Deriv­ing a De­sign Space with DOE and Risk Es­ti­mate

BioSpectrum (India) - - TECHNOLOGY - David Wang Se­nior Data Sci­en­tist

David Wang is a Se­nior Data Sci­en­tist at Sar­to­rius Ste­dim Data An­a­lyt­ics based out of Sin­ga­pore. David has a Ph.D. in Chem­i­cal En­gi­neer­ing, M. Eng. in Con­trol The­ory and En­gi­neer­ing, and B. Sci. in Math­e­mat­ics and Sta­tis­tics. He works on im­prov­ing ef­fi­ciency, op­ti­mal­ity and prof­itabil­ity of prod­uct de­vel­op­ment, process de­vel­op­ment, and man­u­fac­tur­ing pro­cesses (Pharma, Bio­pharma, Chem­i­cal, Food & Feed, Life Sciences, etc.) by ap­ply­ing ad­vanced data an­a­lyt­ics tech­nol­ogy, where the work is fo­cused on data-driven modelling, process mon­i­tor­ing, process con­trol, De­sign of Ex­per­i­ments, PAT and QbD.

DOE is the key tool for QbD and De­sign Space.

De­sign of Ex­per­i­ments (DOE) has been in­creas­ingly used in the bio­phar­ma­ceu­ti­cal in­dus­try for prod­uct and process de­vel­op­ment as a means to sat­isfy reg­u­la­tions around Qual­ity by De­sign (QbD) and to de­rive a com­bi­na­tion of pa­ram­e­ters that en­sure the prod­uct to meet the de­fined qual­ity at­tributes, also known as a De­sign Space. DOE is a tech­nique used in plan­ning ex­per­i­ments and sub­se­quently an­a­lyz­ing the data ob­tained. This tech­nique al­lows us to sys­tem­at­i­cally vary sev­eral ex­per­i­men­tal pa­ram­e­ters si­mul­ta­ne­ously to ob­tain suf­fi­cient in­for­ma­tion us­ing the min­i­mum num­ber of ex­per­i­ments. Based on the ob­tained data, a math­e­mat­i­cal model of the stud­ied process (e.g., a pro­tein pu­rifi­ca­tion pro­to­col or a chro­matog­ra­phy step) is cre­ated. The model can then be used to find an op­ti­mum for the process and to un­der­stand the in­flu­ence of the ex­per­i­men­tal pa­ram­e­ters on the out­come. Mod­ern soft­ware is used to cre­ate the ex­per­i­men­tal de­signs, to ob­tain a model, and to vi­su­al­ize the gen­er­ated in­for­ma­tion (Fig­ure 1 shows an ex­am­ple for find­ing a re­gion where qual­ity at­tribute is sat­is­fied).

De­sign space has to ad­dress risk man­age­ment.

Although DOE can de­rive a re­gion that sup­pos­edly sat­is­fies the qual­ity at­tributes, tak­ing this re­gion as the de­sign space will be overop­ti­mistic. This is be­cause there is al­ways un­cer­tainty in terms of model er­ror and mea­sure­ment ac­cu­racy. With­out con­sid­er­ing this un­cer­tainty, there is a high risk of fail­ure from sim­ply se­lect­ing an op­ti­mum and tak­ing it as the oper­at­ing set­point. Fig­ure 2 il­lus­trates that a re­al­is­tic out­come of model pre­dic­tion (Yield) should be a prob­a­bil­ity dis­tri­bu­tion rather than a sin­gle value when faced with un­cer­tainty in pa­ram­e­ters vari­a­tions, model er­rors, mea­sure­ments sys­tems, and process vari­abil­ity. It can be en­vis­aged that not ev­ery point be­yond the min­i­mum re­sponse con­tour in Fig­ure 1 would guar­an­tee >80% yield, the re­gion for de­sign space in In­sulin pu­rifi­ca­tion ex­am­ple could be smaller than it dis­played in Fig­ure 1.

How to de­fine a re­gion that will ful­fil the prod­uct spec­i­fi­ca­tion pro­file with a qual­ity es­ti­mate.

Sar­to­rius-Ste­dim Biotech ex­perts typ­i­cally use MODDE® De­sign of Ex­per­i­ments So­lu­tion for Bio­pharm process de­vel­op­ment and ser­vices.

They have gained sig­nif­i­cant ex­pe­ri­ence through suc­cess­fully de­liv­er­ing many di­verse process de­vel­op­ment projects, and they have trained a num­ber of bio­pharma sci­en­tists and engi­neers who can eas­ily use the soft­ware.

Given spec­i­fi­ca­tion of pos­si­ble vary­ing ranges of pa­ram­e­ters, Monte Carlo sim­u­la­tion on the DOE model would es­ti­mate a new re­gion that sat­is­fies the qual­ity at­tribute with a risk anal­y­sis cri­te­ria. It would gen­er­ate a prob­a­bil­ity con­tour plot for us to vi­su­al­ize the re­gion with dif­fer­ent lev­els of cer­tainty so that we have con­fi­dence in se­lect­ing the oper­at­ing set­point. In ad­di­tion, the soft­ware has an Op­ti­mizer tool which can eas­ily de­rive a ro­bust set­point which is lo­cated at the cen­tre in the (of­ten highly) ir­reg­u­lar de­sign space vol­ume, far from all the bound­aries. This fur­ther re­duces the risk (Fig­ure 3).

The set­point anal­y­sis that is pro­vided by the soft­ware is an­other ex­cel­lent plat­form for anal­y­sis of ev­ery given set­ting, im­pos­ing prac­ti­cal ad­just­ments to the al­low­able pa­ram­e­ter ranges and eval­u­ates the con­se­quences of such changes. Com­ing back to the In­sulin case study, by reg­u­lat­ing Salt and EtOH set­points and their dis­tur­bances, we can in­spect the pre­dicted

Yield dis­tri­bu­tion (Fig­ure 4). With this, we can un­der­stand how the Yield changes with the Salt and EtOH set­tings and their dis­tur­bances, and de­ter­mine proven ac­cept­able ranges (PAR) for the pa­ram­e­ters.

Fig­ure 2. The ef­fect of vari­a­tion in Salt, EtOH, and model er­ror on the Yield. The out­come from model pre­dic­tion should be a prob­a­bil­ity dis­tri­bu­tion con­sid­er­ing the model er­ror, mea­sure­ment er­rors, and vari­a­tions in pa­ram­e­ters. In­sulin pu­rifi­ca­tion ex­am­ple: Salt and EtOH as pa­ram­e­ters, Yield as re­sponse.

Fig­ure 1. Use of model to vi­su­al­ize and iden­tify the re­gion where Yield is larger than 80% in in­sulin pu­rifi­ca­tion con­sid­er­ing Salt and EtOH fac­tors

Fig­ure 3. The prob­a­bil­ity con­tour plot after Monte Carlo sim­u­la­tion of DOE model. The green area shows 99.9% cer­tainty that Yield > 80%. The out­skirt line in­di­cates that there is 50% cer­tainty that Yield >80%. The Cross-hairs shows the ro­bust set­point, Dot­ted frame shows de­sign space hy­per­cube in 2D.

Fig­ure 4. Set­point anal­y­sis func­tion­al­ity in MODDE. We can ad­just the Salt and EtOH set­tings and their dis­tur­bance ranges in the slid­ing bars (Above) to in­spect their dis­tri­bu­tions and dis­tri­bu­tion of Yield (Be­low).

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