"... A recent review of the data from 19 clinical trials has shown that 5–29% of patients discontinue the anti-TNF-a agent within the 24–30-week treatment period.

Adherence to treatment (also referred to as ‘drug survival’) seems to be highest for etanercept followed by adalimumab and infliximab. Data for longer treatment durations are scarce but suggest an annual drop-out rate in the range 15–25% ..."
http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2133.2011....

"Drug survival in rheumatoid arthritis

Department of Rheumatology and 1Department of Psychology (Physical Health and Rehabilitation), Cannock Chase Hospital, Brunswick Road, Cannock, WS11 2XY, UK

Accepted May 26, 2006.

... ‘Drug survival’ ***** measures the length of time a patient continues to take a particular drug *****: it is a well-recognized measure of drug effectiveness, which encompasses factors such as adverse drug reactions and side-effects, poor adherence, loss of efficacy and others. To measure drug survival, it is simply necessary to ask the patient when starting on a new medication to note the date they stop taking the medication regularly. Although drug survival has been examined in a variety of medical situations, it has not previously been extensively studied in RA.
...
Drug survival is cheap and easy to measure: understanding the factors that contribute to drug survival can only add to our understanding of compliance/adherence. In this case, if we assume that drug survival is a ‘good’ outcome, we need to target our counselling at those who are older/less anxious. Given that beliefs about medications do not appear to influence drug survival, these somewhat counter-intuitive and intriguing findings challenge our approach to promoting compliance/adherence/drug survival in our rheumatology patients.
http://rheumatology.oxfordjournals.org/content/45/9/1178.1.f...


A ce jour il existe très peu d'informations comparant le taux de rétention de ces traitements ("survie du médicament") et les causes de leur d'arrêt, en particulier ..."
http://www.rheumasearch.ch/ProjetsEnCours.html


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Note added at 8 hrs (2017-11-15 14:53:30 GMT)
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IOW how long the drug - NOT the patient will "survive" (i.e. how long the drug will keep being used by the patient) - until the patient gets bored of it, starts forgetting to take it, decides "it's no longer needed", has had enough of unpleasant sides effects etc ...

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Note added at 1 day 2 mins (2017-11-16 06:19:14 GMT)
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well explained:

Dermatologie. Happy drug survival : la clé pour assurer une bonne réponse clinique à long terme

La pratique quotidienne nous apprend quelque chose d’autre. Malgré l’existence d’outils d’évaluation et d’objectifs de traitement pour de nombreuses maladies importantes, le résultat à long terme dans la prise en charge de ces maladies dépend en grande partie d’une variable jusqu’ici sous-estimée, à savoir l’adhésion thérapeutique du patient.

https://www.revmed.ch/RMS/2016/RMS-N-500-501/Dermatologie.-H...

"survie du médicament" / "taux de rétention du traitement" two faces of the same coin one from the viewpoint of the drug (stays "alive" = keeps being used as opposed to "dead" = no one wants it) the other one from the viewpoint of the patient's behaviour.

You could make a parallel with a language [or a book] being dead or alive / [= "surviving"] as long as some people keep using it / reading it - "drug survival" is not exactly some made-up weird figure of speech plucked out of thin air !!!