Optimising HCP Sample Allocation in Pharma: Combining Non-Linear Ensemble Learning, Spatial Lags, and Integer Programming

Johannes Plambeck, Dorian Puleri and Victor Gonzalez
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Johannes Plambeck: Pfizer Inc

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Abstract: Pharmaceutical sample allocation frequently misaligns with prescribing potential, leading to ineciencies in a $30 billion annual budget. We propose a joint learningoptimisation pipeline that allocates Eliquis samples to 11,006 U.S. healthcare providers based on their historical pre- scribing patterns. Our approach merges a quarterly forward indicator of sample drops with 1.2 million weekly HCPweek panels and over 80 engineered featurescovering promotional channels, claims outcomes, marketbasket shares of competing and complementary drugs, de- mographics, and treatment ratiosand applies sparsity ltering. We then train decilebanded CatBoost ensembles, augmented with inversedistance spatial lags, to generate outoffold up- lift estimates for incremental TRx and NBRx. These predictions feed a 01 mixedinteger programme that enforces both HCPlevel and territorylevel pill budget constraints as well as business rules on cost, eectiveness, and sample availability. By comparing tted versus optimized TRx and NBRx responses, our framework projects a an aggregate TRx increase of approximately 17%, while ensuring highvalue physicians are not undersupplied and lowvalue physicians are not oversupplied.

Date: 2025-08-09
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DOI: 10.31219/osf.io/n4ybq_v2

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