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.