Mathematical Modeling Facilitates Pharmaceutical Development

By Lina Sorg

Mathematical modeling has nearly limitless applications. “As modelers in the field, we’re like kids in a candy store,” Sandy Allerheiligen said. “There’s so much we can do.” Allerheiligen, who works at Merck Research Laboratories, gave an invited talk at the SIAM Conference on the Life Sciences. The talk, entitled “Impact of Quantitative and Systems Pharmacology in Drug Discovery and Development: It is All About the Question,” addressed the significance of modeling and data analysis in quantitative and systems pharmacology. Modeling techniques help experimentalists in the pharmaceutical industry understand, develop, and market effective drugs and innovative therapies to patients. 

Pharmaceutical development is a high-stakes practice because most drugs necessitate 13 to 15 years of development from beginning to launch, Allerheiligen said. Thus, identifying ideal dosages and other valuable treatment factors is particularly important. She added that a typical company spends anywhere between two and 12 billion dollars preparing a single new drug for the market, while the public continues to demand cheaper drugs. “You have to find a way to be much more creative in how you discover and find those new drugs so you can reduce the cost,” Allerheiligen said.

Allerheiligen then offered an overview of pharmaceutical development. For every 10,000 or so molecules that are synthesized, about 100 compounds will reach human testing. During this preliminary stage, developers stringently test products for efficacy and safety. Only seven of those 100 compounds actually become drugs.  And only one in every five drugs will recoup the investments of the manufacturing company. With these statistics in mind, Allerheiligen posed the following question:  how much improvement is required in efficacy or safety to truly advance patient care? 

Unfortunately, there is no simple answer. “How do we take a clinical trial patient and know what that real-world patient is going to be like?” she asked. Her group at Merck is working to provide a more lucid understanding of prior data, variabilities in patients, standards of care, and initial behavior of drugs. “It’s about creating multi-disciplinary models integrating biological, pharmacological, clinical, and RW knowledge,” Allerheiligen said. “One of the most valuable aspects is understanding the assumptions that are inherent in the model.”  In some cases this involves thinking heavily about the natural history of a disease.

Merck uses literature databases, real world data, and a variety of models—including quantitative decision models, genomics and outcome models, dropout models, and mechanistic models of disease—to convey trends and help experimentalists understand that experiments are not always directly indicative of truth. “We have to learn to communicate with the experimentalists,” Allerheiligen said, adding that she and her group use visualizations and real-time simulations to convey information to biologists and pharmacologists. “We have to speak their language, understand, and bring them with us.”

Allerheiligen then shared examples of her pharmaceutical modeling in action. A company was working on a variable drug for stroke prevention and contemplating a 30,000-person trial, but troublingly the most prominent side effect was stroke. Merck built a literature-based model that ultimately revealed that the dose necessary for human efficacy did not fall within the range of what was acceptable for human safety; the company did not go forward with their trial and discontinued the drug. Another project involved finding a way to administer an HIV treatment drug to children in the form of chewable tablets. There was concern that the children would develop resistance because of the drug’s concentration levels in tablet form, and the European Medicines Agency (EMA) vetoed the treatment. Merck presented models based on past data to the EMA, which then overturned its decision. The tablets are now available to kids.

Allerheiligen is currently working on ways to eradicate Hepatitis C, and has been thinking heavily about precision medicine. Her work in quantitative and systems pharmacology continues to safely accelerate drug discovery. In the high-stakes environment of pharmaceutical development, Merck’s use of models to refine treatment approaches is certainly a major asset. 

Lina Sorg is the associate editor of SIAM News.