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.
All 4 equations are also multiplied by [hospitalwide aggregate Medicare payments for 3 future years / hospitalwide aggregate Medicare payments for base years]
Details:
Wording on Medicare Website  http://www.cms.gov/Medicare/MedicareFeeforServicePayment/AcuteInpatientPPS/ReadmissionsReductionProgram.html 
Plain Wording 
Wageadjusted DRG
operating amount^{*} = DRG
weight x [(labor share x wage index) + (nonlabor 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). 
Wageadjusted payment = payment weight for condition (DRG) x [labor share x wage index + nonlabor x cola]  transfer adjustment DRG stands for DiagnosisRelated Group, and refers
to a group of similar conditions with similar hospital costs 
Base
Operating DRG Payment Amount =
Wageadjusted DRG operating amount + new technology payment, if
applicable. 
Base pay = wageadjusted payment + technology 
Excess readmission ratio
= riskadjusted predicted
readmissions / riskadjusted 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 AMI1)] + [sum of base operating DRG payments for HF x (excess readmission
ratio for HF1)] + [sum of base operating DRG payments for PN x (excess
readmission ratio for PN1)] + [sum of base operating DRG payments for COPD x (excess
readmission ratio for COPD1)] + [sum of base operating DRG payments for THA/TKA x
(excess readmission ratio for THA/TKA1)] *Note, if a hospitals
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 =

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 
Wageadjusted payment = payment weight for condition (DRG) x [labor share x wage index + nonlabor x cola] transfer adjustment DRG stands for DiagnosisRelated Group, and refers
to a group of similar conditions with similar hospital costs 

Base pay = wageadjusted 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 regrouped = ((#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
hospitals 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) 