Benford 7520 ADA Template

Background

This ADA will look at hospital cost report data that hospitals send to the Centers for Medicare & Medicaid Services (CMS) using the Healthcare Cost Report Information System (HCRIS). Hospitals that work with Medicare must submit a yearly cost report to a Medicare Administrative Contractor (MAC). These reports include details about the hospital, how services are used, costs and charges for different departments, Medicare payments, and financial statements. (https://www.cms.gov/data-research/statistics-trends-and-reports/cost-reports) In the U.S., Medicare makes up about 15% fo all federal spending, covering 68 million people. (https://www.kff.org/medicare/medicare-program-integrity-and-efforts-to-root-out-improper-payments-fraud-waste-and-abuse/). Benford’s Law works well for this data set because Medicare records are large and complex. This data set covers 20,604 records from hospitals in California, Minnesota, Texas, New York, and Virginia.

I. Plan the ADA

A. Statement to be audited

The statement to which this ADA will be applied is the financial data fields in the Five State Hospital Cost Report dataset. The specific variables are Net Patient Revenue, Net Income, FTE, and other figures reported by hospitals in California, Minnesota, New York, Texas, and Virginia for the years 2010-2024.

B. Overall Purpose

This ADA is for risk assessment. It is carried out to see if the financial figures reported by Medicare accepting hospitals match the expected distribution under Benford’s Law.

C. Specific Objective

We expect this ADA to inform assessment of the risk that hospitals have reported inaccurate or false financial data to CMS, which would call for a closer look at certain states, hospitals, or financial figures.

D. Data population, relevance, etc.

The data used in this analysis consists of hospital cost report data (e.g., Net Patient Revenue, Net Income, Gross Assets, Salaries, and inpatient utilization figures) sourced from CMS’s Healthcare Cost Report Information System (HCRIS). This data is relevant because it shows the financial activity that hospitals report to the federal government to get paid through Medicare. Hospitals fill out these reports themselves, increasing the risk of mistakes or dishonest reporting, which this ADA aims to evaluate using Benford’s Law.

E. Selected ADAs

The analysis was conducted using R.

The following R packages were used:

tidyverse: Used to clean and organize the data into a workable format

data.table: Used to quickly and efficiently process the large dataset

benford.analysis: To perform Benford’s Law analysis, which forms the core of this ADA

naniar: To identify and visualize any missing values in the data

mice: To fill in missing data so the dataset is complete before analysis

Visualizations

The following visualizations were created to support the analysis:

Benford’s Law Plots: To display the expected vs. observed digit frequencies

MAD, EMAD, and Excess MAD summary tables: To compare conformity across all five states

Bar Charts: To compare the distribution of first digits in the Five State data and visualize Benford’s Law.

Why The Tools Were Chosen

R was chosen because it is a powerful tool for data analysis. Benford’s Law was used because it is a reliable way to spot unusual patterns in large financial datasets. kableExtra was used to make tables easier to read. Naniar was used to find and display missing data.

II. Access & prepare the data

A. Load libraries

B. Prep data

1. Import

2. Missing analysis

      Provider Number Hcris Year State City Rpt Rec Num Zip Code Ctrl Type FTE
18971               1          1     1    1           1        1         1   1
1289                1          1     1    1           1        1         1   1
344                 1          1     1    1           1        1         1   1
                    0          0     0    0           0        0         0   0
      Beds InpatientDays_MCare InpatientDays_MCaid InpatientDays_Total
18971    1                   1                   1                   1
1289     1                   1                   1                   1
344      1                   1                   1                   1
         0                   0                   0                   0
      Interns_Res NonPaid_Wrkrs Dischg_MotherChild Dischg_Mcare Dischg_Mcaid
18971           1             1                  1            1            1
1289            1             1                  1            1            1
344             1             1                  1            1            1
                0             0                  0            0            0
      Dischg_All SalariesGenAdmin NetIncome CV19_PHE_funding NetIncServPats
18971          1                1         1                1              1
1289           1                1         1                1              1
344            1                1         1                1              1
               0                0         0                0              0
      NetPatRev Contribs InvInc GovtApprop GrAssets FixedEquip
18971         1        1      1          1        1          1
1289          1        1      1          1        1          1
344           1        1      1          1        1          1
              0        0      0          0        0          0
      GrAssetsLessLeases CapLeases Hospital Name Provider Control Type Name
18971                  1         1             1                          1
1289                   1         1             1                          1
344                    1         1             0                          0
                       0         0           344                        344
      County     
18971      1    0
1289       0    1
344        0    3
        1633 2321

C. Transform data

Rows after filtering to positive NetPatRev: 19486 
Rows removed (zero or negative NetPatRev):  1118
Positive NetPatRev Observations by State
State n (positive NetPatRev)
TX 8109
CA 5466
NY 2516
MN 1863
VA 1532

D. Validity checks

[1] "some missing data exists"
[1] 2321

1. Missing update

      Provider Number Hcris Year State City Rpt Rec Num Zip Code Ctrl Type FTE
18971               1          1     1    1           1        1         1   1
1289                1          1     1    1           1        1         1   1
344                 1          1     1    1           1        1         1   1
                    0          0     0    0           0        0         0   0
      Beds InpatientDays_MCare InpatientDays_MCaid InpatientDays_Total
18971    1                   1                   1                   1
1289     1                   1                   1                   1
344      1                   1                   1                   1
         0                   0                   0                   0
      Interns_Res NonPaid_Wrkrs Dischg_MotherChild Dischg_Mcare Dischg_Mcaid
18971           1             1                  1            1            1
1289            1             1                  1            1            1
344             1             1                  1            1            1
                0             0                  0            0            0
      Dischg_All SalariesGenAdmin NetIncome CV19_PHE_funding NetIncServPats
18971          1                1         1                1              1
1289           1                1         1                1              1
344            1                1         1                1              1
               0                0         0                0              0
      NetPatRev Contribs InvInc GovtApprop GrAssets FixedEquip
18971         1        1      1          1        1          1
1289          1        1      1          1        1          1
344           1        1      1          1        1          1
              0        0      0          0        0          0
      GrAssetsLessLeases CapLeases Hospital Name Provider Control Type Name
18971                  1         1             1                          1
1289                   1         1             1                          1
344                    1         1             0                          0
                       0         0           344                        344
      County     
18971      1    0
1289       0    1
344        0    3
        1633 2321
 Provider Number   Hcris Year       State           City       Rpt Rec Num  
 Min.   :0.00    Min.   :0.00   Min.   :0.00   Min.   :0.00   Min.   :0.00  
 1st Qu.:0.75    1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75  
 Median :1.00    Median :1.00   Median :1.00   Median :1.00   Median :1.00  
 Mean   :0.75    Mean   :0.75   Mean   :0.75   Mean   :0.75   Mean   :0.75  
 3rd Qu.:1.00    3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00  
 Max.   :1.00    Max.   :1.00   Max.   :1.00   Max.   :1.00   Max.   :1.00  
    Zip Code      Ctrl Type         FTE            Beds     
 Min.   :0.00   Min.   :0.00   Min.   :0.00   Min.   :0.00  
 1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75  
 Median :1.00   Median :1.00   Median :1.00   Median :1.00  
 Mean   :0.75   Mean   :0.75   Mean   :0.75   Mean   :0.75  
 3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00  
 Max.   :1.00   Max.   :1.00   Max.   :1.00   Max.   :1.00  
 InpatientDays_MCare InpatientDays_MCaid InpatientDays_Total  Interns_Res  
 Min.   :0.00        Min.   :0.00        Min.   :0.00        Min.   :0.00  
 1st Qu.:0.75        1st Qu.:0.75        1st Qu.:0.75        1st Qu.:0.75  
 Median :1.00        Median :1.00        Median :1.00        Median :1.00  
 Mean   :0.75        Mean   :0.75        Mean   :0.75        Mean   :0.75  
 3rd Qu.:1.00        3rd Qu.:1.00        3rd Qu.:1.00        3rd Qu.:1.00  
 Max.   :1.00        Max.   :1.00        Max.   :1.00        Max.   :1.00  
 NonPaid_Wrkrs  Dischg_MotherChild  Dischg_Mcare   Dischg_Mcaid    Dischg_All  
 Min.   :0.00   Min.   :0.00       Min.   :0.00   Min.   :0.00   Min.   :0.00  
 1st Qu.:0.75   1st Qu.:0.75       1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75  
 Median :1.00   Median :1.00       Median :1.00   Median :1.00   Median :1.00  
 Mean   :0.75   Mean   :0.75       Mean   :0.75   Mean   :0.75   Mean   :0.75  
 3rd Qu.:1.00   3rd Qu.:1.00       3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00  
 Max.   :1.00   Max.   :1.00       Max.   :1.00   Max.   :1.00   Max.   :1.00  
 SalariesGenAdmin   NetIncome    CV19_PHE_funding NetIncServPats   NetPatRev   
 Min.   :0.00     Min.   :0.00   Min.   :0.00     Min.   :0.00   Min.   :0.00  
 1st Qu.:0.75     1st Qu.:0.75   1st Qu.:0.75     1st Qu.:0.75   1st Qu.:0.75  
 Median :1.00     Median :1.00   Median :1.00     Median :1.00   Median :1.00  
 Mean   :0.75     Mean   :0.75   Mean   :0.75     Mean   :0.75   Mean   :0.75  
 3rd Qu.:1.00     3rd Qu.:1.00   3rd Qu.:1.00     3rd Qu.:1.00   3rd Qu.:1.00  
 Max.   :1.00     Max.   :1.00   Max.   :1.00     Max.   :1.00   Max.   :1.00  
    Contribs        InvInc       GovtApprop      GrAssets      FixedEquip  
 Min.   :0.00   Min.   :0.00   Min.   :0.00   Min.   :0.00   Min.   :0.00  
 1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75   1st Qu.:0.75  
 Median :1.00   Median :1.00   Median :1.00   Median :1.00   Median :1.00  
 Mean   :0.75   Mean   :0.75   Mean   :0.75   Mean   :0.75   Mean   :0.75  
 3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00   3rd Qu.:1.00  
 Max.   :1.00   Max.   :1.00   Max.   :1.00   Max.   :1.00   Max.   :1.00  
 GrAssetsLessLeases   CapLeases    Hospital Name    Provider Control Type Name
 Min.   :0.00       Min.   :0.00   Min.   :  0.00   Min.   :  0.00            
 1st Qu.:0.75       1st Qu.:0.75   1st Qu.:  0.75   1st Qu.:  0.75            
 Median :1.00       Median :1.00   Median :  1.00   Median :  1.00            
 Mean   :0.75       Mean   :0.75   Mean   : 86.50   Mean   : 86.50            
 3rd Qu.:1.00       3rd Qu.:1.00   3rd Qu.: 86.75   3rd Qu.: 86.75            
 Max.   :1.00       Max.   :1.00   Max.   :344.00   Max.   :344.00            
     County            V34         
 Min.   :   0.0   Min.   :   0.00  
 1st Qu.:   0.0   1st Qu.:   0.75  
 Median :   0.5   Median :   2.00  
 Mean   : 408.5   Mean   : 581.25  
 3rd Qu.: 409.0   3rd Qu.: 582.50  
 Max.   :1633.0   Max.   :2321.00

2. Plausibility checks


  CA   MN   NY   TX   VA 
5941 2039 2827 8231 1566 
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
1.000e+00 2.201e+07 7.231e+07 2.248e+08 2.495e+08 1.009e+10 

  CA   MN   NY   TX   VA 
5466 1863 2516 8109 1532 
[1] 2010 2024

III. Reconsider relevance & reliability

IV. Perform the ADA

A. Benford analysis

B. Drill down

2. Get top 2 suspect groups


State: CA 
      State  Year NetPatRev NetIncome  GrAssets     FTE
     <char> <num>     <num>     <num>     <num>   <num>
  1:     CA  2019 117609888   -448304  77181015  659.23
  2:     CA  2024 111592015  -5829962  99244179  541.11
  3:     CA  2024 110618164   3168933 115453602  344.59
  4:     CA  2011 112629706   6666013         0  888.00
  5:     CA  2012 169064145   6840842  72413914  198.44
 ---                                                   
260:     CA  2019  11075332    120105   4809766   47.54
261:     CA  2020  11076232    425713   4883573   51.65
262:     CA  2022 119031687   5811050  34465799 1400.00
263:     CA  2022  11792069   -740336    424133   71.01
264:     CA  2019  16527905  -4314463    802332  188.38
                            Hospital Name
                                   <char>
  1:                     ST ROSE HOSPITAL
  2:                     ST ROSE HOSPITAL
  3:               SUTTER AMADOR HOSPITAL
  4:             PARADISE VALLEY HOSPITAL
  5:                    OROVILLE HOSPITAL
 ---                                     
260:                TELECARE HERITAGE PHF
261:                TELECARE HERITAGE PHF
262:                          PSYCHIATRIC
263:      OCEAN VIEW PSYCHIATRIC FACILITY
264: BAKERSFIELD BEHAVIORAL HEALTHCARE HO

State: MN 
      State  Year  NetPatRev NetIncome   GrAssets     FTE
     <char> <num>      <num>     <num>      <num>   <num>
  1:     MN  2023 1289237000 -49574000 1080108995 5644.02
  2:     MN  2022  121815279 -18179281  118561638  554.54
  3:     MN  2018  122173145   -176183   89106606  473.06
  4:     MN  2019  124050414   -579437   89987455  474.59
  5:     MN  2014  127304201  10786955  108423457  694.46
 ---                                                     
114:     MN  2022  128558789  11676445   58350561  411.43
115:     MN  2016   12085049   -336804   28678750  101.05
116:     MN  2012  185172958  20202368  153478131 1048.30
117:     MN  2019   12008955   -872723          0   98.62
118:     MN  2022   12377358  -1375255   25334276   96.16
                            Hospital Name
                                   <char>
  1:       HENNEPIN COUNTY MEDICAL CENTER
  2:             NORTHFIELD CITY HOSPITAL
  3: MAYO CLINIC HEALTH SYSTEM - RED WING
  4: MAYO CLINIC HEALTH SYSTEM - RED WING
  5:              DOUGLAS COUNTY HOSPITAL
 ---                                     
114:               NEW ULM MEDICAL CENTER
115:               PRAIRIE RIDGE HOSPITAL
116:  GILLETTE CHILDRENS SPECIALTY HEALTH
117:            SANFORD BEHAVIORAL HEALTH
118:            SANFORD BEHAVIORAL HEALTH

State: NY 
      State  Year NetPatRev NetIncome  GrAssets   FTE
     <char> <num>     <num>     <num>     <num> <num>
  1:     NY  2011 104563675   2766982 124212785 901.0
  2:     NY  2012 103056129   6692537 126319263 868.3
  3:     NY  2013 102158920   8659638 132053797 825.5
  4:     NY  2015 102712195   1429400 134905432 862.2
  5:     NY  2017 108732040    199212 136957893 894.6
 ---                                                 
183:     NY  2021 107594826   5893112 168395844 810.8
184:     NY  2022 109257372  -3753766 173726387 823.6
185:     NY  2015 101658749  -8430340  58521250 777.7
186:     NY  2017 103352087   7330990  52803169 875.6
187:     NY  2023 102180163  -9097137  69634314 751.8
                     Hospital Name
                            <char>
  1:         THE KINGSTON HOSPITAL
  2:         THE KINGSTON HOSPITAL
  3:         THE KINGSTON HOSPITAL
  4:         THE KINGSTON HOSPITAL
  5:         THE KINGSTON HOSPITAL
 ---                              
183: BURKE REHABILITATION HOSPITAL
184: BURKE REHABILITATION HOSPITAL
185:           SOUTH OAKS HOSPITAL
186:           SOUTH OAKS HOSPITAL
187:           SOUTH OAKS HOSPITAL

State: TX 
      State  Year  NetPatRev NetIncome   GrAssets     FTE
     <char> <num>      <num>     <num>      <num>   <num>
  1:     TX  2020  153201489  40369380  202367647  727.81
  2:     TX  2022  156804635  22528578  207312626  784.49
  3:     TX  2024 1510714800 779381326 1145552783 4728.34
  4:     TX  2020  153574339  15068087  252939659  951.15
  5:     TX  2021  158992163   6982891  243554659  818.48
 ---                                                     
512:     TX  2023   18964039   3509997    3744074   94.01
513:     TX  2021   18620197  -3889243   23534312  111.60
514:     TX  2023   15897745  -2197911   23813792  106.12
515:     TX  2021   15727589    276042   25313556   99.24
516:     TX  2024   15087202    868885   19906560   83.20
                            Hospital Name
                                   <char>
  1:     PETERSON REGIONAL MEDICAL CENTER
  2:     PETERSON REGIONAL MEDICAL CENTER
  3:        BAYLOR UNIVERSITY MEDICAL CTR
  4:              CITIZENS MEDICAL CENTER
  5:              CITIZENS MEDICAL CENTER
 ---                                     
512:    PAM REHAB HOSP OF HOUSTON HEIGHTS
513:  SHANNON REHABILITATION HOSPITAL  AN
514:  SHANNON REHABILITATION HOSPITAL  AN
515: ENCOMPASS HEALTH REHABILITATION OF W
516: CLEARSKY REHABILITIATION HOSPITAL OF

State: VA 
     State  Year  NetPatRev NetIncome   GrAssets     FTE
    <char> <num>      <num>     <num>      <num>   <num>
 1:     VA  2021   27749936   1842768    1570952  128.14
 2:     VA  2012  279103321 -16097722          0 1722.59
 3:     VA  2015  279796092  17003815  338309959 1483.69
 4:     VA  2016  273649213  42895660  352820930 1431.80
 5:     VA  2021  125510371  11961765  119190768  570.46
 6:     VA  2018 1206366921 111319057 1076650496 6260.61
 7:     VA  2020 1248207234  72661691 1195916839 6334.97
 8:     VA  2013 1285102315 215386831          0 5863.96
 9:     VA  2024 2770645397 526458411 2874685524 7743.20
10:     VA  2014  277467023  46206378  333358909  940.00
11:     VA  2012  270631530  45891997          0 1193.84
12:     VA  2011  279821804  35433235  195048210 1111.78
13:     VA  2012  273024121  42454977  201468981 1143.29
14:     VA  2013  274180235  42066556  208450413 1115.02
15:     VA  2011  271247465  34853997          0 1369.42
16:     VA  2012  270933508  27182996          0 1271.52
17:     VA  2015  278813670  38530776  289498532 1421.49
18:     VA  2022  123504184   8394936   75325757  527.24
19:     VA  2023  122400040   1239801   79923790  504.00
20:     VA  2017  127315054  10825966  263664292 1767.59
21:     VA  2016  278191302   4160000  238860427 1529.93
22:     VA  2011  124333469   5675000   78308322  593.38
23:     VA  2016  122880813  11017295   96665161  709.04
24:     VA  2021   27715335  -1486965   58794003    0.00
25:     VA  2014   27965303   -885824     822812  199.41
26:     VA  2021  279890000  81143000  299986975 1060.49
27:     VA  2014  124725125  39974155   46545402  271.84
28:     VA  2019  120592684  14739548  187206470  629.28
29:     VA  2020  127606945 -12301056  182459819  607.79
30:     VA  2012  270734545  43104099  227545007 1439.84
31:     VA  2013  275639034  42672472  229782313 1638.34
32:     VA  2013  270571935  44653075  252156983  882.00
33:     VA  2019  122009940  32754080  101864341  385.71
34:     VA  2020  124713475  33744950  101921418  381.45
35:     VA  2021  275704659  28128000  340246540  906.90
36:     VA  2015   12097866  -1516726   16388101   84.05
37:     VA  2016   12045893  -1512033   15986961   82.74
38:     VA  2018   12169804  -3250033   17961090   85.45
39:     VA  2011  273039041   2471121   18331733 1708.75
40:     VA  2015  270369577  -3109660  391716979 1564.58
41:     VA  2024  121108018  16153778   43336343  339.47
42:     VA  2013  270721112  13533376  161433761 1367.99
43:     VA  2014  277684580  16614633  166142055 1315.82
44:     VA  2015  275434608  14661331  168958139 1360.85
45:     VA  2018  278108699  24331902  220448729 1173.36
46:     VA  2020  278311691  42528891  271251925  836.01
47:     VA  2021  124484211  10701767  145073433  371.53
48:     VA  2022  127912631   9005065  147262409  362.50
49:     VA  2020  124133116  10161801  175675846  378.84
50:     VA  2016   27753928 -13105112  155558339  206.73
51:     VA  2024  126071095   1353578  170909109  250.93
52:     VA  2015   12618098   1354295   24355745  118.14
53:     VA  2011   27471004    556582   43642840  195.64
54:     VA  2016   27372780  -4412214   32938825  262.32
55:     VA  2011    1246679   -855020    5911701   10.45
56:     VA  2017    1250294     47087    5609470   12.99
57:     VA  2020   12945882    537667    3168399   70.40
58:     VA  2015   27263251   1148017     229576  147.21
59:     VA  2016   27870728    831458     376105  141.58
60:     VA  2018   27550854   -960523     770975  155.06
61:     VA  2019   27056449    889979     954591  153.35
62:     VA  2020   12862017  -3824234    2731533   91.69
63:     VA  2017   27266091   9031406   26943987  203.01
64:     VA  2024   27705333   5087474   17961369  125.00
65:     VA  2015   12305545    951662    3776568   64.01
66:     VA  2017   12109512   4950882    3979141   69.37
67:     VA  2018   12580228   5301167    4096481   65.60
68:     VA  2023   12463307   2014254    5489560   77.25
69:     VA  2011  276888625  29822034  336143953 2105.50
70:     VA  2012    2720831   -724147   11756182  296.58
71:     VA  2017   27608446   1278324          0  192.49
72:     VA  2011   27750647   3538308   15514135  163.32
73:     VA  2018   12958873  -3214287   20412226  146.47
74:     VA  2019   12984829   -369503   20672095  142.01
75:     VA  2021   12723258  -2984688   13409300  135.20
     State  Year  NetPatRev NetIncome   GrAssets     FTE
    <char> <num>      <num>     <num>      <num>   <num>
                           Hospital Name
                                  <char>
 1:              RUSSELL COUNTY HOSPITAL
 2:                    MARYVIEW HOSPITAL
 3:               AUGUSTA MEDICAL CENTER
 4:               AUGUSTA MEDICAL CENTER
 5:           CULPEPER MEMORIAL HOSPITAL
 6:              CARILION MEDICAL CENTER
 7:              CARILION MEDICAL CENTER
 8:       VCU HEALTH SYSTEM MCV HOSPITAL
 9:       VCU HEALTH SYSTEM MCV HOSPITAL
10:        INOVA LOUDOUN HOSPITAL CENTER
11:               SENTARA LEIGH HOSPITAL
12:            LEWIS GALE MEDICAL CENTER
13:            LEWIS GALE MEDICAL CENTER
14:            LEWIS GALE MEDICAL CENTER
15:   SENTARA VA. BEACH GENERAL HOSPITAL
16:   SENTARA VA. BEACH GENERAL HOSPITAL
17:   SENTARA VA. BEACH GENERAL HOSPITAL
18:         CLINCH VALLEY MEDICAL CENTER
19:         CLINCH VALLEY MEDICAL CENTER
20:     DANVILLE REGIONAL MEDICAL CENTER
21:    SENTARA MARTHA JEFFERSON HOSPITAL
22:    MEMORIAL HOSPITAL OF MARTINSVILLE
23:    MEMORIAL HOSPITAL OF MARTINSVILLE
24:     VCU HEALTH TAPPAHANNOCK HOSPITAL
25:            BEDFORD MEMORIAL HOSPITAL
26:            SENTARA CAREPLEX HOSPITAL
27:          RICHMOND COMMUNITY HOSPITAL
28:          COMMUNITY MEMORIAL HOSPITAL
29:          COMMUNITY MEMORIAL HOSPITAL
30:             INOVA FAIR OAKS HOSPITAL
31:             INOVA FAIR OAKS HOSPITAL
32:                      RESTON HOSPITAL
33:      LEWISGALE HOSPITAL - MONTGOMERY
34:      LEWISGALE HOSPITAL - MONTGOMERY
35:    SENTARA NORTHERN VIRGINIA MED CTR
36: CARILION TAZEWELL COMMUNITY HOSPITAL
37: CARILION TAZEWELL COMMUNITY HOSPITAL
38: CARILION TAZEWELL COMMUNITY HOSPITAL
39:          CHESAPEAKE GENERAL HOSPITAL
40:          CHESAPEAKE GENERAL HOSPITAL
41:                RIVERSIDE WALTER REED
42:           ST. FRANCIS MEDICAL CENTER
43:           ST. FRANCIS MEDICAL CENTER
44:           ST. FRANCIS MEDICAL CENTER
45:           ST. FRANCIS MEDICAL CENTER
46:           ST. FRANCIS MEDICAL CENTER
47:                    STAFFORD HOSPITAL
48:                    STAFFORD HOSPITAL
49: SPOTSYLVANIA REGIONAL MEDICAL CENTER
50:         STONESPRINGS HOSPITAL CENTER
51:         STONESPRINGS HOSPITAL CENTER
52:       BATH COUNTY COMMUNITY HOSPITAL
53:  CARILION STONEWALL JACKSON HOSPITAL
54:        RAPPAHANNOCK GENERAL HOSPITAL
55:   LYNN HOUSE OF POTOMAC VALLEY  INC.
56:   LYNN HOUSE OF POTOMAC VALLEY  INC.
57:                  SSH - HAMPTON ROADS
58:      VIBRA HOSPITAL OF RICHMOND  LLC
59:      VIBRA HOSPITAL OF RICHMOND  LLC
60:      VIBRA HOSPITAL OF RICHMOND  LLC
61:      VIBRA HOSPITAL OF RICHMOND  LLC
62:       UVA TRANSITIONAL CARE HOSPITAL
63:             SHELTERING ARMS HOSPITAL
64:  UVA ENCOMPASS HEALTH REHABILITATION
65:       SHELTERING ARMS HOSPITAL SOUTH
66:       SHELTERING ARMS HOSPITAL SOUTH
67:       SHELTERING ARMS HOSPITAL SOUTH
68:   REHABILITATION HOSPITAL OF BRISTOL
69:   CHILDRENS HOSPITAL OF THE KINGS DA
70: NORTHERN VIRGINIA MENTAL HEALTH INST
71:              POPLAR SPRINGS HOSPITAL
72:                    DOMINION HOSPITAL
73:   THE PAVILION AT WILLIAMSBURG PLACE
74:   THE PAVILION AT WILLIAMSBURG PLACE
75:   THE PAVILION AT WILLIAMSBURG PLACE
                           Hospital Name
                                  <char>

State: CA 
         number duplicates
          <num>      <int>
   1: 813656534          6
   2: 357802533          2
   3: 280978304          2
   4: 481358657          2
   5: 357880901          2
  ---                     
5445:  38373078          1
5446:  17187843          1
5447:  39112909          1
5448:  45545525          1
5449:  24798130          1

State: MN 
         number duplicates
          <num>      <int>
   1:  98074200          2
   2: 124663678          2
   3:  35888136          2
   4: 569343828          1
   5: 565989210          1
  ---                     
1856:  13533476          1
1857:  14352569          1
1858:  12377358          1
1859:  13386582          1
1860:  13110089          1

State: NY 
         number duplicates
          <num>      <int>
   1: 226843840          2
   2:  27402582          2
   3:  22813810          2
   4:  85604676          1
   5:  15267559          1
  ---                     
2509:  38131479          1
2510:  39234627          1
2511:  30280080          1
2512:  27367336          1
2513:  15077253          1

State: TX 
         number duplicates
          <num>      <int>
   1: 277802943          2
   2: 294213077          2
   3: 442308081          2
   4: 360972581          2
   5:  19644851          2
  ---                     
8084:   1315512          1
8085:   6097577          1
8086:  22719045          1
8087:   2670293          1
8088:   5817742          1

State: VA 
        number duplicates
         <num>      <int>
   1: 16835049          2
   2: 50691046          1
   3: 53425033          1
   4: 47057994          1
   5: 54220542          1
  ---                    
1527: 18430019          1
1528: 20928802          1
1529:  5320453          1
1530:  8355491          1
1531:  8484444          1

State: CA 
    State  Year NetPatRev  NetIncome  GrAssets     FTE
   <char> <num>     <num>      <num>     <num>   <num>
1:     CA  2014 357802533 -306018737 252540357 2455.00
2:     CA  2015 357802533  -41259807 249903568 2452.57
3:     CA  2010 813656534 -540572443 653713895 6637.24
4:     CA  2011 813656534 -469982097 654509322 6751.66
5:     CA  2012 813656534 -667230079 606609895 6683.65
6:     CA  2013 813656534 -657197264 655701507 6731.82
7:     CA  2015 813656534 -704730663 657491586 7071.79
8:     CA  2016 813656534 -885195897 663343215 7352.51
                        Hospital Name
                               <char>
1: LAC OLIVE VIEW/UCLA MEDICAL CENTER
2: LAC OLIVE VIEW/UCLA MEDICAL CENTER
3:             LAC+USC MEDICAL CENTER
4:             LAC+USC MEDICAL CENTER
5:             LAC+USC MEDICAL CENTER
6:             LAC+USC MEDICAL CENTER
7:             LAC+USC MEDICAL CENTER
8:             LAC+USC MEDICAL CENTER

State: MN 
    State  Year NetPatRev NetIncome  GrAssets    FTE          Hospital Name
   <char> <num>     <num>     <num>     <num>  <num>                 <char>
1:     MN  2016  98074200   2647150  96341944 452.15 HUTCHINSON HEALTH CARE
2:     MN  2017  98074200    754905  96128754 480.97 HUTCHINSON HEALTH CARE
3:     MN  2022 124663678   6615233 126017583 461.52 LAKEWOOD HEALTH SYSTEM
4:     MN  2023 124663678 -11630029 129727704 479.05 LAKEWOOD HEALTH SYSTEM

State: NY 
    State  Year NetPatRev NetIncome  GrAssets     FTE
   <char> <num>     <num>     <num>     <num>   <num>
1:     NY  2018 226843840  10534507 350921135 1371.43
2:     NY  2019 226843840 -17451619 350921135 1371.43
3:     NY  2011  27402582   3617493  20049546    0.00
4:     NY  2011  27402582   3617493  20049546  258.80
                     Hospital Name
                            <char>
1:        SAMARITAN MEDICAL CENTER
2:        SAMARITAN MEDICAL CENTER
3:       BRUNSWICK HOSPITAL CENTER
4: BRUNSWICK HOSPITAL CENTER  INC.

State: TX 
    State  Year NetPatRev NetIncome  GrAssets     FTE
   <char> <num>     <num>     <num>     <num>   <num>
1:     TX  2013 277802943  34824090 244124717 1742.85
2:     TX  2014 277802943   8696021 244124717 1774.35
3:     TX  2011 294213077  57426455         0 1799.51
4:     TX  2012 294213077  50908777 441055547 1799.51
                   Hospital Name
                          <char>
1:      PROVIDENCE HEALTH CENTER
2:      PROVIDENCE HEALTH CENTER
3: BAPTIST ST. ANTHONYS HOSPITAL
4: BAPTIST ST. ANTHONYS HOSPITAL

State: VA 
    State  Year NetPatRev NetIncome GrAssets    FTE
   <char> <num>     <num>     <num>    <num>  <num>
1:     VA  2011  50691046   4664625 59584552 355.99
2:     VA  2018  16835049   1513948  3710272 130.61
3:     VA  2019  16835049    -64907  3559365 130.42
                        Hospital Name
                               <char>
1:    NORTON COMMUNITY HOSPITAL  INC.
2: RIVERSIDE REHABILITATION INSTITUTE
3: RIVERSIDE REHABILITATION INSTITUTE

State: CA 
[1] 0.001690228

    Pearson's Chi-squared test

data:  bfd_CA$NetPatRev
X-squared = 200, df = 89, p-value = 1.627e-10


State: MN 
[1] 0.002127034

    Pearson's Chi-squared test

data:  bfd_MN$NetPatRev
X-squared = 103.78, df = 89, p-value = 0.1353


State: NY 
[1] 0.001952164

    Pearson's Chi-squared test

data:  bfd_NY$NetPatRev
X-squared = 123.51, df = 89, p-value = 0.009122


State: TX 
[1] 0.001442753

    Pearson's Chi-squared test

data:  bfd_TX$NetPatRev
X-squared = 201.51, df = 89, p-value = 1.054e-10


State: VA 
[1] 0.002246972

    Pearson's Chi-squared test

data:  bfd_VA$NetPatRev
X-squared = 101.22, df = 89, p-value = 0.177

C. Calculate EMAD and ExcessMAD


State: CA 
MAD: 0.001690228 
EMAD: 0.001073346 
ExcessMAD: 0.0006168816 

State: MN 
MAD: 0.002127034 
EMAD: 0.00183852 
ExcessMAD: 0.0002885143 

State: NY 
MAD: 0.001952164 
EMAD: 0.001582047 
ExcessMAD: 0.0003701165 

State: TX 
MAD: 0.001442753 
EMAD: 0.0008812337 
ExcessMAD: 0.0005615198 

State: VA 
MAD: 0.002246972 
EMAD: 0.002027428 
ExcessMAD: 0.0002195443