Multivariate Detection of Multivariate Detection of Aberrant Billing: An Aberrant Billing: An EvaluationEvaluation

Maharaj Singh, Ted Wallace & Martin SchragerMaharaj Singh, Ted Wallace & Martin SchragerNational Government Services, IncNational Government Services, Inc..

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Outline of the studyOutline of the study• Outlier defined• Multivariate method for detecting

Outlier • Detecting outlier billing providers• An evaluation of the methodology • Other factors considered for

future application• Conclusion

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An Outlier An Outlier

•An outlier is not ‘Outlier’. May be we haven’t yet found the ‘right’ Distribution.

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Multivariate MethodMultivariate Method

• We used a Mahalanobis distance as multivariate vector corresponding to each observation in the data set.

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Mahalanobis DistanceMahalanobis Distance

• Mahalanobis distance is a distance measure introduced by Prasanta Chandra Mahalanobis in 1936.

• It is based on Correlation between variables by which different patterns can be identified and analyzed.

• It is a useful way of determining similarity of an unknown sample set to a known one

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Mahalanobis distanceMahalanobis distance

• Mahalanobis distance

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Mahalanobis distance and Multivariate Mahalanobis distance and Multivariate OutliersOutliers

• Mahalanobis D2 is a multidimensional version of a z-score. It measures the distance of a case from the centroid (multidimensional mean) of a distribution, given the covariance (multidimensional variance) of the distribution.

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DD22

• A case is a multivariate outlier if the probability associated with its D2 is 0.05 or less. D2 follows a chi-square distribution with degrees of freedom equal to the number of variables included in the calculation.

• Mahalanobis D2 requires that the variables be metric, i.e. interval level or ordinal level variables that are treated as metric.

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Mahalanobis Distance from EllipsoidMahalanobis Distance from Ellipsoid

• Mahalanobis distance measure is based on correlations among the variables by which different patterns can be identified and analyzed.

• The region of constant Mahalanobis distance around the mean forms an ellipsoid when more than two variables are used.

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Multivariate trimming …Multivariate trimming …

• The χ2 plot for multivariate data is not resistant to the effect of outliers.

• A few discrepant observations can affect the mean vector, and can potentially influence the outcome.

• In order to avoid the effect of a few discrepant observations, we used multivariate trimming which involved an iterative process of setting aside the observations with largest squared distance and the trimmed statistics are computed from the remaining observations.

• At the end of this iterative process, the new squared distance values are computed using the robust statistics.

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Chi Square plot for the datasetChi Square plot for the datasetχ2

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The Data Set: Paid ClaimsThe Data Set: Paid Claims

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Indices for the Id of Indices for the Id of observationsobservations

– Billing providers• Location, • Size • Specialty

– HCPCS used – Primary

Diagnoses

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Matrix of Utilization Variables: AmountMatrix of Utilization Variables: Amount

• Cost– Charges Billed– Charges denied– Reimbursement

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Matrix of Utilization Variables: RateMatrix of Utilization Variables: Rate

• Rate – Reimbursement per

beneficiary– Service Units per

beneficiary– Service units per

service dates per beneficiary

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Matrix of Utilization Variables: VolumeMatrix of Utilization Variables: Volume

• Volume– Number of claims– Number of

beneficiaries– Number of service

units rendered– Number of service

days

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The cost: Medicare trust The cost: Medicare trust fund $$$fund $$$

• For each observation the amount paid is a function of the rate and the volume.

• However for each observation Id, the rate and volume variables are also highly inter-correlated.

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Methodology for Paid Claim Methodology for Paid Claim Data SetData Set

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Data StepsData Steps

• The line-level (detailed) paid claim data was summarized by id (provider-HCPCS combination) with summary of the utilization variables (cost, rate and volume).

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Principal ComponentsPrincipal Components

• The variables in the matrix of the paid claims dataset were converted into principal components.

• The distance squared was computed as unique sum of squares principal components.

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Multivariate TrimmingMultivariate Trimming

• The iterative process of multivariate trimming was used.

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DD22 and Expected Chi Square and Expected Chi Square ValueValue

• Corresponding to the square distance the expected chi square value along with its probability were computed.

χ2

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Outlier ObservationsOutlier Observations

• The observations with probability < .05 are treated as outliers and are flagged.

• The flagged observations are treated as candidates for probe by medical review and/or treated as potential CERT errors and referred to the Provider Education Unit.

Outlier

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Outlier Observations PrioritizedOutlier Observations Prioritized

• Finally the outlier observation were prioritized by the magnitude of distance measure, expected chi-square value and the probability associated with measure.

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Evaluation of Outlier Evaluation of Outlier ClassificationClassification

• Once each observation in the dataset has been classified as an outlier or non-outlier by using chi-square distribution, we used logistic regression to find out the estimate of the goodness of fit of the model.

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C StatisticsC Statistics

• In order to find out how accurately we were able identity the outlier observations we used C Statistics.

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C Statistics…C Statistics…

• The value of c statistics varies from 0.5 ( randomly assigning to one of the other category) to 1.0 where the observations are correctly assigned to the categories.

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An example from Paid An example from Paid Claim DatasetClaim Dataset

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Think about Some Random Think about Some Random Numbers??Numbers??

4 - 100 - 40 - 60

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Outlier Proportion of NGS UtilizationOutlier Proportion of NGS Utilization

• Provider HCPC Line 03.46%• Provider Counts 99.49%• Total Reimbursement

37.90%• Total Units 58.78%• Provider HCPC Benes

44.21%• Provider HCPC Claims 48.21%

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Model EvaluationModel Evaluation

• The outlier model for NGS data was evaluated by using goodness of fit test.

• The NGS combined data set has 930,260 Provider HCPC Lines.

• Of the total lines there were 32,145 were outliers lines.

• The Chi Square for the model was 344144.04 with Probability being < 0.0001.

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C statistics C statistics

• Association of Predicted Probabilities and Observed Responses

Percent Concordant 94.9% Percent Discordant 3.6%Percent Tied 1.5%

c statistic 0.956

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Past and Future ApplicationPast and Future Application

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Current ApplicationCurrent Application

• Used as a single factor in determining multivariate statistical outliers– Problem areas– HCPC codes– Individual Providers

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Current ApplicationCurrent Application

• Positives– Confidence (statistically valid

methodology)– Consistent methodology regardless of

problem area– Lack of clinical bias

• Negatives– Difficult to interpret– Volume of provider/HCPC

combinations required for valid analysis

– Lack of clinical bias

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Future ApplicationFuture Application

• Using the squared distance as a factor in determining outlier problem areas

• Using the squared distance as a factor in determining the aberrancy index of a provider

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Future Application – Problem Future Application – Problem AreasAreas

Problem AreaCERT Factor

Factor 2

Factor 3

Squared Distance Factor

Weight 1

Weight 2

Weight 3

Weight 4

Aggregate Index

Problem Rank

Problem Area 5 10 10 8 0.33872 4 1 2 4 6,735.49 1

Problem Area 10 8 6 9 0.86849 4 1 2 4 5,947.40 2

Problem Area 3 10 8 1 0.75349 4 1 2 4 5,301.40 3

Problem Area 7 10 4 3 0.06234 4 1 2 4 5,024.94 4

Problem Area 9 9 6 3 0.18039 4 1 2 4 4,872.16 5

Problem Area 8 8 1 1 0.43183 4 1 2 4 3,672.73 6

Problem Area 2 6 6 2 0.99527 4 1 2 4 3,798.11 7

Problem Area 6 4 10 1 0.74227 4 1 2 4 3,096.91 8

Problem Area 4 8 2 2 0.22331 4 1 2 4 3,889.32 9

Problem Area 1 2 1 3 0.66469 4 1 2 4 1,765.87 10

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Future Application – Problem Future Application – Problem ProvidersProviders

ProviderCERT Factor

Factor 2

Factor 3

Squared Distance Factor

Weight 1

Weight 2

Weight 3

Weight 4

Aggregate Index Provider Rank

Provider 4 10 10 8 0.55720 4 1 2 4 6,822.88 1

Provider 6 10 5 7 0.98560 4 1 2 4 6,294.24 2

Provider 2 7 2 10 0.12170 4 1 2 4 5,048.68 3

Provider 10 4 6 10 0.89450 4 1 2 4 4,557.80 4

Provider 7 6 9 6 0.13890 4 1 2 4 4,555.56 5

Provider 1 6 1 8 0.23790 4 1 2 4 4,195.16 6

Provider 5 4 3 5 0.79580 4 1 2 4 3,218.32 7

Provider 8 2 2 5 0.20110 4 1 2 4 2,080.44 8

Provider 3 3 1 2 0.55390 4 1 2 4 1,921.56 9

Provider 9 2 5 1 0.69240 4 1 2 4 1,776.96 10

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The multivariate modelThe multivariate model

• By using multivariate model only 4% of total Provider-HCPC combinations lines were identified as outliers.– However the 4% of the total lines have

captured almost 100% of the NGS providers and questioned their 40% of their payment in the Quarter 4 of 2007.

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Testing of the model as Testing of the model as classifierclassifier

• Using multivariate model with multivariate trimming we were able to identify each observation (provider-hcpcs combination) to be as outlier or non-outlier.

• Using this method we were able identify outliers with a very high concordance ( 94.6%).

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ConclusionConclusion

• We used multivariate statistical method to identify aberrant billing and utilization in the claim data set and tested the validity of the method by using logistic regression.

• We also noted that statistical method alone is not enough and we need to add other factors to add value to the process of identifying the problem areas as well finding the high value target.

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