Sampling in Pharmaceutical and Chemical Industries

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Samplig i Pharmaceutical ad Chemical Idustries Itroductio There are some characteristics of the pharmaceutical ad chemical idustries that make a differece o how samplig ispectios are performed.

1 Samplig i Pharmaceutical ad Chemical Idustries Itroductio There are some characteristics of the pharmaceutical ad chemical idustries that make a differece o how samplig ispectios are performed. The product characteristics are give by biological, chemical, ad physical measuremets. It is ofte related to batch productio. At least for the pharmaceutical idustry they are ofte highly regulated by govermet authorities with high demads o quality stadards ad level of documetatio. The measuremet methods beig used iclude both slow ad expesive off-lie methods ad fast ad cheap o-lie measuremets. The tred i these idustries is that more of the fast ad cheap o-lie methods become available ad to some extet replace the off-lie methods. This also meas that larger samplig ad data evaluatio becomes a itegrated part of samplig ispectio ad batch release. The US Food ad Drug Admiistratio (FDA) has recetly lauched a process aalytical techology (PAT) iitiative supportig this developmet, see [1]. A desired goal of the PAT framework is to desig ad develop processes that ca cosistetly esure a predefied quality at the ed of the maufacturig process. Such procedures would be cosistet with the basic teet of quality by desig ad could reduce risks to quality ad regulatory cocers while improvig efficiecy. Gais i quality, safety, ad/or efficiecy vary depedig o the product ad are likely to come from the followig actios: improvig eergy ad material use ad icreasig capacity. There are obviously large beefits to gai from this developmet for the customers i terms of quality, safety, ad cost. There will still be a eed to perform off-lie measuremets ad classical samplig ispectio ad release testig i the pharmaceutical ad chemical idustries as there may be o alterative. Samplig uder Measuremet Ucertaity Samplig of discrete items i lots for ispectio is maily used i the medical device part of the idustry. Figure 1 is a example of a perso with diabetes ijectig himself with a prefilled isuli pe. The example illustrates the critical eviromet for certai medical products, hece the eed for documeted high quality products. This is why, for this part of the idustry, there may be a specific eed for takig measuremet ucertaity ito cosideratio. Samplig plas for ispectio by attributes are give i the ISO stadard series ISO 859 []; ad similar plas for ispectio by variables are give by the ISO stadard series ISO 3951 [3]. It is a geeral idea at least amog statisticias that samplig by variables is a more efficiet procedure for acceptace samplig, tha samplig by attributes. This idea is supported by the fact that uder a correct model, a parametric estimator of the fractio ocoformig is reducig productio cycle times by usig o-lie measuremets ad cotrols; prevetig rejects, scrap, ad reprocessig; cosiderig the possibility of real-time release; icreasig automatio to improve operator safety ad reduce huma error; facilitatig cotiuous processig to improve efficiecy ad maage variability usig small-scale equipmet (to elimiate certai scale-up issues) ad dedicated maufacturig facilities, Figure 1 Perso with diabetes ijectig himself with a prefilled isuli pe

2 Samplig i Pharmaceutical ad Chemical Idustries more efficiet tha the oparametric estimator based upo the crude cout of ocoformig items i the sample. I idustrial praxis, a importat issue is the presece of measuremet errors. I the measuremet situatio, the ideal situatio is of course that measuremet errors are egligible compared to the tolerace iterval of the item to be measured. This is ot always the case, though. For medical devices there are ofte high requiremets o certai critical parameters, e.g. the dosig accuracy. This agai leads to high requiremets o the idividual compoets i the tolerace stack up. Both the ISO stadards metioed before [, 3] cosider the case of egligible measuremet errors. Therefore, i the followig, we shall discuss the implicatios of usig acceptace samplig by variables uder measuremet error. The theory for acceptace samplig by variables uder a ormal distributio dates back to the papers by Lieberma ad Resikoff [4] ad [5]. The curret ISO stadard with samplig plas, ISO 3951 [3], is based upo this origial idea of basig the test upo a miimum variace, ubiased estimate of the fractio ocoformig i the process. A descriptio of the theory may be foud i [6]. I [7], Owe ad Chou, cosider the effect of measuremet error ad a costat offset error o the operatig characteristic (OC) curves (see Sigle Samplig by Attributes ad by Variables) ofthe oe-sided plas. I [8], Thyregod ad Melgaard, however, exted these cosideratios to the doublesided plas i the case of measuremet error ad a radom laboratory bias. We shall assume that items i a lot are produced from a i-cotrol process. Let X deote the quatity of iterest. We shall assume that the distributio of X over the items i a lot may be described by idepedet ad idetically distributed (i.i.d.) radom variables that follow a ormal distributio with mea E(X) = µ ad V(X) = σ. It should be oted, that i pharmaceutical ad chemical processes the assumptio of idepedet items i a lot ofte must be challeged. Simple graphical methods such as plottig the items i the order of productio will ofte reveal correlatios that must be take ito accout. Let the specificatio limits for X be upper limit, U, ad lower limit, L, respectively. The fractio of ocoformig items, p, is the fractio of items below Lor above U. I the related article Variables Samplig uder Measuremet Error the case of high-frequecy measuremet error is discussed i detail. High-Frequecy Measuremet Error Assume that the quatity of iterest caot be measured without measuremet error. Let Y = Y(X) deote the measuremet result for a item with value X. Assume that Y i = X i + E i (1) where E 1,...,E are i.i.d. ad ormally distributed with E(E i ) = 0adV(E i ) = σ i.let,asusual, Y = Y i () ad sy = (Y i Y) ( 1) (3) The Y follows a ormal distributio with E(Y) = µ ad V(Y) = (σ + σe )/, ad s y /σ follows a (1 + σe /σ )χ (f )/f distributio with f = 1, ad Y ad sy are idepedet. For simplicity we will use the OC curves, correspodig to the oe-sided plas, which are similar to the oes give i ISO These will be close to the double specificatio limits case, whe σ σ max. It is show i [8] that by usig the same samplig pla from ISO 3951 but i this case radom measuremet error is preset accordig to the model (1) the OC curve is give by { } L 1 (p) = P U Y s y k = P {t 1,δ1 k } (4) where δ 1 = z p / 1 + σ e /σ. Oe thig to remark is that the OC curve i the case of radom measuremet oise is always to the left of the oisefree OC curve, which meas that i the case of high-frequecy measuremet oise; there is a higher chace of rejectig the batch. A example from ISO 3951 is give by Figure. Low-Frequecy Measuremet Error Assume istead that the major part of the measuremet error is a radom laboratory or istrumet bias that affects all measuremets i the same maer, i.e. Y i = X i + B (5)

3 Samplig i Pharmaceutical ad Chemical Idustries 3 Pa Percetage defective Pa Percetage defective Figure OC curves uder high-frequecy measuremet error, AQL = 6.5, code K, =, σ e = 0.σ, the dashed curve is for the model without measuremet error Figure 3 OC curves uder low-frequecy measuremet error, AQL = 6.5, code K, =, σ B = 0.σ, the dashed curve is for the model without measuremet error where B varies from lot to lot as i.i.d. ad ormally distributed with E(B) = 0 ad V(B) = σb. Uder this assumptio we have that Y follows a ormal distributio with E(Y) = µ ad V(Y) = σb + σ e /, ad sy /σ follows a χ (f )/f distributio with f = 1, ad Y ad sy are idepedet. Thus, i this case the ucertaity of the estimate, Y,ofthe positio, is heavily iflueced by the measuremet ucertaity, but the estimate, sy of the process spread is ot affected. The OC curve for this model is the give by { } U Y L (p) = P k s y = P t k 1,δ 1 + σb /σ (6) where δ = z p / 1 + σb /σ.ifwelet = 1 + σb /σ (7) i the equatio for L (p) we see, that the equatio is very close to the oise-free oe, but with a sample size of. The oly differece is that the degrees of freedom i the t distributio are ot chaged. This meas, that approximately the OC curve i case of a systematic measuremet error is similar to the OC curve of the oise-free case, but with a reduced sample size. I the example give by Figure 3, we have a sample size of = ad a measuremet ucertaity of σ B = 0.σ. Approximately this correspods to the OC curve of the oise-free case with a sample size of = = 16.7 (8) 1 + (0.) This fact is also revealed from Figure 3. It is importat to otice the differece betwee the oisefree case ad the situatios with high-frequecy as well as low-frequecy oise. Especially for testig i the pharmaceutical ad chemical idustries the measuremet ucertaity is ot egligible. This requires that the measuremet method is well documeted, icludig quatificatio of the high- ad low-frequecy measuremet error. Sice the ifluece of a low-frequecy measuremet error ca be large, as show i the previous example, steps will ormally be take to miimize this effect, e.g. by calibratig betwee samplig of lots. Bulk Samplig Purpose ad Procedure of Bulk Samplig Chemical aalyses of bulk materials as powder or liquids are ofte foud i the pharmaceutical ad chemical idustries by its ature. Samplig ca be used for the ispectio of raw materials, itermediate products, or fial product release. I this case a lot is a defiite quatity of bulk material. The quality

4 4 Samplig i Pharmaceutical ad Chemical Idustries of the lot is measured by a sigle suitable quality idicator, e.g. the cotet of active igrediet. It is assumed that the mea quality of the lot is to be determied ad that this is the factor used for determiig the acceptability of the lot. I this case, acceptace samplig plas ad procedures for the ispectio of bulk materials are foud i ISO 1075 [9]. A umber of icremets (smaller volumes), k, of the same size are take radomly from the lot. These icremets are mixed ito a gross sample. From this gross sample a laboratory sample is prepared ad a umber of samples, m, is take from this laboratory sample ad aalyzed idividually. The results, x i, i = 1,...,m, are combied ito a sigle mea value that is represetative of the lot. The mea value of the aalyzed samples is used as the estimate of the mea quality of the lot. The mea is calculated as x = m i=1 x i m (9) The ucertaity (variace) of this mea value is give by V(x) = σ A k + σ B + σ C (10) m where σa is the variace of the icremets from the bulk due to variatios betwee cotaiers ad withi cotaiers, σb is the variace associated with the preparatio of the laboratory sample take from the gross sample, σc is the variace describig the ucertaity from preparig ad aalyzig the idividual samples for aalyses take from the laboratory sample. The model above is a simple statistical model describig the bulk samplig situatio. To have a statistical ratioale for the choice of k, the umber of cotaiers to sample from, ad the choice of m, the umber of chemical aalyses to perform, some estimates of the variace compoets must be foud, e.g. from desiged statistical experimets, see [9]. Retestig of Bulk Materials Retestig is whe ew laboratory samples are take from the gross sample of a lot to be aalyzed because of suspicious aalytical results. For specific chemical or biochemical laboratory aalysis, a large umber of steps are ivolved ad the aalyses are ot always fully automated. I these cases there is a possibility of occasioal (huma) errors affectig the results. Therefore, there are well-described procedures for good maufacturig practice (GMP) icludig procedures for hadlig out-of-specificatio (OOS) measuremet results, see [10]. I the case of discrete items hadled i the sectio titled Samplig uder Measuremet Ucertaity, the ISO stadards have built-i procedures o how to hadle the situatio of OOS results ad batch rejectio. The procedure [10], applies to laboratory testig. It applies to the situatio described previously where the mea quality of the lot is of iterest. It does ot apply if the purpose of the aalyses is to measure uiformity of a lot, e.g., cotet uiformity, release profile, ad powder bled. To idetify the cause of the OOS result, statistical hypothesis testig may be relevat. Hypothesis testig may cosist of repetitio of the test procedure or part of the procedure, or of experimets desiged specifically with the purpose of idetifyig a aalytical problem. Below is a example of retestig. Use of t-test to Compare OOS Results ad Retest Results. The t-test is appropriate i a retest situatio where a OOS result is compared to a group of results obtaied specifically, to compare it to the earlier result, as described by Søre Aderse [11]. The test statistic is give by T = OOS m retest /(s retest (1 + 1/m)) (11) where m retest ad s retest are the mea ad stadard deviatio of the retest results ad m is the umber of retests. The retest samples should be represetative of the lot beig sampled, i.e., use the gross sample from the previous test or create a ew gross sample based o icremets radomly take from the lot. The calculated test statistic, T, is compared to the critical value of the t-test, give e.g., i [11]; if T is greater tha the 5% critical value, the OOS is cosidered a statistical outlier. If the OOS result is cosidered a statistical outlier, we have a strog idicatio that the result is due to a laboratory error. A qualified perso should the be able to evaluate the ecessary steps to evetually release the batch.

5 Samplig i Pharmaceutical ad Chemical Idustries 5 Refereces [1] FDA PAT iitiative: PAT.htm, 005. [] ISO 859, series Samplig Procedures for Ispectio by Attributes, Iteratioal Orgaizatio for Stadardizatio, [3] ISO (1989). Samplig Procedures ad Charts for Ispectio by Variables for Percet Nocoformig, Iteratioal Orgaizatio for Stadardizatio, Geeva. [4] Resikoff, G.J. (195). A ew two-sided acceptace regio for samplig by variables, Techical Report No. 8, Applied Mathematics ad Statistics Laboratory, Staford Uiversity, Staford. [5] Lieberma, G.J. & Resikoff, G.J. (1955). Samplig plas for ispectio by variables, Joural of the America Statistical Associatio, [6] Schillig, E.G. (198). Acceptace Samplig i Quality Cotrol, Marcel Dekker, New York. [7] Owe, D.B. & Chou, Y.-M. (1983). Effect of measuremet error ad istrumet bias o operatig characteristics for variables samplig plas, Joural of Quality Techology 15, [8] Melgaard, H. & Thyregod, P. (001). Acceptace samplig by variables uder measuremet ucertaity, i Frotiers i Statistical Quality Cotrol, H.-J. Lez & P.Th. Wilrich, eds, Physica-Verlag, Heidelberg, Vol. 6, pp [9] ISO (000). Acceptace Samplig Plas ad Procedures for the Ispectio of Bulk Materials, Iteratioal Orgaizatio for Stadardizatio. [10] Guidace for Idustry Ivestigatig Out-of-Specificatio (OOS) Test Results for Pharmaceutical Productio, Ceter for Drug Evaluatio ad Research (CDER) ad U.S. Food ad Drug Admiistratio, 006. [11] Aderse, S. (004). A Alterative to the ESD Approach for Determiig Sample Size ad Test for Out-of- Specificatio Situatios, Pharmaceutical Techology, May 004. HENRIK MELGAARD

FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures

FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals