients' first hospital stay times the national ratio of admissions to readmissions. This multiplication (equation 4 below) is easier to remember and analyze than the official penalty formula (equation 1), and mathematically the same. The following four equations summarize the equivalence, and more detailed steps are below.

[sum of base pay] x [{#READMIT} / #expected readmissions - 1], the official formula, which can be separated out as:
[avg.base pay x #admit] x [{#EXTRA READMIT + #EXPECTED} / #expected - #expected / #expected], and we can subtract #EXPECTED - #expected, so
avg.base pay x #admit x [#EXTRA READMIT / #expected], and to get penalty per extra readmit we divide by #EXTRA READMIT:
avg.base pay x #admit / #expected readmissions

All 4 equations are also multiplied by [hospital-wide aggregate Medicare payments for 3 future years / hospital-wide aggregate Medicare payments for base years]

Details:

Wording on Medicare Website - http://www.cms.gov/Medicare/Medicare-Fee-for-Service-Payment/AcuteInpatientPPS/Readmissions-Reduction-Program.html

Plain Wording

Wage-adjusted DRG operating amount^* = DRG weight x [(labor share x wage index) + (non-labor share x cola, if applicable)]

^*Note, If the case is subject to the transfer policy, then this amount includes an applicable payment adjustment for transfers under § 412.4(f).

Wage-adjusted payment = payment weight for condition (DRG)

x [labor share x wage index

+ non-labor x cola]

- transfer adjustment

DRG stands for Diagnosis-Related Group, and refers to a group of similar conditions with similar hospital costs

Base Operating DRG Payment Amount = Wage-adjusted DRG operating amount + new technology payment, if applicable.

Base pay = wage-adjusted payment + technology

Excess readmission ratio = risk-adjusted predicted readmissions / risk-adjusted expected readmissions

excess ratio = #readmit / #expected

adjusted for patient mix

Aggregate payments for excess readmissions

= [sum of base operating DRG payments for AMI x (excess readmission ratio for AMI–1)]

+ [sum of base operating DRG payments for HF x (excess readmission ratio for HF–1)]

+ [sum of base operating DRG payments for PN x (excess readmission ratio for PN–1)]

+ [sum of base operating DRG payments for COPD x (excess readmission ratio for COPD–1)]

+ [sum of base operating DRG payments for THA/TKA x (excess readmission ratio for THA/TKA–1)]

*Note, if a hospital’s excess readmission ratio for a condition is less than/equal to 1, then there are no aggregate payments for excess readmissions for that condition included in this calculation.

Potential penalty

= (sum of Base pay) x (#readmit / #expected –1) for heart attacks

+ (sum of Base pay) x (#readmit / #expected –1) for heart failures

+ (sum of Base pay) x (#readmit / #expected –1) for pneumonia

+ (sum of Base pay) x (#readmit / #expected –1) for obstructed lungs

+ (sum of Base pay) x (#readmit / #expected –1) for knee or hip replacement

Each line is positive or zero. Last 2 items' penalty payments start October 2014, based on hospital visits now.

Aggregate payments for all discharges = sum of base operating DRG payments for all discharges

Pay for all = total Base pay for all patients

Ratio = 1 – (Aggregate payments for excess readmissions / Aggregate payments for all discharges)

Ratio = 1 – (Potential penalty / pay for all in 3 base years)

Readmissions Adjustment Factor =

For FY 2013, the higher of the Ratio or 0.99 (1% reduction);
For FY 2014, the higher of the Ratio or 0.98 (2% reduction).

Factor = Ratio, and not less than floors for years when penalty is paid

Floor is 97% from Oct'14 to Sep'15, so maximum penalty is 3% of hospital's base Medicare income from all patients. Only 15 hospitals are expected to be on the 98% floor in 2014, so the floor's effect is rare.

Readmissions Payment Adjustment Amount = [Base operating DRG payment amount x readmissions adjustment factor] – base operating DRG payment amount.

*The readmissions adjustment factor is always less than 1.0000, therefore, the readmissions payment adjustment amount will always be a negative amount (i.e., a payment reduction).

Penalty = Base pay x Factor –Base pay

= Base pay x (Factor – 1)

Penalty is applied to every payment in the 3 future years when it is imposed, so

Total penalty = Pay for all in 3 future years x (Factor – 1)

Each readmission stays in database for 3 years, so it can accrue penalties each of those years.

Plain Wording	Equivalent Math - Examples of calculations are in Spreadsheet
Wage-adjusted payment = payment weight for condition (DRG) x [labor share x wage index + non-labor x cola] -transfer adjustment DRG stands for Diagnosis-Related Group, and refers to a group of similar conditions with similar hospital costs
Base pay = wage-adjusted payment + technology
excess ratio = #readmit / #expected adjusted for patient mix
	Define #Extra = number of extra readmissions =( #readmit – #expected), but never below zero So #readmit = #Extra + #expected
	The fraction (#readmit / #expected –1) is used for each condition in next section, and can be re-grouped = ((#Extra + #expected) / #expected –1) = (#Extra / #expected +1 –1) = (#Extra / #expected)
Potential penalty = (sum of Base pay) x (#readmit / #expected –1) for heart attacks + (sum of Base pay) x (#readmit / #expected –1) for heart failures + (sum of Base pay) x (#readmit / #expected –1) for pneumonia + (sum of Base pay) x (#readmit / #expected –1) for obstructed lungs + (sum of Base pay) x (#readmit / #expected –1) for knee or hip replacement Each line is positive or zero. Last 2 items' penalty payments start October 2014, based on hospital visits now.	Potential penalty = = (average Base pay x #admit) x (#Extra / #expected) for each condition = #Extra x average Base pay x (#admit / #expected) for each condition Each line is positive or zero, and is adjusted for patient mix
Pay for all = total Base pay for all patients
Ratio = 1 – (Potential penalty / pay for all in 3 base years)
Factor = Ratio, and not less than floors for years when penalty is paid Floor is 97% from Oct'14 to Sep'15, so maximum penalty is 3% of hospital's base Medicare income from all patients	Factor = [ 1 – (Potential penalty / pay for all in 3 base years) ]
Penalty = Base pay x Factor –Base pay = Base pay x (Factor – 1)
Penalty is applied to every payment in the 3 future years when it is imposed, so Total penalty = Pay for all in 3 future years x (Factor – 1) Each readmission stays in database for 3 years, so it can accrue penalties each of those years.	= Pay for all in 3 future years x ( [ 1 – (Potential penalty / pay for all) ] - 1 ) = Pay for all in 3 future years x ( – Potential penalty / pay for all in 3 base years) = – Potential penalty x (Pay for all in 3 future years / pay for all in 3 base years) If a hospital has about the same Medicare billings in past and future, the parenthesis is about 1, and the penalty is the Potential penalty as defined above, subject to the 3% or other floor. If billings rise or fall x% in the future, the penalty also rises or falls x%. So we can calculate the potential penalty for each extra readmission, beyond the national average, after taking into account the hospital’s patient mix
Spreadsheet shows both calculations give the same result, see the "Medicare Calcs" tab in the spreadsheet	Actual penalty per extra readmission, for each condition = #Extra x average Base pay x (#admit / #expected) x (Pay for all in 3 future years / pay for all in 3 base years) divided by #Extra = average Base pay x (#admit / #expected) x (Pay for all in 3 future years / pay for all in 3 base years)