Engineering a $12M Impact Audit Recommender with GLMs

Commercial insurance policies are often issued on an estimated payroll or revenue basis. At the close of the policy year, an audit is performed to reconcile actual exposures against initial estimates.

However, physical and detailed audits are resource-intensive. Selecting accounts at random or via simplistic heuristic filters yields high false positives.

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1. The Core Mathematical Formulation

Instead of a single black-box binary classifier ("Will this policy have an audit adjustment: Yes/No?"), we decomposed the problem into two distinct statistical targets:

1. Probability of Non-Zero Exposure Delta ($P(Y > 0)$): Modeled via a Binomial GLM with logit link.
2. Expected Recoverable Premium Magnitude ($E[D \mid Y > 0]$): Modeled via a Gamma GLM with log link.

python
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import statsmodels.api as sm
import statsmodels.formula.api as smf

# Step 1: Probability of Adjustment
logit_model = smf.glm(
    formula="adjustment_flag ~ revenue_growth + prior_audit_variance + industry_risk_idx",
    data=training_df,
    family=sm.families.Binomial()
).fit()

# Step 2: Severity of Adjustment (Conditioned on adjustment)
gamma_model = smf.glm(
    formula="recoverable_premium ~ log_payroll + employee_count_ratio + state_mod",
    data=training_df[training_df['adjustment_flag'] == 1],
    family=sm.families.Gamma(link=sm.families.links.Log())
).fit()

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2. Triage Decision Matrix

By multiplying $P(Y > 0) \times E[D \mid Y > 0]$, we obtain the Expected Audit Value (EAV).

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3. Results & Operational Impact

• Estimated $12 Million annual increase in recovered premium.
• $50,000+ direct reduction in unnecessary on-site audit expenses.
• Audit turnaround cycle shortened from 45 days to 14 days on low-variance policies.