Current status of Bayesian clinical trials for oncology, 2020

Background Bayesian methods had established a foothold in developing therapies in oncology trials. Methods: We identified clinical trials posted on the ClinicalTrials.gov database focused on Oncology trials with a Bayesian approach in their design. Differences in study characteristics such as design, study phase, randomization, masking, purpose of study, main outcomes, gender, age and funding involvement according to Bayesian approach were assessed using Chi-squared or Fisher's exact tests. Results: We identified 225 studies with Bayesian components in their design addressing oncological diseases. The most common designs were Bayesian Toxicity Monitoring (26.4%), Model-based designs (36%) Model-assisted designs (8%). Statistical methods such as Bayesian logistic regression model (59.4%), Bayesian piecewise exponential survival regression (10.9%) and the Continual reassessment method (9.4%) were the most used. Conclusions: Bayesian trials are more common in the early phases of drug development specifically in phase II trials (43.6%). Cancer institutes or Hospitals funded most of the studies retrieved. This type of design has increased over time and represent an innovative means of increasing trial efficiency.


. Introduction
Ran dom ized con trolled tri als (RCTs) have long been rec og nized as the gold stan dard for the eval u a tion of the ef fi cacy and safety of clin ical in ter ven tions, val ued for their sta tis ti cal rigor and meth ods to avoid bias. Fre quen tist sta tis ti cal frame work has dom i nated the field of clin i cal tri als over the past six decades but nowa days, Bayesian designs have be come in creas ingly used in clin i cal tri als, par tic u larly in the early phase of de vel op ment clin i cal tri als which are clin i cal in vesti ga tions that ex am ine and eval u ate safety and ef fi cacy of a new drug used in hu man sub jects [ 1 -3 ].
Bayesian in fer ence is con di tioned on the data and not on the design, so it can still main tain va lid ity as long as the prior dis tri b u tion and the prob a bil ity model are cor rectly spec i fied. It ap pro pri ates differ ent lev els of vari abil ity nat u rally un der the hi er ar chi cal model assump tion and al lows for the in cor po ra tion of in for ma tion of two types: that which ac cu mu lated in the trial and that which was obtained out side of the trial. In cor po rat ing both types of in for ma tion into the analy sis strength ens the ev i dence for mak ing an in fer ence [ 4 ].
The con tin u ous learn ing that is pos si ble in the Bayesian ap proach en ables in ves ti ga tors to mod ify tri als in mid course. Mod i fi ca tions include stop ping the trial, adding and drop ping treat ment arms, and ex -tend ing ac crual be yond that orig i nally tar geted when the an swer to the ques tion posed is not sat is fac to rily known [ 5 ].
There is an in ter est in the Bayesian ap proach, high lighted by the FDA's com mit ment to fa cil i tate the ad vance ment and use of com plex adap tive, Bayesian, and other novel clin i cal trial de signs. In 2004, the FDA is sued a Crit i cal Path Ini tia tive re port stat ing that "The med ical prod uct de vel op ment process is no longer able to keep pace with ba sic sci en tific in no va tion. Only a con certed ef fort to ap ply the new biomed ical sci ence to med ical prod uct de vel op ment will suc ceed in modern iz ing the crit i cal path [ 6 ].
The way On col ogy clin i cal tri als are de signed and per formed has changed over time. can cer ther a peu tic re search has largely shifted from a fo cus on cy to toxic agents to newer drugs that act through inhibit ing can cer cell growth and sur vival mech a nisms while pro tect ing healthy cells to the ex tent pos si ble [ 7 ].
Eval u a tion of new ther a pies for can cer has suf fered a par a digm shift in the last years. The use of in no v a tive and more ef fi cient de signs is a pri or ity for the sci en tific com mu nity; nev er the less, the use of this kind of de sign is not yet wide spread [ 8 ].Tra di tional clin i cal tri als require spec i fi ca tion of the sam ple size in ad vance. This can be in ef ficient when lim ited in for ma tion is avail able at the de sign stage, es pecially re gard ing the likely ef fect size. Bayesian ap proach has been used to an swer more treat ment ques tions and to fos ter more ef ficiently and novel de signs and their per for mance in less time [ 9 ]. In gen eral, adap tive clin i cal trial de signs are eas ier to im ple ment within the Bayesian frame work.
Clin i cal Tri als.gov is a Web -based re source that pro vides pa tients, their fam ily mem bers, health care pro fes sion als, re searchers, and the pub lic with easy ac cess to in for ma tion on pub licly and pri vately supported clin i cal stud ies on a wide range of dis eases and con di tions. The Web site is main tained by the Na tional Li brary of Med i cine (NLM) at the Na tional In sti tutes of Health (NIH) [ 10 ].
Clin i cal Tri als.gov is de signed to pro vide a pub lic list ing of ini tiated, on go ing, and com pleted stud ies, and to serve as a source of summary re sults in for ma tion to com ple ment the med ical lit er a ture. The orig i nal fo cus was on fa cil i tat ing iden ti fi ca tion and re trieval of in forma tion about spe cific stud ies on in ves ti ga tional drug prod ucts for poten tial study par tic i pants [ 11 ]. It is con sid ered the world's largest clini cal trial reg istry, pub lic and ac ces si ble to all cit i zens [ 12 ].
In this cross -sectional study, we aimed to char ac ter ize the main char ac ter is tics of Bayesian On col ogy Clin i cal tri als in ClinicalTrials. gov for a 20 -year pe riod (1990 -2020) through a sys tem atic analy sis of reg is tered tri als.

1 . Study design
This is a cross -sectional analy sis, in clud ing all in ter ven tional studies that were reg is tered on clinicaltrials. gov in 2020 with a Bayesian ap proach in the de sign or analy sis.

2 . Procedures
We queried ClinicalTrials. gov for the terms "On col ogy, Can cer, Tumors" in the ti tle and con di tion or dis ease. In other terms we in cluded "Bayesian" and search man u ally each trial look ing for in for ma tion about Bayesian ap proach em ployed. Us ing this search strat egy, 225 tri als were iden ti fied. The search was re stricted to in ter ven tional trials. Two re view ers (MF and PG) ex tracted data and checked each other's work for ac cu racy.

3 . Inclusion criteria
1 Trial documentation available 2 . Clinical trials of any phase 3 . Trial investigating an intervention (s) on humans. 4 . Registered or published until the moment of the search. 5 . A Bayesian design clinical trial defined to be a trial with an approach for learning from evidence as it accumulates.

4 . Exclusion criteria
1 Observational studies De f i n i tions for vari ables col lected in the ClinicalTrials. gov database are avail able at http:// prsinfo. clinicaltrials. gov/ definitions. html . The ex tracted data el e ments in cluded the fol low ing:

1 . Dose finding
• Model -based de signs in cluded the fol low ing meth ods Bayesian Con tin ual re assess ment method (B -CRM), Mod i fied con tin ual reassess ment method (mCRM), Bayesian lo gis tic re gres sion model (BLRM), Bayesian Time -to -event con tin ual re assess ment method (TITE -CRM), Bayesian model av er ag ing con tin ual re assess ment method (BMA -CRM).
• Model -assisted de signs in cluded Bayesian op ti mal in ter val (BOIN).

3 . Pharmacokinetics parameters
•Max i mum A Pos te ri ori Bayesian Es ti ma tion. (MAP).

4 . Bayesian Toxicity Monitoring
• Sequential monitoring as the Bayesian method of Thall, Simon and Estey [ 13 ], Bayesian method of Thall and Sung [ 14 ] and Bayesian method of Thall and Cook [ 15 ] and comprised Bayesian stopping boundaries and other monitoring approaches.
No spec i fied Bayesian ap proach in cluded those stud ies that did not spec ify what kind of Bayesian meth ods were em ployed. The most fre quent terms found were "Bayesian model", "Bayesian ap proach" and "Bayesian method".

5 . Classification of funding involvement
For analy sis pur poses of this re search, we re clas si fied the in for mation of se lected tri als in three groups: In dus try, Acad emy and Na tional in sti tutes of Can cer or Hos pi tals. Fund ing source was de fined as indus try if the lead spon sor was from in dus try, as acad emy if the lead spon sor was from a uni ver sity and as Na tional in sti tutes of Can cer or Hos pi tals if the lead spon sor was from one of these in sti tu tions.

6 . Phases
Tri als were clas si fied as early phase (phase 0, I, or I/ II), late phase (phase II/ III, III, or IV).

7 . Intervention model
Types of in ter ven tion mod els in clude sin gle group as sign ment, paral lel as sign ment, cross -over as sign ment, and se quen tial as sign ment.

8 . Allocation
The types of al lo ca tion are ran dom ized al lo ca tion, non ran dom ized and not ap plic a ble in case of one group of treat ment.

9 . Masking
Types of mask ing in clude open la bel, sin gle blind mask ing, dou bleblind mask ing and triple -blind mask ing.

10 . Purpose
Treat ment, Sup port ive care, Di ag nos tic, Pre ven tion and Other.

11 . Main outcomes
Ef fi cacy com prised Com plete re sponse, Over all sur vival, Pro gression -free sur vival Re lapse -free sur vival and Time to Dis ease Pro gression.
Tox i c ity in cluded Dose lim ited tox i c ity and in ci dence of ad verse events.
Dose find ing in cluded those stud ies were Max i mum Tol er ated Dose was as sessed.

12 . Recruitment status
Not yet re cruit ing: The study has not started re cruit ing par tic ipants.
Re cruit ing: The study is cur rently re cruit ing par tic i pants. Ac tive, not re cruit ing: The study is on go ing, and par tic i pants are re ceiv ing an in ter ven tion or be ing ex am ined, but po ten tial par tic ipants are not cur rently be ing re cruited or en rolled.
Ter mi nated: The study has stopped early and will not start again. Com pleted: The study has ended nor mally, and par tic i pants are no longer be ing ex am ined or treated.
With drawn: The study stopped early, be fore en rolling its first partic i pant.
Un known: A study on ClinicalTrials. gov whose last known sta tus was re cruit ing; not yet re cruit ing; or ac tive, not re cruit ing but that has passed its com ple tion date, and the sta tus has not been last ver ified within the past 2 years.

13 . Intervention
In ter ven tions in clude drugs, med ical de vices, pro ce dures, vac cines, and other prod ucts that are ei ther in ves ti ga tional or al ready avail able.

14 . Age or age group
The age groups were child (birth -17), adults and older adults (more than 18 years old) and all ages.

15 . Gender
A type of el i gi bil ity cri te ria that in di cates whether el i gi bil ity to par tic i pate in a clin i cal study is based a per son's self -representation of gen der iden tity or gen der.

16 . Enrollment/ sample size
The num ber of par tic i pants in a clin i cal study. The "es ti mated" enroll ment is the tar get num ber of par tic i pants that the re searchers need for the study.

17 . Statistical analysis
All el e ments were ex tracted di rectly from the data base, which contains raw, row -by -row data for all reg istry records into a commaseparated val ues (csv) data file. We per formed a de scrip tive analy sis of clin i cal tri als reg is tered be tween 1990 and 2020 in the ClinicalTrials. gov data base.
De scrip tive sta tis tics were pri mar ily used to sum ma rize the trial char ac ter is tics: cat e gor i cal vari ables are re ported as fre quen cies and per cent ages, while con tin u ous vari ables are re ported as mean and stan dard de vi a tion. The Fish er's ex act test was used to com pare trial char ac ter is tics. All sta tis ti cal tests were two -sided with a sta tis ti cal sig nif i cance at the 0.05 level. All the data were an a lyzed us ing SPSS 24.0.

. Results
From the to tal 329,502 stud ies reg is tered in the data base, 59,973 were On col ogy tri als and from them 225 in ter ven tional stud ies (0.4%) were el i gi ble for in clu sion in our analy ses (Bayesian ap proach). The trial se lec tion process is shown in Fig. 1 .   Fig. 1 . Flow chart of the re view.
Most of the stud ies were in an early phase de vel op ment (95.1%). Sin gle group as sign ment de sign was the most fre quent with 65.3% mean ing that all par tic i pants re ceived the same in ter ven tion and the ma jor ity of them were Open la beled (97.8%). Ran dom iza tion was not ap plic a ble in 130 out of 225 stud ies (57.8%). 96.4% of On col ogy trials eval u ated dis ease treat ment ver sus 1.3% sup port ive care. Main out come re lated to ef fi cacy (48.4%) was found in al most half of the stud ies while look ing for the Dose Lim it ing Tox i c ity or ad verse events (Tox i c ity) reached 31.6%. Among the 225 el i gi ble clin i cal tri als, 160 (71.1%) tri als were eval u at ing Drugs, fol lowed by stud ies eval u at ing Bi o log i cal prod ucts (13.3%). We found that phase, in ter ven tional model, al lo ca tion and main out come are sig nif i cant as so ci ated with the Bayesian de signed used. (Chi -Squared test, p -value < 0.05). Bayesian de signs are more likely to be used in early phases than in late phases and are less likely to be used in par al lel or crossover clin ical tri als ( Table 1 ).
Model -based de signs were ac counted for 28.4% (64/ 225). From them the most fre quent meth ods were the Bayesian Lo gis tic re gres sion with 59.4% and the Bayesian piece wise ex po nen tial sur vival re gression with 10.9%. Model av er age con tin ual re assess ment method and Bayesian piece wise ex po nen tial sur vival re gres sion were the most com mon Bayesian meth ods im ple mented in phases I/ II ( Fig. 2 ).
Ap prox i mately one -quarter of all tri als were us ing Bayesian Tox i city Mon i tor ing (26.2%) ap proach, the most fre quent was the Bayesian method of Thall, Si mon, and Estey. Among the Model -assisted methods, Bayesian op ti mal in ter val (BOIN) was the most fre quent de sign (94.4%). Around 30% of the stud ies has not de clared a spe cific Bayesian method.
144 stud ies (64.0%) re ported Na tional In sti tutes of Can cer or Hospi tals as the main source of fund ing in volve ment while 60 (26.7%) reported in dus try in volve ment ( Table 2 ). Fig. 3 shows Bayesian de sign seg re gated by trial fun der. Af ter the re clas si fi ca tion of source of fund ing, we found that Can cer in sti tutes are us ing this kind of de sign more than other fund ing in sti tu tions.
Most Bayesian stud ies in cluded both male and fe male par tic i pants (84.4%). 103 (45.8%) stud ies were in the process of re cruit ing and only 5.3% stud ies were al ready com pleted. Among these, 66.6% of them had re ported re sults of trial on ClinicalTrials. gov .
Av er age years of clin i cal trial du ra tion was of 4.63 with SD 3.19. Mean of par tic i pants per trial was 86 CI95% (71.1 -101.3).
The ther a peu tic area of all the in ter ven tion was man u ally sorted and the dis tri b u tion of ther a peu tic area is pre sented in Fig. 4 . The top 5 ther a peu tic ar eas were Hema to log i cal can cers (15.9%), Solid tu mors (10.6%), Brain tu mors (12.7%), Gas troin testi nal (10.1%), and Lung can cer (8.6%). Table 1 Main char ac ter is tics of clin i cal tri als.

. Discussion
This re view ex plores the use of Bayesian de signs in pub lished and pub licly avail able On col ogy tri als found in Clinicaltrials. gov . reg istry as the only in for ma tion source. We demon strated that Bayesian tri als were pre dom i nantly used in early -phase stud ies with a gen er ally small pro por tion of ran dom ized and par al lel as sign ment stud ies. Most of them were one group as sign ment and with open la bel de sign. Con sequently, these stud ies were dom i nant (66.8%) in our study.
Pub lished lit er a ture like our re view is lim ited for com par ing obtained re sults with those of other au thors, but there is a re search performed at the MD An der son Can cer Cen ter that has stud ied Bayesian ap proach in their clin i cal tri als in 2019. They re ported that Bayesian tri als were more com mon in phase I/ II tri als [ 16 ].
There are some re views re gard ing On col ogy tri als but not specif ically with a Bayesian ap proach in the de sign or analy sis that have reported sim i lar re sults about the main char ac ter is tics of clin i cal tri als in this med ical spe cialty [ 17 , 18 ]. It is com mon in On col ogy tri als to find this kind of phases fre quently [ 19 ].  We found that ap prox i mately half of the tri als stud ied ef fi cacy (response to treat ment) mean while other au thors re ported more stud ies mon i tor ing tox i c ity [ 13 ].

M. Fors and P. González
Com pared with tri als for sup port ive care, pre ven tion or di ag nos tic, more tri als were treat ment -oriented, mainly fo cused on new drugs eval u a tion.
Our re sults have shown that the Bayesian lo gis tic re gres sion model was the most used in phases I al though it can be found in other early phases. The BLRM is an other mod i fi ca tion of the CRM which up dates the es ti mate of the dosetoxicity curve based on the ac cu mu lat ing data and as signs the next co hort of pa tients to the cur rently es ti mated "op ti mal" dose [ 20 ].
Model av er age con tin ual re assess ment method and Bayesian piecewise ex po nen tial sur vival re gres sion were the most com mon Bayesian meth ods im ple mented in phases I/ II. In gen eral, CRM is a modelbased de sign for phase I tri als, which aims to find the max i mum tol erated dose (MTD) of a new ther apy. The CRM has been shown to be more ac cu rate in tar get ing the MTD than tra di tional rule -based approaches such as the 3 + 3 de sign, which is used in most phase I trials [ 21 ].
Bayesian method of Thall, Si mon, and Estey is Bayesian se quen tial mon i tor ing de signs for sin gle -arm clin i cal tri als. These au thors presented a Bayesian de ci sion cri te ria and mon i tor ing bound aries for early ter mi na tion of stud ies with un ac cept ably high rates of ad verse out comes or with low rates of de sir able out comes [ 13 ].
Bayesian Op ti mal In ter val (BOIN) was the most fre quent de sign among as sisted -models de signs. One ad van tage of in ter val de signs is that they are sim ple to im ple ment in prac tice. Be cause the in ter val is pre spec i fied, dur ing trial con duct, the de ci sion of which dose to admin is ter to the next co hort of pa tients does not re quire com pli cated com pu ta tions, but only a sim ple com par i son of the ob served tox i c ity rate at the cur rent dose with the pre spec i fied in ter val bound aries [ 22 ].
It ap pears that in the aca d e mic com mu nity the in ter est, or the knowl edge, for us ing Bayesian de signs are lim ited. Of the 225 tri als only a mi nor ity (9.8%) eval u ated new ther a peu tic al ter na tives funded by uni ver si ties. It seems that re searchers of In sti tutes of can cer are lead ing the way with in no v a tive Bayesian ap proaches in the treat ment in can cer re lated dis eases.
Ac cord ing to the study per formed by Califf et al. re ported that a great num ber of stud ies are funded by or ga ni za tions other than in dustry or the Na tional In sti tutes of Health. Most tri als reg is tered were rela tively small sam ples, with the av er age num ber of 80 par tic i pants per trial. Califf also re ported that most in ter ven tional tri als reg is tered between 2007 and 2010 were small, with 62% en rolling 100 or fewer par tic i pants [ 23 ].
More than half tri als were com pleted, and 66.6% of tri als had results avail able on the ClinicalTrials. gov , which in our con sid er a tion is a step for ward clin i cal tri als trans parency.
Sev eral clin i cal tri als are now run ning with de sign of Bayesian approach, maybe the rea son is the com pu ta tional ad van tage and complex is sue in data analy sis give the up -gradation of Bayesian ap proach over clas si cal meth ods [ 24 ].

. Conclusions
Bayesian tri als are more com mon in the early phases of drug devel op ment and rep re sent an in no v a tive means of in creas ing trial ef ficiency. This type of de sign has in creased over time among re searchers work ing at can cer in sti tutes or hos pi tals. Op ti miza tion of clin i cal trials is one of pos si ble ap proaches to speed the drug de vel op ment process mak ing bet ter use of all avail able in for ma tion. Bayesian sta tistics pro vides the op por tu nity to make clin i cal tri als more ef fi cient.

Strengths
We have pro vided a com pre hen sive de scrip tive and an a lytic assess ment of the cur rent in for ma tion re gard ing On col ogy Bayesian clin i cal tri als in the ClinicalTrials. gov reg istry from 1990 to Feb ru ary 2020. We fol lowed a strict analy sis to ar rive at re li able re sults.

Limitations
There are some lim i ta tions to this analy sis. Not all the in for ma tion re gard ing de sign was clear or com plete, some stud ies had lim ited spec i fi ca tion on the kind of Bayesian ap proach was used. Not all studies had a reg u larly up dated in for ma tion, which may lead to in ac curately re ported data. There are some clin i cal tri als world wide that are not reg is tered in this data base im ply ing that the clin i cal tri als included in this man u script may not be a rep re sen ta tive sam ple of studies with this de sign.

Data availability
The raw data that sup port the find ings of this study are avail able from the cor re spond ing au thor upon rea son able re quest.

Author contributions
M.F., P.G. con ceived the re search, M.F. processed data; M.F., P.G an a lyzed the data, wrote and con tributed to man u script edit ing.

Declaration of competing interest
The au thors de clare no com pet ing in ter ests.