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Multivariate Detection of Aberrant Billing: An Evaluation

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Multivariate Detection of Aberrant Billing: An Evaluation

Maharaj Singh, Ted Wallace & Martin Schrager

National Government Services, Inc.

Outlier defined

Multivariate method for detecting Outlier

Detecting outlier billing providers

An evaluation of the methodology

Other factors considered for future application

Conclusion

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

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

- 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

- Mahalanobis distance

- 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.

- 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.

- 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.

- 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.

- Billing providers
- Location,
- Size
- Specialty

- HCPCS used
- Primary Diagnoses

- Cost
- Charges Billed
- Charges denied
- Reimbursement

- Rate
- Reimbursement per beneficiary
- Service Units per beneficiary
- Service units per service dates per beneficiary

- Volume
- Number of claims
- Number of beneficiaries
- Number of service units rendered
- Number of service days

- 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.

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

- 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.

- The iterative process of multivariate trimming was used.

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

- 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

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

- 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.

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

4 - 100 - 40 - 60

- Provider HCPC Line 03.46%
- Provider Counts99.49%
- Total Reimbursement37.90%
- Total Units 58.78%
- Provider HCPC Benes 44.21%
- Provider HCPC Claims48.21%

- 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.

- Association of Predicted Probabilities and Observed Responses
Percent Concordant 94.9%

Percent Discordant3.6%

Percent Tied 1.5%

c statistic 0.956

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

- 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

- 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

- 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.

- 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%).

- 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.