Selection bias and auditing policies for insurance claims

Selection bias results from a discrepancy between the range of estimation of a statistical model and its range of application. This is the case for fraud risk models, which are estimated on audited claims but applied on incoming claims in the design of auditing strategies. Now audited claims are a minority within the parent sample since they are chosen after a severe selection performed by claims adjusters. This article presents a statistical approach that counteracts selection bias without using a random auditing strategy. A two-equation model on audit and fraud (a bivariate probit model with censoring) is estimated on a sample of claims where the experts are left free to take the audit decision. The expected overestimation of fraud risk derived from a single-equation model is corrected. Results are close to those obtained with a random auditing strategy, at the expense of some instability with respect to the regression components set. Then we compare auditing policies derived from the different approaches.