Maths and medicine, improving clinical studies

By defi­ni­tion, each indi­vi­dual is unique, which makes cli­ni­cal research com­pli­ca­ted. Cli­ni­cal trials on volun­teers are conduc­ted to ascer­tain the effi­ca­cy of a par­ti­cu­lar medi­ca­tion. But because not eve­ryone reacts in the same way to the same treat­ment ; effects are dif­fi­cult to mea­sure. Some volun­teers expe­rience clear bene­fits, while others seem imper­vious, or under­go a nega­tive reac­tion. In order to unders­tand the effect of a drug, we must the­re­fore unders­tand this varia­tion bet­ween indi­vi­duals, and Marc Lavielle is rising to that challenge.

With the aid of mathe­ma­tics, he is hel­ping doc­tors and bio­lo­gists improve their unders­tan­ding of the drugs they test. “I ana­lyse data from cli­ni­cal trials, often from the ini­tial phase invol­ving few patients. My col­leagues and I then model the drug’s phar­ma­co­ki­ne­tics,” he says. Through algo­rithms and sta­tis­tics, he is able to repro­duce the effects of the drug in the body via com­pu­ter simu­la­tion. “The second phase can then be opti­mi­sed, increa­sing the chances of signi­fi­cant results.” The risk of fai­ling to ascer­tain whe­ther or not a drug is effec­tive after seve­ral weeks of cli­ni­cal trials is one of the major draw­backs in cli­ni­cal research.

Lavielle believes that a bet­ter unders­tan­ding of indi­vi­dual varia­tion could help avoid this pro­blem. The goal is to figure out how to select patients who will react best to treat­ment and avoid those like­ly to expe­rience side effects. But this is no easy task. We need to unders­tand the bio­lo­gi­cal signals, and which genes indi­cate how a patient may react. Unders­tan­ding these effects is cen­tral to per­so­na­li­sed medi­cine : once the drug is autho­ri­sed, doc­tors would pres­cribe it only to those who are like­ly to respond well. 

Inte­gra­ting indi­vi­dual variation

Lavielle’s work uses mixed-effect models that can be repre­sen­ted gra­phi­cal­ly. “All the models have the same layout,” he explains. “They represent how the drug is absor­bed and dis­tri­bu­ted throu­ghout the orga­nism, meta­bo­li­sed and, final­ly, eli­mi­na­ted.” But models vary from indi­vi­dual to indi­vi­dual : some people absorb the drug slo­wer ; others eli­mi­nate it more qui­ck­ly, and so on.”

Some­times these dif­fe­rences can be explai­ned by conven­tio­nal medi­cal cri­te­ria, such as the patient’s weight. But with new DNA sequen­cing tech­no­lo­gy, we can now iden­ti­fy other, gene­tic variables. “Phar­ma­co­ge­ne­tics uses gene­tic data to unders­tand why some patients respond to a cer­tain treat­ment while others don’t,” Lavielle adds. “The suc­cess of a model depends on our abi­li­ty to unders­tand varia­tions bet­ween individuals.”

In order to do this, he feeds bio­lo­gi­cal data into his mathe­ma­ti­cal tools. “It is vital to work with experts in the field to inter­pret results and use cri­te­ria that make sense from a bio­lo­gi­cal stand­point,” he stresses.

Opti­mi­sing cli­ni­cal research

The terms of the pro­blem are set ; all that is nee­ded is the right for­mu­la to des­cribe the effects of a drug or the deve­lop­ment of a tumour over time, while taking into account the way these pro­cesses vary from one indi­vi­dual to ano­ther. This is the work of the mathe­ma­ti­cian. Once this is done, he can present his simu­la­tion tool to doctors.

“Using these models, we can gene­rate vir­tual patients and simu­late their res­ponse,” he says. This means we can create vir­tual cli­ni­cal trials. “The advan­tage of vir­tual patients is that we can give them any treat­ment without cau­sing harm. We don’t have to wor­ry about ethi­cal constraints. Above all, it saves a great deal of time!” A digi­tal model can run in a mat­ter of seconds, whe­reas phase one of a real-life trial – where drug tole­rance is asses­sed to help define dosage and fre­quen­cy for sub­sequent trials – may take one to two years.

These models can be used in all cli­ni­cal trials, in or out­side of per­so­na­li­sed medi­cine. “But when they are built using data from a phase 3 trial [eva­lua­ting treat­ment effi­ca­cy], we get a real­ly good des­crip­tion of how the drug behaves,” he adds. “By com­bi­ning cli­ni­cal data from a patient with that from cli­ni­cal trials, we will be able to pre­dict their res­ponse to treatment.”

Pre­dic­ting patient response

This could enable us to iden­ti­fy patients like­ly to respond to a treat­ment, and those who may have side effects or deve­lop resis­tance, which is cru­cial infor­ma­tion for cli­ni­cal appli­ca­tions. There is one pres­sing pro­blem – more mathe­ma­ti­cians are nee­ded in the medi­cal field. No won­der bio­phar­ma­ceu­ti­cal giant Sano­fi has been fun­ding the Nume­ri­cal Inno­va­tion and Data Science for Heal­th­care spon­sor­ship pro­gram at École poly­tech­nique since Decem­ber 2019 !

At the same time, start-ups are inves­ting in the field. Lixoft, the brain­child of Marc Lavielle and Jérôme Kali­fa, was foun­ded in 2011. The com­pa­ny sells soft­ware to help desi­gn cli­ni­cal trials and may also enter the medi­cal device mar­ket with a tool to iden­ti­fy patients most like­ly to respond to a par­ti­cu­lar treat­ment, using their bio­lo­gi­cal data. “We’re still consi­de­ring this option,” Lixoft CEO Jona­than Chau­vin says. “But there are a lot of regu­la­to­ry constraints.” Ano­ther aspect that must be taken into account.