24th Annual Institute on Research and Statistics April 15, 2003 CSUSMedi-Cal Recovery

Kathleen Gallagher, RPS I

MA Statistics UC Berkeley 1977

DHS A&I

Medi-Cal

• Medi-Cal is the California implementation of the Federal Medicaid Program

• Medical practitioners get a billing number and bill for services

• Audits & Investigations recovers bad billing

Sampling Frame

• Medi-Cal commonly uses three years due to a statute of limitations

• Sampling unit

• I use a beneficiary

• SCO uses beneficiary/date of service

Statistics for brown bag

1 1 white $100 51 1 pink $2002 2 white $100 52 2 pink $2003 3 white $100 53 3 pink $2004 4 white $100 54 4 pink $2005 5 white $100 55 5 pink $2006 6 white $100 56 6 pink $2007 7 white $100 57 7 pink $2008 8 white $100 58 8 pink $2009 9 white $100 59 9 pink $200

10 10 white $100 60 10 pink $20011 11 white $100 61 11 pink $20012 12 white $100 62 12 pink $20013 13 white $100 63 13 pink $20014 14 white $100 64 14 pink $20015 15 white $100 65 15 pink $20016 16 white $100 66 16 pink $20017 17 white $100 67 17 pink $20018 18 white $100 68 18 pink $20019 19 white $100 69 19 pink $20020 20 white $100 70 20 pink $20021 21 white $100 71 21 pink $20022 22 white $100 72 22 pink $20023 23 white $100 73 23 pink $20024 24 white $100 74 24 pink $20025 25 white $100 75 25 pink $20026 26 white $100 76 26 pink $20027 27 white $100 77 27 pink $20028 28 white $100 78 28 pink $20029 29 white $100 79 29 pink $20030 30 white $100 80 30 pink $20031 31 white $100 81 1 red $30032 32 white $100 82 2 red $30033 33 white $100 83 3 red $30034 34 white $100 84 4 red $30035 35 white $100 85 5 red $30036 36 white $100 86 6 red $30037 37 white $100 87 7 red $30038 38 white $100 88 8 red $30039 39 white $100 89 9 red $30040 40 white $100 90 10 red $30041 41 white $100 91 11 red $30042 42 white $100 92 12 red $30043 43 white $100 93 13 red $30044 44 white $100 94 14 red $30045 45 white $100 95 15 red $30046 46 white $100 96 16 red $30047 47 white $100 97 17 red $30048 48 white $100 98 18 red $30049 49 white $100 99 1 black $50050 50 white $100 100 2 black $500

total 17,400.00mean 174std dev 89.47

Total BenesTotal Paid Avg Std Dev ALPHA Z-SCORE ERROR MEAN STD DEV POPULATION N 100 17,400.00 174 89.47 0.05 1.645 0.1 174 89.47 100 71.54 0.72 0.99 41.95

1.645 0.05 174 89.47 100 71.54 0.72 0.25 74.30 0.1 1.282 0.2 174 89.47 100 43.45 0.43 3.96 9.89 sample 10

1.282 0.1 174 89.47 100 43.45 0.43 0.99 30.50

From A Book

Levy, P. and Lemeshow, S.,

Sampling of Populations Methods and Applications,

3rd Edition, John Wiley & Sons, 1999.

Formula 3.14

02/03/03 Sample Size Calculation For

Brown Bag MD

Medi-Cal Provider no. 00Cbag

Population is Medi-Cal beneficiaries whom provider serviced inSeptember 10,1999 through September 9, 2002 for all procedurecodes.

Sample size is :

Confidence level=.90 = .10 = .20Z

(1-) = 1.282

N = 100 Medi-Cal beneficiaries that Medi-Cal paid at least $1 tothis provider.

Levy & Lemeshow 1999, page 74 (3.14)

Mean payment per beneficiary= 174.00 standard deviation = 89.47

n = (1.282)2

N Vx

2 /(((1.282)

2 ( 89.47 / 174.00 )

2 )+ ((N-1)

2 ) )

= ( 1.282 )2100( 89.47 / 174.00 )

2 / (((1.282)

2 ( 89.47 / 174.00 )

2 )+ ((99) (.20)

2 ))

= 10

Estimated Overpayment

• Lower limit of a one-sided 90 percent confidence interval

• OneR SQL7.0 Application written by contractor: R Systems

Brown Bag - 00C0000B - GROUP 1, STRATUM 1REVIEW # 244

SUM PAID * OVERPT# COUNT AMT PAID AMT PAID ** 2 AMT OVER AMT OVER ** 2 ( CROSS- TERMS)

1 4 100.00 10,000.0000 50.00 2,500.0000 5,000.00002 4 100.00 10,000.0000 50.00 2,500.0000 5,000.00003 4 100.00 10,000.0000 75.00 5,625.0000 7,500.00004 4 100.00 10,000.0000 50.00 2,500.0000 5,000.00005 4 100.00 10,000.0000 50.00 2,500.0000 5,000.00006 4 100.00 10,000.0000 50.00 2,500.0000 5,000.00007 2 200.00 40,000.0000 100.00 10,000.0000 20,000.00008 2 200.00 40,000.0000 100.00 10,000.0000 20,000.00009 2 200.00 40,000.0000 100.00 10,000.0000 20,000.000010 2 200.00 40,000.0000 100.00 10,000.0000 20,000.0000

Total 32 1,400.00 220,000.0000 725.00 58,125.0000 112,500.0000

GROUP 1 STATISTICS SAMPLE UNITS (n): 10TOTAL PAID: 17,400.00POPULATION SIZE (N): 100

AMT PAID DATA AMT OVER DATA

TP1 (sum of x) : 1,400.0000 TO1 (sum of y): 725.0000TP2 (sum of x*x) : 220,000.0000 TO2 (sum of y*y): 58,125.0000VP = TP2 - (n*Xbar*Xbar) : 24,000.0000 VO =TO2-(n*Ybar*Ybar): 5,562.5000Average (Xbar) : 140.0000 Average (Ybar) : 72.5000Variance : 2,666.6667 Variance: 618.0556STANDARD DEVIATION : 51.6398 STANDARD DEVIATION: 24.8607

RATIO OF THE MEANS R=TO1/TP1: 0.5179

RATIO2 R*R*TP2: 58,998.7245

RATIO3 2*R*CROSS-TERMS: 116,517.8571

EST. OVERPAYMENT R*TOTAL PAID 9,010.7143

ITEM 1 TO2 - RATIO3 + RATIO2: 605.8673ITEM 2 (N*N(1-(n/N)))/(n(n-1)): 100.0000

VARIANCE OF OVERPAYMENT 1 * 2: 60,586.7347

STD DEVIATION OF OVERPAYMENT : 246.1437

PRECISION Z-Score*STD DEV: 315.5562 one-sided confidence: 90.00

Z-Score 1.2820

STATISTICS REVIEW # 244

SAMPLE UNITS (n): 10TOTAL PAID: 17,400.00POPULATION SIZE (N): 100

ESTIMATED OVERPAYMENT: 9,010.71 one-sided confidence: 90.00 %VARIANCE OF OVERPAYMENT: 60,586.7347STD DEVIATION OF OVERPAYMENT: 246.1437 Z-Score: 1.2820PRECISION Z-Score*STD DEV: 315.5562DEMAND AMOUNT: 8,695.16

Cochran, W.G., SamplingTechniques, 3rd ed. New York: John Wiley and Sons, 1977 formulas (6.1) (6.10)

Federal Guideline• Department of Health & Human Services

• Centers for Medicare & Medicaid Services (CMS)

• Program Memorandum B-02-007 http://cms.hhs.gov/manuals/pm_trans/B02007.pdf

• Use of Statistical Sampling for Overpayment Estimation When Performing Administrative Reviews of Part B Claims

Sampling

• I. E. Consult with a statistical expert

• Standard is someone with a master’s degree in statistics or equivalent

Sample Design and Estimation Competition for JSM 2003

• Http://www.amstat.org/education

• Graduate, Professional, and Continuing Education

• Sample Design and Estimation Competition

Sponsored by

• 2003 Joint Program Committee

• Cambridge University Press

• Duxbury

• Ernst and Young

• Insightful

• Oxbury Press

• SAS

• Springer-Verlag

• SPSS

• Statpoint

Eligibility

• Students enrolled in graduate program for at least one semester during 2002-2003

Prizes

• Based on statistical approach

• sample size

• sampling error

• relative precision

• written work

• presentation skills

• software and books awarded

Design Specifications

• Estimate misstated amount

• with 90 percent confidence

• 10 percent relative precision

Dataset

• Simulated population

• 51,827 “book values”