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

Author

Listed:
  • Plambeck, Johannes

    (Pfizer Inc)

  • Puleri, Dorian
  • Gonzalez, Victor

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.

Suggested Citation

  • Plambeck, Johannes & Puleri, Dorian & Gonzalez, Victor, 2025. "Optimising HCP Sample Allocation in Pharma: Combining Non-Linear Ensemble Learning, Spatial Lags, and Integer Programming," SocArXiv n4ybq_v2, Center for Open Science.
    • Handle: RePEc:osf:socarx:n4ybq_v2
    DOI: 10.31219/osf.io/n4ybq_v2
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    References listed on IDEAS

    as
    1. Kissan Joseph & Murali Mantrala, 2009. "A model of the role of free drug samples in physicians’ prescription decisions," Marketing Letters, Springer, vol. 20(1), pages 15-29, March.
    2. Stefano DellaVigna & Matthew Gentzkow, 2019. "Uniform Pricing in U.S. Retail Chains," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(4), pages 2011-2084.
    3. Ricardo Montoya & Oded Netzer & Kamel Jedidi, 2010. "Dynamic Allocation of Pharmaceutical Detailing and Sampling for Long-Term Profitability," Marketing Science, INFORMS, vol. 29(5), pages 909-924, 09-10.
    4. Maya Fey Hallett & Trine Kjær & Line Bjørnskov Pedersen, 2024. "The Use of Nudge Strategies in Improving Physicians’ Prescribing Behavior: A Systematic Review and Meta-analysis," Medical Decision Making, , vol. 44(8), pages 986-1011, November.
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