Analytcal Procedure Valdaton and the Qualty by Desgn Paradgm Erc Rozet 1,*, Perre Lebrun 1, Jean-Franços Mchels 1, Perceval Sondag 1, Tara Scherder, Bruno Boulanger 1 Arlenda s.a., Lège, Belgum & Arlenda Inc, New-Jersey, USA 1 Arlenda S.A., 1 avenue de l hôptal, 4000 Lège, Belgum Arlenda Inc., 13 Ewng Drve, Flemngton, New Jersey, USA * Correspondng author: Erc Rozet, Arlenda S.A., 1 avenue de l hôptal, 4000 Lège, Belgum (+343664397, Fax: +343669683) emal: erc.rozet@arlenda.com 1
Abstract Snce the adopton of the ICH Q8 document concernng the development of pharmaceutcal processes followng a Qualty by Desgn (QbD) approach, there have been many dscussons on the opportunty for analytcal procedure developments to follow a smlar approach. Whle development and optmzaton of analytcal procedure followng QbD prncples have been largely dscussed and descrbed, the place of analytcal procedure valdaton n ths framework has not been clarfed. Ths artcle ams at showng that analytcal procedure valdaton s fully ntegrated nto the QbD paradgm and s an essental step n developng analytcal procedure that are effectvely ft for purpose. Adequate statstcal methodologes have also ther role to play: such as desgn of experments, statstcal modellng and probablstc statements. The outcome of analytcal procedure valdaton s also an analytcal procedure Desgn Space and from t, control strategy can be set. Keywords : Qualty by Desgn, Tolerance Intervals; Method Valdaton; Ft for Purpose;
1 Introducton The concept of qualty by desgn (QbD) has been adopted n the pharmaceutcal ndustry through several ntatves such as the FDA s cgmp for the 1st Century [1] and Process Analytcal Technology (PAT) [] as well as wth the regulatory documents ICH Q8 [3], Q9 [4] and Q10 [5] and the FDA gudance on Process Valdaton [6]. The general am s to swtch from the qualty by testng (QbT) paradgm prevously mplemented n the pharmaceutcal ndustry to a development amng at mprovng the understandng of the processes and products and hence mprovng products qualty, processes effcency and regulatory flexblty. QbD s not new and nvolves many qualty and statstcal tools and methods, such as statstcal desgns of experments, multvarate statstcs, statstcal qualty control, and so on. In order to rase the qualty of pharmaceutcal products, t has been recognzed that ncreasng the testng of fnal products (.e. QbT) s not adequate [7]. Instead, to ncrease the qualty of pharmaceutcal products, qualty must be bult nto the products (.e. QbD) as already done n many other ndustres. It requres understandng how varables nvolved n formulaton and manufacturng processes nfluence the qualty of the fnal product. Analytcal procedures are also processes and QbD should also be mplemented for the development of analytcal procedures. Several authors recently stated that Qualty-by-Desgn (QbD) enables to develop analytcal procedures n a systematc and scentfc approach [8-1]. The understandng and dentfcaton of varables affectng method performance s acheved at an earler stage [8-1]. Accordng to ICH Q8(R) [6], QbD can be seen as an optmzaton strategy combnng Desgn of Experments (DoE) and Desgn Space (DS). However, developed analytcal procedures are not drectly usable n laboratores as they have to demonstrate that they are ndeed ft for ther purpose. Ths demonstraton of ftness of purpose s generally acheved durng the analytcal procedure valdaton phase. 3
The am of ths artcle s to show that analytcal procedure valdaton s fully ntegrated nto the QbD paradgm and s an essental step n developng analytcal procedure that are useful for ther routne applcatons. Smlar statstcal methodologes are also mplemented n analytcal procedure valdaton among whch are desgn of experments and statstcal modelng. The outcome of analytcal procedure valdaton s also an analytcal procedure Desgn Space and from t control strategy can be further defned. Analytcal Target Profle and analytcal procedure valdaton The development of a Qualty by Desgn complant analytcal procedure starts by the defnton of ts Analytcal Target Profle (ATP) whch ams at defnng the ntended purpose of the procedure. The ATP comples a set of characterstcs defnng what analyte or analytes wll be measured, n whch matrx, over what concentraton range(s) as well as the requred performance crtera of the method together wth specfcatons for these last ones. These specfcatons and characterstcs should be lnked to the ntended purpose of the analytcal procedure. Examples of ATP for the nterested readers can be found n the followng references [8-11,13]. The requrements of quanttatve performances ncluded n the ATP are then the valdaton acceptance lmts that must be reached by the analytcal procedure durng the valdaton phase. In addton, several authors have gone further n the defnton of the ATP by ncludng maxmum acceptable rsk of makng wrong decsons usng the results generated by analytcal procedures [13]. 3 Crtcal Qualty Attrbute n analytcal procedure valdaton The Crtcal Qualty Attrbutes (CQAs) of the analytcal procedure are the responses that are measured to judge the qualty of the developed analytcal procedures. CQAs are defned as a physcal, chemcal, bologcal or mcrobologcal property or characterstc that should be wthn an approprate lmt, range, or dstrbuton to ensure the desred product qualty [3]. For chromatographc analytcal procedures the CQAs can be related to the method selectvty, such as 4
the resoluton (R S ) or separaton (S) crtera [1]. Other CQAs can be the run tme of the analyss, sgnal to nose rato, the precson and the trueness of the analytcal procedure, the lower lmt of quantfcaton or the dosng range of the analytcal method. These CQAs may be drectly modeled through a multvarate (non-)lnear model. However n other stuatons, the modeled responses may be dfferent than the CQAs. The CQAs are obtaned after the modelng of these prmary responses. For chromatographc methods, the usual key CQA s resoluton of the crtcal par when optmzng selectvty. However resoluton depends on the retenton factor of the two chromatographc peaks nvolved. Therefore, the retenton factors are drectly modeled nstead of the resoluton. The resoluton can then be computed from these modeled responses. Nonetheless, CQAs are not lmted to separatve technques or only related to the qualtatve performance of the analytcal procedure. Hghly mportant assays n the development and control of pharmaceutcal products are quanttatve ones. Other examples than chromatographc quanttatve procedures are mmunoassays such as ELISA, q-pcr, relatve potency assays, and so on. The fnal am of any quanttatve analytcal procedures s to provde analytcal results of adequate qualty n order to make relable decsons wth them. Hence crtcal qualty attrbutes for quanttatve procedures should be at least related to ther quanttatve performances. The valdaton characterstcs that are trueness, precson, lnearty, range, LOQ of the analytcal procedure and the accuracy of the results obtaned by the procedure are key CQAs. They should be ncluded nto the defnton of the ATP together wth ther respectve acceptance values. The valdaton phase of any quanttatve analytcal procedure s therefore fully n lne wth the QbD framework. The CQA that should be montored durng analytcal procedure valdaton are measures related to random error (e.g. ntermedate precson CV), systematc error (e.g. bas or recovery) or the combnaton of both whch s total error. 5
4 Crtcal Process Parameters n Analytcal Procedure Valdaton Analytcal Procedures Valdaton also nvolves several factors that are crtcal process parameters. The frst man factor s concentraton/amount/potency range over whch the procedure s ntended to quantfy the analyte. Ths factor s a fxed factor and s represented by samples called valdaton standards or qualty control samples of known concentraton/amount/potency. By opposton, sources of varablty that wll be encountered durng the future routne use of the procedure must be ncluded n the valdaton desgn as random factors, such as operator, equpment, reagent batch or days. The combnaton of these sources of varablty s generally called runs or seres. 5 Desgn of Experments n Analytcal Procedure Valdaton ICH Q8 and FDA gudelne hghly promote the use of adequate desgn of experments when developng pharmaceutcal processes. The man desgns used n analytcal procedure valdaton are nested desgns or (fractonal) factoral desgns or a combnaton of both. These desgns are used to estmate varance components. To have precse estmatons, the use of more than two levels of each factor s recommended. Nonetheless, the varous sources of varaton ncluded nto the analytcal procedure valdaton are generally combned nto seres or runs to mmc the way analytcal procedures are effectvely employed routnely. Suppose that for each of the th concentraton level of the valdaton standards, the number of runs s J and that n each run, K replcates are performed. The valdaton experments can then be descrbed, for each of the th concentraton level studed, by a one way Analyss Of Varance (ANOVA) random model wth runs (or seres) as random factor: X ( 0, σ ), ε ~ N( 0 σ ), jk µ + α, j + ε, jk, α, j ~ N α,, jk, ε, = Eq. 1 6
where µ s the overall mean of the th concentraton level studed of the valdaton standard, µ + α, j s the mean n run j (j: 1 to J),, jk ε s the resdual error, σ α, s the run-to-run varance, and σ ε, s the wthn-run or repeatablty varance, both for the th concentraton level. The overall varablty of the analytcal method s measured by the ntermedate precson varance σ = σ α + σ. All these parameters of the varance components model can be estmated by I. P.,, ε, REML methods [14]. 6 Desgn Space and Analytcal Procedure Valdaton In the ICH pharmaceutcal development gudelne Q8 [3], the DS s defned as the multdmensonal combnaton and nteracton of nput varables (e.g. materal attrbutes) and process parameters that have been demonstrated to provde assurance of qualty. Therefore, the multdmensonal combnaton and nteracton of nput varable corresponds to a subspace, so-called the DS, where assurance of qualty has been proven. The man concept lyng behnd the ICH Q8 defnton of DS s assurance of qualty (also known as qualty rsk management). It has been already shown that mean response surface obtaned durng analytcal procedure development do not defne properly a DS as there s no assurance that the CQAs reach ther acceptance lmts. Instead probablty maps answer ths DS requrement properly [1,15]. Analytcal procedure valdaton also allows defnng a DS: t s the range of concentraton where t has been demonstrated that the procedure provdes assurance of qualty results.e., π P ( λ < X µ < λ) Eq.. = T The objectve of the valdaton phase can be summarsed to evaluate whether the relablty probablty π that each future result wll fall wthn predefned acceptance lmts (λ) s greater than or equal to a mnmum clamed level π mn [16]. The statstcal problem here s two-fold: the probablty π needs to be estmated and the uncertanty n ts estmaton must be taken nto 7
account when comparng t to π mn. Ths s not an easy problem to solve snce t has no exact small sample soluton n frequentst statstcs. Nonetheless, several approaches have been proposed to answer ths am. 6.1 β-expectaton tolerance ntervals A frst one s to compute β-expectaton tolerance ntervals of a defned coverage probablty (e.g. 95%) at each concentraton level of the valdaton standards usng the one way ANOVA random model descrbed n Eq. 1 and comparng t to preset acceptance lmts as shown n Fgure 1. Usng ths approach, each future result has at least 95% probablty to fall wthn these acceptance lmts. Lebrun et al. [17] have shown that β-expectaton tolerance ntervals are equvalent to Hghest Posteror Densty (HPD) ntervals. A non-neglgble amount of analytcal procedures have been valdated n such a way [16, 18-19]. Fgure 1 shows an accuracy profle obtaned for the valdaton of an analytcal procedure depctng at each concentraton level of the valdaton standards the 95% β - expectaton tolerance nterval. 8
Fgure 1.: Accuracy profle, depctng at each concentraton level of the valdaton standards the correspondng 95% β -expectaton tolerance ntervals (blue dashed lnes). The acceptance lmts have been set at +/-15% around the known concentraton values of the valdaton standards (black dotted lnes). The red contnuous lne shows the relatve bas of the assay. The green dots are the analytcal results of the valdaton standards expressed n relatve error values. 6. Out Of Specfcaton probablty Another approach s to estmate the probablty to obtan future results outsde the preset acceptance lmts (Out Of Specfcaton, OOS). Dewé et al.[0] has proposed to compute ths probablty for results followng the one way ANOVA random model descrbed n Eq. 1. An example s shown n Fgure for the same prevous analytcal procedure. The DS s then the range of concentraton over whch ths probablty s smaller than a preset maxmum value (e.g. 0.05). For each concentraton level ths probablty s computed as: π Bet = P [ X > µ λ] + P[ X < µ + λ] = P t ( f ) T, T, ( µ T, λ) X > + P t( f ) < KRˆ + 1 ˆ σ 1+ ( + ) ˆ I. P., σ I. P., N Rˆ 1 ( µ + λ) T, X KRˆ 1+ N + 1 ( Rˆ + 1) Eq. 3. where J s the number of runs and K the number of replcates by seres, N=JK. X s the mean concentraton of the results obtaned by the method for the th concentraton level and ˆ σ s the I. P., ntermedate precson standard devaton for each th concentraton level. t(f) s a student dstrbuton wth f degrees of freedom computed based on the Satterthwate approxmaton [1] and Rˆ s the rato between the run-to-run varance and the wthn-run (or repeatablty) varance of each 9
concentraton level. The use of a Student dstrbuton s justfed as t s the predctve dstrbuton n ths model as demonstrated by Lebrun et al. [17]. Fgure.: Rsk profle, gvng at each concentraton rang of the valdaton standards the probablty to have future analytcal results fallng outsde an acceptance value of +/- 15% around the known concentraton values of the valdaton standards,.e. OOS probablty. The maxmum OOS probablty has been set at 5%. 6.3 Contnuous modelng across concentraton range: the Bayesan way If between-run varances and repeatablty varances can be assumed homogenous across the concentratons levels of the valdaton standards, a sngle lnear mxed model can be ftted to the valdaton data, ncludng concentraton as a fxed factor. The two prevous approaches to defne a DS can then be extended to ths stuaton. A less trval stuaton would be to model the analytcal procedure results over the concentraton range n case of heteroscedastcty of between-run and/or repeatablty varance. Determnaton of β 10
-expectaton tolerance ntervals or probablty of OOS n these cases could be based on Bayesan approaches as no frequentst solutons are avalable []. In ths context model Eq. s rewrtten as the followng lnear model wth random slopes and ntercepts and resdual varance ncreasng wth concentraton: X jk = + β1µ T, + u0, j + u1, j µ T, β 0 + ε Eq. 4. jk where the subscrpts stands for the I concentraton levels of the valdaton standards, j for the J number of seres or runs and k for the K number of replcates per run. µ T, s the th concentraton level of the valdaton standard and s consdered as a reference or conventonal true value. θ β 0 = β1 are the fxed effects. Addtonally, u0, j U = j are the random effects of the j th runs and u1, j are also assumed comng from a normal dstrbuton: U ~ N( 0, σ Σ ) Eq. 5. j u x Fnally, ε jk s the resdual error assumed to be ndependent and comng from a normal dstrbuton of varance σ. Ths varance s also gven as beng dependent on the concentraton level. Ths phenomenon s frequently observed n real lfe stuatons. The general form of ths varance functon s a power of the concentraton: ( µ ) γ σ = σ Eq. 6. T, 11
Fgure 3 llustrates a probablty profle for an analytcal procedure usng ths model and estmated usng MCMC smulatons. It depcts the concentraton range over whch the analytcal procedure s ft for ts purpose. Ths range represents the analytcal procedure valdaton Desgn Space. Fgure 3: Bayesan rsk profle, modelng over the concentraton range studed the probablty to have future analytcal results fallng outsde an acceptance value of +/- 15% around the known concentraton values of the valdaton standards,.e. OOS probablty. The maxmum OOS probablty has been set at 5%. The Lower lmt of quantfcaton corresponds to the concentraton where the OOS probablty crosses the maxmum OOS probablty value of 5%. 7 Control Strategy Qualty by Desgn development of analytcal procedure s useless wthout defnng control strategy to ensure that the procedure remans under control durng ts routne applcaton and detect devatons. Valdaton Analytcal procedure valdaton also allows defnng a control strategy usng qualty control samples. Indeed, the experments performed allow e.g. defnng β-expectaton tolerance ntervals that can be used as ntal control lmts when buldng analytcal procedure control charts [3]. Out of control methods can effcently be detected and correctve actons realzed by followng the daly performances of analytcal methods on such charts. Indeed, the use of β- expectaton tolerance ntervals ensures an adequate balance between consumer and producer rsks [3]. 1
8 Concluson Analytcal procedure valdaton fts entrely wthn the QbD paradgm. In fact when comparng t wth pharmaceutcal development, analytcal procedure valdaton can be seen at the stage of process valdaton as defned by the recent FDA gudelne [6]. Analytcal procedure valdaton s then the performance qualfcaton of the assay. In ths context, seeng analytcal procedure valdaton as an addtonal burden n analytcal procedure development lmted to the ICHQ[4] check lst exercse should dsappear: the valdaton phase s the confrmaton of the usefulness of the developed procedure for ts future daly applcaton. References [1] U.S. Food and Drug Admnstraton (FDA), Department of Health and Human Servces, Pharmaceutcal Qualty for the 1st Century A Rsk-Based Approach Progress Report, May 007. http://www.fda.gov/aboutfda/centersoffces/cder/ucm18080.html [] Unted States Food and Drug Admnstraton (FDA), Gudance for ndustry PAT-A framework for nnovatve pharmaceutcal manufacturng and qualty assurance, FDA, 004. [3] Internatonal Conference on Harmonzaton (ICH) of Techncal Requrements for Regstraton of Pharmaceutcals for Human Use, Topc Q8 (R): Pharmaceutcal Development, Geneva, 009. [4] Internatonal Conference on Harmonzaton (ICH) of Techncal Requrements for Regstraton of Pharmaceutcals for Human Use, Topc Q9: Qualty Rsk Management, Geneva, 005. [5] Internatonal Conference on Harmonzaton (ICH) of Techncal Requrements for Regstraton of Pharmaceutcals for Human Use, Topc Q10: Pharmaceutcal Qualty System, Geneva, 008. 13
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