P.O. Box 2393
Princeton, NJ 08543-2393
Telephone (609) 799-3535
Fax (609) 799-0005
www.mathematica-mpr.com
MEMORANDUM
TO:
Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
SUBJECT:
Outlier and Reliability Analyses for Hospital Total Care
Costs
DATE: 6/22/2011
A. Purpose of Memo
This memo provides information related to treatment of cost outliers (or extreme high
values), various potential reliability thresholds, and implications for minimum sample size
criteria. More specifically, it describes the results of using various rules for treatment of cost
outliers and reliability for the hospital total care cost analysis. We test a range of thresholds at
which to truncate costs and present thresholds that improve explanatory power and reliability but
at the same time introduce minimal distortion in costs as measured by a reduction in the
proportion of total costs profiled. We do this separately for raw costs and standardized costs, for
different payer types (Medicare, Medicaid, and commercial), and different hospital types
(prospective payment system [PPS] hospitals and critical access hospitals [CAHs]). We
recommend a goal of either moderately high or high reliability (for reasons mentioned below) for
hospital profiles based on raw costs and standardized costs, and given this goal and the
recommended thresholds, calculate the minimum number of discharges needed per hospital to
fulfill the stipulated level of reliability. Finally, we compare these minimum numbers of
discharges to the actual distribution of discharges for each payer type and hospital type, and
identify the number of hospitals that would be excluded from peer grouping altogether because
the hospitals fail to meet the minimum sample size criterion for each of the three payer types as
well as the number of hospitals for which a certain payer-specific cost measure might not get
reported because the number of discharges available to calculate the measure fails to meet the
payer-specific minimum sample size criterion. 1
B. Background
Health care cost data is highly skewed, with costs for most patients during any particular
time period being low and predictable, and for a minority of patients being high and variable.
Due to this skewness, outlier observations can severely limit the explanatory power or the ability
1
A hospital will be included in peer grouping as long as it meets the minimum sample size criterion for at least
one payer type.
An Affirmative Action/Equal Opportunity Employer
MEMO TO: Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
DATE:
6/22/2011
PAGE:
2
to account for variation in patients’ costs of a regression-based risk adjustment model. A
previous memo described this issue in detail and recommended truncating costs to reduce
skewness. 2 In this method, costs above a given threshold are replaced with the value of that
threshold. Truncating these costs is a way of recognizing that not enough data are available to
accurately predict the expected cost for rare high-cost events that can have a disproportionate
impact on overall mean costs, which can lead to a single random case distorting the overall ratio
of actual to expected cost for a particular practice. This approach, therefore, reduces their impact
by imposing a ceiling. It also recognizes that some extreme values may be errors.
In addition to improving explanatory power, truncating costs may also be expected to
improve reliability (or consistency) because it reduces the total variance in costs. Reliability can
be measured as R = Nρ/(1+(N-1)ρ, and is a function of N, the number of discharges attributed to
a hospital and ρ, the intraclass correlation (ICC). The ICC is calculated as the ratio of the
variance between hospitals’ mean costs and the total variance which is the sum of variance
between hospitals’ mean costs and variance within each hospital’s costs. The higher the betweenvariance relative to the total variance (or the higher the ICC), the more reliably profiling can
distinguish actual differences in performance between hospitals. Truncating improves reliability
by reducing the total variance in costs, which happens through a reduction in the within-variance
in costs, unless truncation of outliers disproportionately impacts the mean costs of certain
hospitals.
Therefore, determining the minimum sample size (N) to achieve a given level of reliability
requires measuring the ICC and stipulating the required reliability level. We present the options
of using R=0.4, a moderate level of reliability, R = 0.6, a moderately high level of reliability, or
R=.8, a high level of reliability, to calculate minimum Ns for raw costs and standardized costs
for the two hospital types and the three payer types. We present these potential thresholds of
reliability to compare how they balance the need for reliable cost profiles with the need to
include the majority of hospitals in Minnesota in peer grouping and performance reporting. 3
Truncation comes at the cost of excluding some recorded expenditures and distorting the
actual distribution of costs, and therefore, hospital profiles. The proportion by which total costs
are reduced when the threshold is imposed is one measure of that distortion. Therefore, in
recommending thresholds we have been mindful of balancing the tradeoff between high
2
Schone, Eric and Aparajita Zutshi. “Considerations in Performing Outlier Adjustments for Hospitals and
Physician Clinics—Revised.” Princeton, NJ: Mathematica, April 29, 2011.
3
For more detail on reliability and other statistical issues, please refer to a previous memo - Schone, Eric
“Statistical Issues for Reporting Cost Measures in Hospital and Physician Peer Grouping Reports.” Princeton, NJ:
Mathematica, December 7, 2010.
MEMO TO: Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
DATE:
6/22/2011
PAGE:
3
explanatory power and reliability and excluding a significant proportion of the health care dollars
spent in hospitals in Minnesota.
C. Methodology
We tested the following truncation rules and evaluated them according to their effects on
explanatory power, reliability, and proportion of costs profiled:
a. Arbitrary Dollar-value cutoff: Truncate at $100,000.
b. Global percentile cutoff: Truncate at 95th, 98th, 99th, and 99.5th percentile based on
all discharges for a given cost type, hospital type, and payer type.
c. Major diagnostic category (MDC)-specific percentile cutoff: Truncate by MDC at
95th, 98th, 99th, and 99.5th percentile based on all discharges for a given cost type,
hospital type, payer type, and MDC.
We also compared the effects of these rules to the effects of a model based on
untransformed costs.
1.
Estimating explanatory power, reliability, and proportion of costs profiled
As a measure of explanatory power, we used the R-squared from a discharge-level ordinary least
squares model predicting cost as a function of patient characteristics such as age, gender, and
ADGs. R-squared is the proportion of variance in the dependent variable (i.e., costs) which can
be explained by the independent variables (i.e., age, gender, and ADGs). A higher R-squared
implies that the independent variables are good predictors of the variation in the dependent
variable. As a measure of reliability, we used the intraclass correlation (ICC) from a hierarchical
linear model predicting cost as a function of age, gender, and ADGs, with a random intercept for
each hospital. The random intercept captures the individual “effect” of each hospital on the
overall variation in costs and explicitly accounts for the possibility that costs within a hospital
are likely to be more similar (reflecting the hospital’s effect) than costs across hospitals. This
specification allows us to split the the overall variation in hospital costs into two components: (1)
variation across hospitals’ mean costs and (2) variation across discharges within each hospital’s
costs. The ICC is the ratio of the variation between hospitals’ mean costs to the total variation in
hospital costs. Each model was run separately for raw costs and standardized costs for each of
the three payer types—Medicare, Medicaid, and commercial, two hospital types—CAHs and
PPS hospitals, and for the 10 rules for transforming costs (including the untransformed cost
model).
MEMO TO: Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
DATE:
6/22/2011
PAGE:
4
Finally, to calculate the proportion of costs profiled, we divided the sum of truncated costs
by the sum of untransformed costs for each truncation rule, cost type, payer type, and hospital
type.
Appendix A contains a series of tables showing the effect of the different truncation rules
and untransformed costs on explanatory power, reliability, and proportion of costs. In general,
we find that global percentile cutoffs perform better on explanatory power and reliability (as
measured by the ICC) than the MDC-specific percentile cutoffs and only slightly worse on the
proportion of costs profiled. Further, we find that the global 99th percentile achieves a
reasonable balance between high explanatory power and reliability and a small reduction in
proportion of costs profiled. The global 99th percentile also generally performs better than the
$100,000 cutoff. However, there are two instances—raw costs in PPS hospitals paid by Medicaid
and commercial payers, respectively—where the global 99th percentile ends up excluding much
more than five percent of the costs. This happens because these two cost distributions are
considerably more skewed than the other cost distributions, with a larger number of very high
cost stays in the upper tail of the distribution. Because as a general rule of thumb we do not want
to exclude more than 5 percent of costs due to truncation, we recommend making an exception in
these two instances and truncating at the global 99.5th percentile.
D. Implications for Minimum Sample Size
Based on the ICCs from the selected truncation rules for the different cost, payer, and
hospital type combinations, we calculated the minimum sample sizes needed to achieve
reliability levels of 0.4, 0.6, and 0.8. Table 1 shows these minimum sample sizes along with Rsquared, ICC, and proportion of costs profiled from the selected rules. For reporting of overall
and payer-specific hospital costs, we present options of using minimum sample sizes based on
either reliability=0.6 (moderately high reliability) or 0.8 (high reliability), while for reporting
detailed costs, such as a breakdown by MDCs, we recommend minimum sample sizes based on
reliability=0.4 (moderate reliability).
As the table shows, the minimum sample sizes increase with the level of reliability. Further,
for each level of reliability, the minimum sample sizes required to fulfill that level are higher for
standardized costs than raw costs except for the case of discharges paid by Medicaid in PPS
hospitals where the opposite is true. Because we want to report reliable values of both types of
costs when they are reported, when minimum sample sizes required for standardized costs and
raw costs differ, we impose the larger of the two. Therefore, for all hospital and payer types we
select the minimum sample sizes for standardized costs as our reporting standards except in the
case of Medicaid discharges in PPS hospitals where we select the minimum sample sizes for raw
costs as our reporting standards.
MEMO TO: Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
DATE:
6/22/2011
PAGE:
5
Table 1: Effects of Selected Truncation Rules on R-Squared, Intraclass Correlation, Minimum Sample
Size, and Proportion of Costs Profiled
Proportion of
Costs Profiled
R
squareda
Intraclass
Correlationb
CAHs
Medicare
Medicaid
Commercial
All-payer
0.140
0.250
0.207
0.100
0.070
0.065
6
9
10
14
20
22
36
53
58
98.35
98.31
97.56
98.00
PPS Hospitals
Medicare
Medicaid
Commercial
All-payer
0.152
0.196
0.206
0.093
0.092
0.100
7
7
6
15
15
14
39
39
36
96.97
96.00
94.67
95.58
0.156
0.283
0.249
0.043
0.059
0.053
15
11
12
33
24
27
89
64
71
98.65
97.94
94.13
96.59
Minimum Sample Size
R=0.4
R=0.6
R=0.8
Raw Costs
Standardized Costs
CAHs
Medicare
Medicaid
Commercial
All-payer
PPS Hospitals
Medicare
0.159
0.072
9
19
51
97.58
Medicaid
0.223
0.196
3
6
16
94.68
Commercial
0.275
0.039
16
37
99
94.80
All-payer
95.75
Note:
Except for raw costs in PPS hospitals paid by Medicaid and commercial payers, we used the
global 99th percentile for truncating costs. For raw costs in PPS hospitals paid by Medicaid
and commercial payers, we used the global 99.5th percentile for truncating costs.
a
A higher R-squared implies that the independent variables are good predictors of the
variation in the dependent variable.
b
A higher ICC implies that profiling can reliably distinguish actual differences in performance
between hospitals.
We apply the selected reporting standards for the three levels of reliability (R=0.4, R=0.6,
and R=0.8) to the distribution of discharges across CAHs and PPS hospitals to identify the
number of hospitals of each type that fail to meet these minimum sample size standards for a
given payer type and would therefore be excluded from reporting on those payer-specific costs. 4
We also identify hospitals that fail to meet the standards for each of the three payer types and
4
The distribution of attributed discharges across hospitals in Minnesota over the payer-specific measurement
periods is shown in Appendix B.
MEMO TO: Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
DATE:
6/22/2011
PAGE:
6
would therefore be excluded from peer grouping altogether. This is because hospitals would be
included only as long as the hospital meets the minimum sample size standard for at least one
payer type. Table 2 shows the selected standards for minimum sample sizes and their effects on
the number of hospitals excluded from reporting payer-specific costs and from peer grouping
altogether. 5
Table 2: Number of hospitals not meeting minimum N for all-payer and payer-specific costs
Minimum
N (R=0.4)
Number of
hospitals
not
meeting
minimum N
(R=0.4)
Minimum
N (R=0.6)
Number of
hospitals
not
meeting
minimum N
(R=0.6)
Minimum N
(R=0.8)
Number of
hospitals
not
meeting
minimum N
(R=0.8)
CAHs (n=78)
All-payer costs*
0
1
9
Medicare costs
15
2
33
3
89
11
Medicaid costs
11
32
24
44
64
66
Commercial costs
12
4
27
10
71
27
PPS Hospitals (n=53)
All-payer costs*
1
1
1
Medicare costs
9
5
19
5
51
6
Medicaid costs
7
9
15
10
39
10
Commercial costs
16
1
37
1
99
1
Note:
*The “all-payer” numbers refer to the number of hospitals that would be excluded from peer
grouping altogether under each level of reliability because they lack the minimum number of
discharges needed for each of the three payer types.
As shown in Table 2, imposing a higher reliability standard results in higher minimum Ns
and greater number of hospitals being excluded from peer grouping altogether or from reporting
on a given cost measure. This is more evident for reporting of payer-specific costs than total
costs because reporting of total costs only requires that a hospital satisfy the minimum N
criterion for at least one payer type. For reporting of total costs, moderately high reliability
(R=0.6) can be achieved by only excluding one hospital each from the group of CAHs and PPS
hospitals from this reporting. Further, no additional PPS hospitals are excluded from reporting of
overall costs if reliability is increased to 0.8; however, 8 additional CAHs are lost to attain this
high level of reliability. For payer-specific costs, Medicaid-paid discharges in CAHs experience
5
Table 2 is produced from a comparison of minimum sample sizes between raw costs and standardized costs
for the different hospital types and payer types shown in Appendix C.
MEMO TO: Katie Burns, MDH
FROM:
Aparajita Zutshi and Eric Schone, Mathematica
DATE:
6/22/2011
PAGE:
7
the greatest degree of exclusion from reporting with 44 of 78 and 66 of 78 CAHs being excluded
at R=0.6 and R=0.8, respectively.
E. Recommendations
As a preparation for risk adjustment of hospital total care costs, we recommend addressing
cost outliers by truncating them at the 99th percentile (and in a few cases the 99.5th percentile).
In the process, we improved the explanatory power of the linear regression model that will be
used to risk adjust costs and also improved reliability (by increasing the ICC) compared to the
untransformed model. We selected recommended truncation rules for different cost types,
hospital types, and payer types, by balancing the need for high explanatory power and reliability
with minimum distortion in costs as measured by a reduction in the proportion of costs profiled.
The recommended rules for addressing cost outliers and three options for reliability
standards yielded the minimum sample of discharges to achieve those standards. Based on these
minimum sample sizes, we find that we will be able to meet a high reliability standard of 0.8 and
still include 98 percent of the PPS hospitals in peer grouping. To meet this high standard,
however, we would end up excluding about 12 percent of the CAHs from peer grouping, but if
the standard is lowered to 0.6, we would be able to include 98 percent of CAHs as well. For
reporting of payer-specific costs, we can meet a moderately high level of reliability (0.6) at the
cost of excluding about 10 percent of the hospitals (13 percent of CAHs and 2 percent of PPS
hospitals) from reporting on commercial costs and less than 10 percent of the hospitals from
reporting on Medicare costs. For discharges paid by Medicaid, however, in order to meet a
reliability level of 0.6 we would end up excluding over 50 percent of CAHs and nearly 20
percent of PPS hospitals. Choosing a high level of reliability of 0.8 for reporting of payerspecific costs does not worsen exclusion for PPS hospitals but severely worsens exclusion for
CAHs, particularly in the case of Medicaid costs. Because many hospitals have a small
proportion of Medicaid covered stays, it is natural for them to be excluded from the ranking on
Medicaid costs. However, this exclusion does not affect a hospital's overall performance as
overall scores will be adjusted for payer-mix.
cc: Project Team
Appendix A
The Effect of Truncation Rules on Explanatory Power,
Reliability, and Proportion of Costs Profiled
RAW COSTS
Raw Commercial Costs in CAHs
Rule
Proportion of Costs
Profiled
R squared
Intraclass Correlation
Untransformed
0.172
0.055
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.238
0.218
0.207
0.198
0.061
0.063
0.065
0.064
91.18
95.76
97.56
98.64
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.224
0.209
0.201
0.195
0.182
0.068
0.067
0.064
0.063
0.061
93.98
96.86
98.10
98.89
99.82
R squared
Intraclass Correlation
Raw Medicaid Costs in CAHs
Rule
Proportion of Costs
Profiled
Untransformed
0.223
0.052
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.281
0.262
0.250
0.241
0.078
0.075
0.070
0.065
93.57
96.94
98.31
99.07
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.277
0.246
0.240
0.224
0.223
0.075
0.067
0.064
0.053
0.052
95.13
98.11
98.92
99.92
100.00
Raw Medicare Costs in CAHs
Rule
Proportion of Costs
Profiled
R squared
Intraclass Correlation
Untransformed
0.121
0.076
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.143
0.142
0.140
0.138
0.114
0.105
0.100
0.095
94.58
97.34
98.35
98.97
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.145
0.143
0.140
0.137
0.125
0.111
0.104
0.097
0.093
0.080
94.69
97.56
98.57
99.11
99.93
Raw Commercial Costs in PPS Hospitals
Rule
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.110
0.055
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.300
0.256
0.229
0.206
0.134
0.121
0.109
0.100
80.65
88.07
91.99
94.67
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.271
0.232
0.206
0.184
0.216
0.115
0.105
0.096
0.087
0.104
84.00
90.13
93.41
95.68
93.57
Raw Medicaid Costs in PPS Hospitals
Rule
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.118
0.057
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.257
0.233
0.216
0.196
0.193
0.132
0.110
0.092
83.98
90.47
93.53
96.00
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.242
0.211
0.195
0.178
0.183
0.114
0.096
0.088
0.080
0.082
86.89
92.71
95.16
96.97
97.25
Raw Medicare Costs in PPS Hospitals
Rule
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.122
0.056
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.162
0.155
0.152
0.150
0.116
0.101
0.093
0.086
91.44
95.36
96.97
97.92
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.153
0.151
0.149
0.145
0.143
0.100
0.093
0.087
0.079
0.073
92.40
95.66
97.07
98.18
99.05
STANDARDIZED COSTS
Standardized Commercial Costs in CAHs
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.124
0.039
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.298
0.268
0.249
0.223
0.054
0.055
0.053
0.047
88.60
92.40
94.13
95.84
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.266
0.220
0.193
0.169
0.179
0.049
0.042
0.041
0.036
0.042
90.77
94.17
95.95
97.53
97.92
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.240
0.041
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.319
0.297
0.283
0.270
0.067
0.063
0.059
0.054
93.54
96.44
97.94
98.87
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.289
0.265
0.249
0.243
0.240
0.050
0.045
0.050
0.046
0.041
95.71
98.19
99.30
99.75
100.00
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.133
0.036
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.169
0.161
0.156
0.151
0.041
0.043
0.043
0.043
95.00
97.67
98.65
99.15
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.164
0.158
0.154
0.150
0.133
0.047
0.046
0.044
0.043
0.036
95.46
97.81
98.72
99.22
100.00
Rule
Standardized Medicaid Costs in CAHs
Rule
Standardized Medicare Costs in CAHs
Rule
Standardized Commercial Costs in PPS Hospitals
Rule
R squared
Intraclass Correlation
Proportion of Costs
Profiled
Untransformed
0.154
0.034
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.334
0.299
0.275
0.252
0.045
0.041
0.039
0.039
86.48
92.11
94.80
96.66
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.305
0.275
0.254
0.236
0.246
0.036
0.037
0.038
0.039
0.039
89.09
93.59
95.75
97.22
97.04
Intraclass Correlation
Proportion of Costs
Profiled
Standardized Medicaid Costs in PPS Hospitals
Rule
R squared
Untransformed
0.146
0.036
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.265
0.241
0.223
0.207
0.147
0.194
0.196
0.167
84.93
91.81
94.68
96.68
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.244
0.226
0.207
0.188
0.192
0.219
0.234
0.195
0.130
0.137
87.10
92.94
95.88
97.78
97.97
Intraclass Correlation
Proportion of Costs
Profiled
Standardized Medicare Costs in PPS Hospitals
Rule
R squared
Untransformed
0.137
0.050
100.00
Global percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
0.161
0.161
0.159
0.156
0.085
0.078
0.072
0.067
91.99
95.96
97.58
98.55
MDC specific percentiles
95th Percentile
98th Percentile
99th Percentile
99.5th Percentile
$100,000
0.157
0.158
0.156
0.153
0.150
0.076
0.073
0.068
0.064
0.058
92.66
96.35
97.84
98.76
99.52
Appendix B
Distribution of Attributed Hospital Admissions in Minnesota
Distribution of Attributed Admissions in Minnesota (January 2008 - December 2008 for Medicare and
July 2008 - June 2009 for Other Payers)
Number
Number of
of
hospitals discharges
Percentile
Mean
10th
25th
50th
75th
681
315
43
316
CAHs
Medicare
Medicaid
Commercial
78
78
78
78
37,731
18953
2,596
16,182
484
243
33
208
108
69
0
20
206
128
2
45
340
201
18
112
PPS
Hospitals
Medicare
Medicaid
Commercial
53
53
53
53
350,703
119,662
38,306
192,735
6,617
2,258
723
3,637
1,493
33
0
716
2,046
718
183
914
3,330
1,320
298
1,896
All
Hospitals
Medicare
Medicaid
Commercial
131
131
131
131
388,434
138,615
40,902
208,917
2,965
1,058
312
1,595
139
69
0
31
300
140
4
89
814
315
38
390
90th
1,127
451
114
515
10,051
3,150
924
5,178
16,691
6,388
2,083
9,731
2,770
946
251
1,363
10,051
3,150
924
5,178
Appendix C
Number of CAHs and PPS Hospitals not Meeting Minimum Sample Sizes
for Raw Costs and Standardized Costs for each Payer Type and for all
Payer Types
Number of hospitals not meeting minimum N for each payer type and overall
Minimum
N (R=0.4)
Number of
hospitals
not
meeting
minimum N
(R=0.4)
Minimum
N (R=0.6)
Number of
hospitals
not
meeting
minimum N
(R=0.6)
Minimum N
(R=0.8)
Number of
hospitals
not
meeting
minimum N
(R=0.8)
Raw Costs
CAHs
Total
0
0
2
Medicare
6
2
14
2
36
4
Medicaid
9
29
20
43
53
61
10
3
22
8
58
21
Commercial
PPS Hospitals
Total
1
1
1
Medicare
7
5
15
5
39
6
Medicaid
7
9
15
10
39
10
Commercial
6
1
14
1
36
1
Standardized Costs
CAHs
Total
0
1
9
Medicare
15
2
33
3
89
11
Medicaid
11
32
24
44
64
66
Commercial
12
4
27
10
71
27
PPS Hospitals
Total
1
1
1
Medicare
9
5
19
5
51
6
Medicaid
3
8
6
9
16
10
16
1
37
1
99
1
Commercial