Examples of BDS Projects

Sample Plans: How much does an insurance company owe for underpayments?

Hospitals allege that the insurance amounts provided for patient services are underpayments under their contract and they seek payment through arbitration with the insurance company. Occasionally, there are counter claims for overpayments on the part of the insurance company. The number of claims can be quite large, up to tens of thousands; adjudicating those claims is often time-consuming and costly. We have been asked to develop sampling plans that are highly reliable, and, at the same time, control the sample size needed to estimate the amount due to the hospitals. Using modern sampling procedures, our sample designs are efficient resulting in workable sample sizes with coefficients of variations that range from 2% to 5%, substantially less than the 10% recommended in the statistical literature. We have successfully critiqued and rebutted arguments from statisticians, economists and accountants representing opposing insurance companies who recommended much larger sample sizes and less efficient designs.

Sample Plans: How much can a company claim as Qualified Research Expenditures?

Companies seek to take tax credits for qualified research activities following the guidelines provided by the IRS. There are usually complex issues that must be addressed creatively, such as incomplete information about qualifying research expenditures (QREs); client requirements for separate project category estimates; QRE estimates across several tax years; wide variability in the data; and short filing dates with the need for sample sizes that allow for adequate review by tax specialists. We apply our expertise in this area to develop sample plans for either employees or projects that will satisfy IRS rules and address these issues. After the plans have been implemented and estimated QREs have been provided, we apply appropriate estimation procedures, along with precision estimates, and recommend the type of estimate that will satisfy IRS rules. We produce reports that document our work for submission if the tax credit allowances are challenged by the IRS.

Survey:  What’s safe for babies?

Recent studies have found that babies may suffocate in cribs with bumpers. An alternative product, mesh liners, was in use but no data were available to estimate its safety. A mesh-liner manufacturer asked us to conduct a survey of parents to determine whether mesh liners presented any risk of injury. We addressed a number of issues including: identifying and gaining access to a population of mothers who were subscribers to a national parenting magazine; designing the survey to reduce the time spent responding by using multiple branching and skip patterns for the survey items; creating incentives to encourage survey response; and analyzing the data to adjust for demographic variables prevalent in the research literature and for missing data. The analysis compared mothers’ reports of crib bumper, mesh liner, and no barrier incidents using multivariate logistic regression models calculating the odds of an injury incident occurring. We adjusted for missing responses for one or more adjustor variables using a Markov Chain Monte-Carlo method in SPSS to create a pooled data set with 15 imputed data sets. We published the results of the study, “Reports of Injury Risks and Reasons for Choice of Sleep Environments for Babies,” in the peer-reviewed Maternal and Child Health Journal. 

Sampling:  Is Expert Judgment Better than a Random Sample?

The federal government reimburses universities for indirect energy costs associated with government grants and other government sponsored research. A major university’s reimbursement was questioned by federal oversight statisticians because the University staff used a judgement sample of buildings that in their expert opinion best represented the campus. The University’s accounting firm requested our review of this procedure, which we were unable to support. We developed a creative stratified random sampling plan that took into account large energy-use buildings as well as the type of space within buildings, and the plan was accepted by federal government statisticians. Our analysis of the results found that the University lost millions of dollars using their judgement sampling procedure that had under-estimated their indirect energy recovery costs for a number of years. Partnering with an accounting firm, we continued to develop sampling plans to analyze indirect energy costs for over 15 universities including Johns Hopkins, Duke, Stanford, Harvard, Tulane and the Universities of Pennsylvania, Chicago, Washington, and Wayne State.

Fraud:  Did the Faculty Double-Dip?

A whistle blower charged that faculty and other university staff on 10-month contracts were paid twice for the month that overlapped between the spring semester and their summer federal grant or contract work projects. We were requested to develop a statistically valid sampling plan to use in an independent review and to incorporate a request by Federal auditors at the Department of Justice for a plan that allowed for review of the largest grant/contract projects. Determining sample size was challenging because there was no historical data on overcharge rates, so we based the sample size on a range of overcharge rates that was not more than 10% of the estimated overcharge rate. Our analysis found that overcharges did occur and we estimated the extent of those overcharges weighted to account for the plan’s stratification.

Errors: Is there an easier method to identify incorrect purchasing card transactions?

A major university instituted procedures to allow personnel to purchase a variety of goods and services costing no more than $2,500 using University-issued purchasing cards. A major accounting firm asked us to design a sampling plan and procedures to monitor incorrect purchasing card transactions that could be repeated over time. We created two stratified sampling plans for four object code strata that allowed for ease in future calculation of the total number of errors for a given time period. With Design 1, transactions were randomly selected proportionately from each stratum so that transaction errors could be directly combined across strata. With Design 2, an equal number of transactions was randomly selected from each strata with transaction errors weighted together for a final count. We recommended Design 2 because it was easier to implement and made further recommendations for implementation and estimation procedures.

Discrimination: Is it likely that all employees released from a company were over the age of 50?

During a reduction in force, a company released 8 employees, all of whom were over the age of 50. The employees were able to obtain the list of individuals considered for release so the starting population was known. For their lawsuit, we determined the probability was approximately 1 in 1000 that all of the employees released would have been over the age of 50 by chance alone. This information proved useful for the lawsuit.

Survey: Are there predictors of security compromise?

Psychological experts classified each respondent as having either serious violations or minor/no violations from a long questionnaire administered to military employees. Using responses to the questionnaire items and working with military psychology experts, we developed several statistical regression models to identify significant predictors of personnel with serious violations that showed stability across statistical methods. The military planned to use the significant predictors to screen personnel for security clearances.