Optimising HCP Sample Allocation in Pharma: Combining Non-Linear Ensemble Learning, Spatial Lags, and Integer Programming
Johannes Plambeck, Dorian Puleri, Victor Gonzalez · 2025
Pharmaceutical sample allocation frequently misaligns with prescribing potential, leading toineciencies in a $30 billion annual budget. We propose a joint learningoptimisation pipelinethat 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 with1.2 million weekly HCPweek panels and over 80 engineered featurescovering promotionalchannels, claims outcomes, marketbasket shares of competing and complementary drugs, de-mographics, and treatment ratiosand applies sparsity ltering. We then train decilebandedCatBoost ensembles, augmented with inversedistance spatial lags, to generate outoffold up-lift estimates for incremental TRx and NBRx. These predictions feed a 01 mixedintegerprogramme that enforces both HCPlevel and territorylevel pill budget constraints as wellas business rules on cost, eectiveness, and sample availability. By comparing tted versusoptimized TRx and NBRx responses, our framework projects a an aggregate TRx increase ofapproximately 17%, while ensuring highvalue physicians are not undersupplied and lowvaluephysicians are not oversupplied.