Skip to main content
SpringerLink
Log in

Perspectives on the Role of Mathematics in Drug Discovery and Development

  • Special Issue: Mathematics to Support Drug Discovery and Development
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The goals of this article and special issue are to highlight the value of mathematical biology approaches in industry, help foster future interactions, and suggest ways for mathematics Ph.D. students and postdocs to move into industry careers. We include a candid examination of the advantages and challenges of doing mathematics in the biopharma industry, a broad overview of the types of mathematics being applied, information about academic collaborations, and career advice for those looking to move from academia to industry (including graduating Ph.D. students).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Allen RJ, Rieger TR, Musante CJ (2016) Efficient generation and selection of virtual populations in quantitative systems pharmacology models. CPT Pharmacomet Syst Pharmacol 5(3):140–146. https://doi.org/10.1002/psp4.12063

    Article  Google Scholar 

  • Beal SL, Sheiner LB, Boeckmann AJ, Bauer RJ (eds) (2017) NONMEM 7.4 users guides. ICON plc, Gaithersburg, Maryland, USA. https://nonmem.iconplc.com/nonmem743/guides

  • Berry SM, Carlin BP, Jack Lee J, Müller P (2010) Bayesian adaptive methods for clinical trials. Chapman & Hall/CRC, Boca Raton

    Book  MATH  Google Scholar 

  • Bonate PL (2011) Pharmacokinetic-pharmacodynamic modeling and simulation, 2nd edn. Springer, New York

    Book  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • D’Argenio DZ, Schumitzky A, Wang X (2009) ADAPT 5 user’s guide: pharmacokinetic/pharmacodynamic systems analysis software. Biomedical Simulations Resource, Los Angeles

    Google Scholar 

  • Davidian M, Giltinan DM (1995) Nonlinear models for repeated measurement data. CRC Press, Boca Raton

    Google Scholar 

  • Dawood Z, Coudray N, Kim RH, Nomikou S, Moran U, Weber JS, Pavlick AC, Wilson M, Tsirigos A, Osman I (2018) Prediction of response and toxicity to immune checkpoint inhibitor therapies (ICI) in melanoma using deep neural networks machine learning. J Clin Oncol. https://doi.org/10.1200/jco.2018.36.15_suppl.9529

    Google Scholar 

  • Desmée S, Mentré F, Veyrat-Follet C, Sébastien B, Guedj J (2017) Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer. BMC Med Res Methodol 17:105. https://doi.org/10.1186/s12874-017-0382-9

    Article  MATH  Google Scholar 

  • Friedrich C (2016) A model qualification method for mechanistic physiological QSP models to support model-informed drug development. CPT Pharmcomet Syst Pharmacol 5(2):43–53. https://doi.org/10.1002/psp4.12056

    Article  Google Scholar 

  • Gabrielsson J, Weiner D (2017) Pharmacokinetic and pharmacodynamic data analysis: concepts and applications, 5th edn. Swedish Pharmaceutical Press, Stockholm

    Google Scholar 

  • Gelman A, Lee D, Guo J (2015) Stan: a probabilistic programming language for Bayesian inference and optimization. J Educ Behav Stat 40(5):530–543. https://doi.org/10.3102/1076998615606113

    Article  Google Scholar 

  • Gronsbell J, Minnier J, Sheng Yu, Liao K, Cai T (2018) Automated feature selection of predictors in electronic medical records data. Biometrics. https://doi.org/10.1111/biom.12987

    Google Scholar 

  • Kadir T, Gleeson F (2018) Lung cancer prediction using machine learning and advanced imaging techniques. Transl Lung Cancer Res 7(3):304–312

    Article  Google Scholar 

  • Lenhart S, Workman JT (2007) Optimal control applied to biological models. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  • Lindstrom MJ, Bates DM (1990) Nonlinear mixed effects models for repeated measures data. Biometrics 46(3):673–687

    Article  MathSciNet  Google Scholar 

  • Martin R, Teo KL (1994) Optimal control of drug administration in cancer chemotherapy. World Scientific, Singapore

    MATH  Google Scholar 

  • MATLAB (2018b) The MathWorks, Inc, Natick

  • Mentré F, Mallet A, Baccar D (1997) Optimal design in random-effects regression models. Biometrika 84(2):429–442. https://doi.org/10.1093/biomet/84.2.429

    Article  MathSciNet  MATH  Google Scholar 

  • Monolix version 2018R1 (2018) Antony, France: Lixoft SAS. http://lixoft.com/products/monolix/

  • Moore H (2018) How to mathematically optimize drug regimens using optimal control. J Pharmacokinet Pharmacodyn 45(1): 127–137. https://doi.org/10.1007/s10928-018-9568-y

  • Mould DR, Upton RN (2012) Basic concepts in population modeling, simulation, and model‐based drug development. CPT Pharmacomet Syst Pharmacol 1:e6. http://www.nature.com/doifinder/10.1038/psp.2012.4

  • Mould DR, Upton RN (2013) Basic concepts in population modeling, simulation, and model‐based drug development—part 2: introduction to pharmacokinetic modeling methods. CPT Pharmacomet Syst Pharmacol 2:e38. http://www.nature.com/doifinder/10.1038/psp.2013.14

  • Pharmacometrics at FDA. https://www.fda.gov/AboutFDA/CentersOffices/OfficeofMedicalProductsandTobacco/CDER/ucm167032.htm. Accessed May 14, 2017

  • Phoenix NLME 8.1 (2018) Certara, LP. St Louis

  • Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2018) nlme: linear and nonlinear mixed effects models. R package version 3.1-131.1. https://CRAN.R-project.org/package=nlme

  • Pontryagin LS (1959) Optimal control processes II. Uspekhi Matematicheskikh Nauk 14:3–20 (in Russian)

    Google Scholar 

  • Rizopoulos D (2012) Joint models for longitudinal and time-to-event data with applications in R. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  • Sager JE, Jingjing Yu, Ragueneau-Majlessi I, Isoherranen N (2015) Physiologically based pharmacokinetic (PBPK) modeling and simulation approaches: a systematic review of published models, applications, and model verification. Drug Metab Dispos 43:1823–1837

    Article  Google Scholar 

  • Smith RC (2014) Uncertainty quantification. SIAM, Philadelphia

    MATH  Google Scholar 

  • Swan G (1984) Applications of optimal control theory in biomedicine. Marcel Dekker, New York

    MATH  Google Scholar 

  • Wong CH, Siah KW, Lo AW (2018) Estimation of clinical trial success rates and related parameters. Biostatistics 14:14–19

    Google Scholar 

Download references

Author information

Author notes

  1. Richard Allen and Helen Moore have contributed equally to this work.

Authors and Affiliations

  1. Internal Medicine Research Unit, Pfizer Inc, Cambridge, MA, 02139, USA

    Richard Allen

  2. Oncology R&D, AstraZeneca, Waltham, MA, 02451, USA

    Helen Moore

Authors
  1. Richard Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Helen Moore
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard Allen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Allen, R., Moore, H. Perspectives on the Role of Mathematics in Drug Discovery and Development. Bull Math Biol 81, 3425–3435 (2019). https://doi.org/10.1007/s11538-018-00556-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-018-00556-y

Keywords

Search

Navigation