Smilde, Age Klaas

English

Multivariate techniques used in this thesis are described in Part I. Techniques to select markers are of special interest. Quantitative methods like the induced-variance- and determinant criterion work well in practice. Other techniques - DISNORM, Procrustus analysis and variants - are worth trying. Another important issue is the use of three-way methods. These methods provide a general framework for thinking about calibration problems. ... Zie: Summar

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   University of GroningenMultivariate calibration of reversed-phase chromatographic systemsSmilde, Age KlaasIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1990Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Smilde, A. K. (1990). Multivariate calibration of reversed-phase chromatographic systems. [Thesis fullyinternal (DIV), University of Groningen]. [s.n.].CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 13-02-2023SrnruÍraryMult ivariate techniques used in this thesis are described inPar t  I .  Techn iques  to  se lec t  markers  a re  o f  spec ia l  in te res t . 'Quant i -tat ive methods l ike the induced-variance- and determinant cr i ter ionwork well  in practice. Other techniques - DISNORM, Procrustus ana-lysis and variants - are worth trying. Another important issue is theuse of three-way methods. These rnethods provide a general frameworkfor thinking about cal ibrat ion problems.Part I I  gives recent relevant developments in the f ield of stat ion-ary -  and mob i le  phase op t in ísa t ion  o f  reversed-phase sys tems;  ca l ib -ra t ion  in  GC,  TLC and RP-HPLC and re la ted  misce l laneous top ics .  Oneof the important conclusions of Part I I  is the idea that correctionof retention values to compensate for changÍng measurement condit ionsis performed best with a set of compounds similar to thecompounds o f  in te res t .  The ca l ib ra t ion  s t ra teg ies  presented  inChapter  8  re ly  on  th is  p r inc ip le :  re fe rence s tandards  (markers )  a reselected which are specif ic for the separation problem at hand,The ca l ib ra t ion  s t ra teg ies ,  p resented  in  Chapter  8 ,  a re  d iv ided int\ro groups: the two- and three-way approaches. I f  a stat ionary phaseis  conce ived as  an  ob jec t ,  then a  t ra in ing  se t  o f  re ten t ion  va luesoD,  a t  1eas t ,  f i ve  s ta t ionary  phases  is  needed to  per fo rm the  th ree-way approach. I f  Che training set is smaller, the two-way approacheshave to be used.The two-way approaches have two versions. The f irst version tr iesto model the relat ionship between retention values of markers and ofnon-markers  in  the  t ra in ing  se t ,  Th is  re la t ionsh ip  i s  used sub-sequently to predict the retention of non-markers on a new staËionaryphase using the retention values of markers on that new stat ionaryphase.  Th is  vers ion  is  tes ted  in  Par ts  I I I  and  IV .  The second vers iontr ies to model the relat ionship between retention values of markerson the  in i t ia l  s ta t ionary  phase(s)  and the  new one(s) .  Pred ic t ions  o fretention values of non-markers on the new stat ionary phase(s) can beobtained using this relat ion and the measured retention values of thenon-markers  on  the  in i t ia l  phase(s ) .  Th is  second vers ion  has  no t  beent e s  t e d .Both  tes ted  th ree-way s t ra teg ies  bear  the  same charac ter is t i cs ,  Thetraining set can be represented by a data cube in which a stat ionaryphase,  the  ob jec t ,  i s  charac ter ised  by  the  capac i ty  fac to rs  o fso lu tes  obca ined a t  d i f fe ren t  mob i le  phase compos i t ions .  Th is  da tacube is  decomposed.  On a  new s ta t ionary  phase,  re ten t íon  va lues  o fthe markers have to be measured at a l i rnited nunrber of mobile phasecompos i t i -ons .  Pred ic t ions  o f  the  re ten t ion  va lues  o f  the  non-markersat the nobile phase composit ions used in the trainÍng set, can beobtained using the previously developed decomposit ion. The same holdsfor the retention values of the markers at the non-selected rnobi lephase compos i t ions .IÈ is Ímportant to understand clearly the dif ferences between thetwo- and three-way approaches. These dif ferences can be explainedkeeping in mind two aspects.First,  the t\ .ro-way approaches dif fer from the three-way approacheswith respect to the experimental effort in the training- and calÍb-rat ion step. The three-way methods need a large training set whereas343the two-way methods do not. In the cal ibrat ion step only a fewmeasurements are needed to cal ibrate a new stat ionary phase i f  athree-way approach is chosen. On the contrary, wÍth a two-way ap-proach moïe measurements are needed in the cal ibrat ion step.Second, the two-way approaches dif fer from the three-way approacheswith respect to the way in which the rnobi le phase composit ion ishand led .  The ca l ib ra t ion  w i th  two-way approaches Ís  d iscussed f i rs t -1y ,  I f  p red íc t ions  o f  re ten t ion  va lues  on  a  nerd  s ta t ionary  phase aredes i red  a t  a  spec i f i c  mob i le  phase compos i t ion ,  the  new s ta t ionaryphase has to be cal ibrated by measuring the retention values of themarkers  a t  tha t  mob i le  phase compos i t ion .  Th is  par t i cu la r  mob i lephase compos i t ion  is  no t  necessar i l y  one o f  the  mob i le  phases  used inthe  t ra in ing  se t  ( the  in i t ia l  s ta t ionary  phases) .  For  the  th ree-wayapproaches the  s Í tua t ion  is  d i f fe ren t .  Pred ic t ions  o f  re ten t ionvalues on a new stat ionary phase can only be obtained at the mobilephase compos i t ions  present  in  the  t ra in ing  se t .  However ,  fo r  thecal ibrat ion of a new stat ionary phase and contrary to the tvro-waycase,  i t  i s  no t  necessary  to  measure  the  re ten t ion  va lues  o f  themarkers at each rnobi le phase composit ion on that ne\^l stat ionaryphase.  Marker  re ten t ion  va lues  a t  a  smal l  number  o f  se lec ted  mob i lephase composit ions suffíce to cal ibrate the whole ner4r stat i-onaryphase in  the  th ree-way case.In  Par t  I1 I ,  the  f i rs t  vers ion  o f  the  two-way approach and bo thth ree-way approaches are  tes ted .  Of  th is  f i rs t  vers ion  o f  the  two-wayapproach,  t \ ro  d i f fe ren t  var ian ts  a re  used.  One var ian t  uses  thernob i le  phase compos i t ions  exp l i c i t l y  in  the  mode l ,  con t ra ry  to  thesecond var ian t .  A  t ra in ing  se t  o f  re ten t ion  measurements  o f  n ine  tes tso lu tes  on  a  C1,  a  C18 and a  CN s ta t ionary  phase a t  s ix  rnob i le  phasecompos i t ions  (mix tu res  o f  r . ra te r ,  ace ton i t r !1e  and methano l )  Í s  used.Reten t ion  is  p red ic ted  on  a  C6 ,  a  C8 and a  Pheny l  s ta t ionary  phase,For  de ta i led  d iscuss ions  and conc lus ions ,  re fe rence is  made to  therespec t ive  sec t ions .  The resu l ts  o f  the  t \ to -way approaches a t resummar ized and d iscussed f i rs t l y .Four  d i f fe ren t  se ts  o f  markers  a re  eva lua ted :  markers  se lec ted  w i ththe  induced-var iance c r i te r ion ;  se lec ted  w i th  the  de terminant  c r i -te r ion ;  a  homologous ser ies  and bad markers .  The des ign  mat r ices  o fthese four  marker -se ts  d i f fe red  cons iderab ly  w i th  respec t  to  thedegree o f  mu1t ico l l Ínear i ty .  The des ign  mat r ix  o f  the  homologousmarkers has a very high degree of mult icol l inearity, the desígnmatrix of the bad markers and the markers chosen with the induced-var iance c r i te r ion  have a  h igh  degree o f  mu l t i co l l inear i ty .  Thedesign matrix of the determinant markers has a moderate degree ofm u l t i c o l l i n e a r i t y .The pred ic t ions  based on  the  mode ls  where  the  induced-var Íance-  anddeterminant  markers  a re  used are  good:  re la t i ve  p red ic t ion  er ro rs  o fthe capacity factors are between 5 and 10t. The homologous- and badmarkers performed clearly r{/orse. The predict ive performance of theinduced-variance- and determinant markers does not dif fer much. Bothmarker -cho ice  c r i te r ia  a re  sens i t i ve  to  ou t l ie rs ;  the  re ten t ion  o fthe solute paracetamol is badly predictable and therefore this solutecan be regarded as an outl ier. However, both the induced-varlance-and determinant cr i ter ion select this solute as a marker.The degree of mult icol l inearity seems to affect the performance of344cross  -va l ida t i<ive ly  r idge-bet te r  resu l tsco l l inear i ry )  1variance markebetter than thro f  the  es t imat :o f  mu l t i co l l ineexp l i c i t  nob i lAmemiya ,s  p red ivariance markett ion performs sbe a  re la t ion  bva l Ída t ion .There is no cse t  ( the  new sre . g .  w Í t h  r e s p e lh igher  p red ic r ip a r t i a l  I e a s tt ra Ín ing-  and ta r i t y ,  such a  rY e t ,  s p e c i f i c  i rs ta t ionary  phasrh igh  pred ic r ionin the trainingThe average rp red ic ted  by  ac8)  ro  35r  (ToLd i f fe rence in  p rway models (pAIva l ida t ion  c r i teB e s i d e s ,  m o r e  t ht h e s i s .  A  d i r e c td i f f i cu l t  becaus ,and three-way alseem to  p red ic ts ta t ionary  phasebu i ld  rhe  ca l ib rprob lems in  thebehaviour of retnents .  Reten t ionmean o f  the  re te rphases which arecompos i t ion .  Ano,ments .  Dur ing  thconsequent ly  d r i fthe performance oThree-way modelbe  deve loped.  I texp l i c i t l y  accourents .  I f  such  modconti.nuous rangegreat importancecross-val idation. The selection of the k and c parameters in respect-i ve ly  r idge-  and Ste in  regress lon  w i th  c ross-va l ida t ion  leads  tobetter results for the determinant markers (a lower degree o,f mult i-col l inearity) than for the induced-variance markers. rf  the induced-var iance markers  a re  used,  Hoer l ' s  cho ice  o f  the  k  parameter  i sbe t te r  than the  c ross-var ida tory  cho ice .  The c ross-va l ida tory  cho iceof the estimation method is also sl ightly better for a lower degreeof  rnu l t i co l r inear i ty .  The se lec t lon  o f  a  mode l  w ich-  o r  w ichout  theexp l ic i t  nob i le  phase compos i t ions ,  i s  per fo rmed bet te r  w i thAmemiya's predict ion cri terion than cross-val idation for the induced-variance markers. rf  the determÍ-nant markers are used, cross-val ida-t ion performs sl ightly better in this respect. Again there seems tobe a relat ion between mult icoLlÍnearity and the performance of cross-va l ida t ion .There is no clear preference for an estimation nethod. I f  the testse t  ( the  new s ta t ionary  phase)  does  no t  resemble  the  t ra in ing  se t ,e .g .  w i th  respec t  to  the  pa t te rn  o f  mu l t i co l l inear i ty ,  OLS might  g iveh igher  p red ic t ion  er ro rs  than r idge regress ion ,  S te in  regress ion  orpar t ia l  leas t  squares .  Cr i te r ia  co  judge the  s imi la r i t y  be tweent ra in ing-  and tes t  se t  a re  impor tan t .  l í i th  respec t  to  mu l t i co l l ine-ar i t y ,  such a  c r i te r ion  is  p roposed and seems to  work  reasonab le .Yet ,  spec i f i c  in te rac t ions  be tween a  so lu te ,  a  mob i le  phase and a  newstationary phase on which retention predict ion is desired may causeh igh  pred ic t ion  er ro rs  i f  these spec i f i c  in te rac t ions  are  no t  p resentin  the  t ra in ing  s tage.The average relat ive predict ion error for a capacity factor whenpred ic ted  by  a  th ree-way mode l ,  i s  l_3* .  I t  ranges  f rom 3 .6 t  (EHB onC8)  to  35 t  (TOL on CN)  fo r  rhe  un fo ld -P lS  mode l .  A l though no  c leard i f fe rence in  p red ic t i ve  per fo rmance was no t iced  be tween bo th  th ree-way models (PARAFAC and unfold-PLS), i t  is worthwhile developingva l ida t ion  c r i te r ia  w i th  wh ich  a  cho ice  can be  made in  p rac t ice .Bes ides ,  more  th ree-way mode ls  a re  ava i lab le ,  bu t  no t  tes ted  in  th isthes is .  A  d i rec t  compar ison  be tween the  two-  and th ree-way methods  isdif f icult  because of the above mentioned dif ferences between the two-and three-way approaches. On the one hand, the two-way approachesseem to  p red ic t  be t te r ,  bu t  use  more  measurements  to  ca l ib ra te  a  newstatÍonary phase. On the other hand, more measurements are used tobui ld the cal ibrat ion model with in the three-way case. One of theproblems in the three-way cal ibrat ion is the presence of non-l inearbehaviour of retention with respêct to nixing mobile phase compo-nents. Retention of a solute measured at a ternary mixture is not themean of the retention values of that solute at the tr^ro binary mobilephases which are mixed f i f ty-f i f ty to rnake the ternary mobile phasecompos i t ion .  Another  p rob lem wh ich  ar ises  is  d r i f t  in  the  measure-ments. During the training stage, the stat ionary phases changed andconsequently dri f t  in the measurements Íras observed. How this effectsthe performance of three-way (and two-way) models is not y.et c1ear.Three-way nodels reckoning with non-l inear rnixing behaviour shouldbe developed. I t  is also worthwhile developing three-way models thatexplÍci t ly account for the inf luence of the rnobi le phase consti tu-en ts .  I f  such  mode ls  a re  ava i lab le ,  the  pred ic t ion  o f  re ten t ion  a t  acont inuous  range o f  mob i le  phase compos i t ions  is  poss ib le .  Th is  i s  o fg rea t  impor tance fo r  op t im isa t ion  o f  separa t ions  and cor rec t ion?/ ,  (s t r a t e g i e s .In Part IV a data set is used consi-st ing of retention measurementsof sixteen test solutes on six octadecyl stat ionary phases fromdifferent batches at nine r inobi le phase composit ions (mixtures ofr^rater, methanol and acetonitr i le). Three dif ferent anaryst/apparatuscombinations are used to bui ld up this training set. The dif ferencesbetween three of these octadecyl stat ionary phases, al l  three of themmeasured by a dif ferent analyst/appaxatus combination, are visual izedusing analysis of vari-ance. rt  appears that the retention values ofthe solutes on the three stat ionary phases díffer signif icantly. Thedifferences between the stat ionary phases with respect to the reten-t ion values depend on the mobile phase composit ion. These threedifferent stat ionary phases are chosen to test a two-r^/ay approach.Two stat ionary phases are chosen as the training set and the thirds ta t ionary  phase is  used as  tes t  se t .  The pred ic t ion  o f  capac i tyfactors on this third stat ionary phase is performed with an averagere la t i ve  p red ic t ion  er ro r  o f  5 -6 t .  A  two-h lay  var ian t  in  wh ich  nocal ibratíon measurements have to be performed on the new stat ionaryphase,  g ives  an  average re la t i ve  p red ic t ion  er ro r  o f  9* .  Th is  i sÍ ro rse  than the  va lue  o f  5 -6 t  above,  because the  reproduc ib i l i t y  i sabout  3 t .  The va lue  o f  9*  can be  regarded as  the  pred ic t ion  er ro r  ona ner{7 stat ionary phase íf  a priori  knowledge of the new stat ionaryphase is  no t  ava i lab le .  Pred ic t ion  er ro rs  shou ld  be  judged keep ing  inmind tha t  smal l  p red ic t ion  er ro rs  may d is tu rb  conp le te ly  a  chromato-gram.  Very  good pred ic t ions  are  needed to  p red ic t  a  separa t ionc o r r e c t l y .The application of three-way models for the cal ibrat ion of theoc tadecy l  (C18)  s ta t ionary  phases  hras  no t  comple te ly  success fu l .  A l lsix statíonary phase were used to evaluate the three-way approacheswi th .  The f i rs t  p robrem is  the  se lec t j .on  o f  a  combina t ion  o f  so lu tes(rnarkers) and mobile phase composit ions which together are capable ofca l ib ra t Íng  a  new s ta t ionary  phase and pred ic t íng  re ten t ion  o f  a l lo ther  so lu tes  a t  a l l  o ther  rnob i le  phase compos i t ions ,  s ta t i s t i ca ltechniques for the simultaneous selection of variables from twocategor ies ,  as  in  the  th ree-way case,  a re  no t  ava i lab le .  Thesetechniques have to be developed. A "quick and dirty ' ,  approach basedon the induced-variance is used in Part I I I  and gives adequateresu l ts .  In  Par t  IV ,  such an  approach is  a lso  used and per fo rmesbet te r  than an  a l te rna t ive  s t ra tegy  o f  var Íab1e se lec t Íon .Especial ly the aspect of the dif ferent analyst/apparatus combina-tíons inf luences the performance of the three-way models. This aspectseems to hamper unfold-Pl,S more than PARAFAC. This may be due to themore r igíd model structure of PARAFAC. Two solut ions for the problernof dif ferent analyst/apparatus combinations in the training set (andperhaps  in  the  tes t  se t )  a re  ou t l ined .  ïhe  f i rs t  idea  is  to  use  adifferent kind of centering and scal ing in the data cube. The secondidea is to make hybrid models: models with an MANOVA aspect toaccount for the dif ferences between analyst/apparatus combinationsand latent variable three-way models to account for the dif ferencesbetween the stat ionary phases.Both  th ree-way rnode ls  a re  sens i t i ve  to  ou t r ie rs .  The tes t  so lu tescomprised benzene derivatives, some steroids and phenobarbical.  someof the test solutes - the steroids and phenobarbital -  l rere badly346predictable arThe connectiorsolutes and thiga ted .  Of  u tthree-way modew e I 1 .The cause o:rnethod with rUnfold-PLS iso f  degrees  o fc r i te r ia  to  asb e  t e s t e d .predictable and showed deviat ing behaviour in the three-way models.The connection between the degree of heterogeneity of the set ofsolutes and the performance of the three-way models should be invest-igated. Of utmost importance are diagnostic tools to evaluate thethree-way models. Some diagnostic tools are tested and seem to workw e 1 l .The cause of the dif ferences between the PARAFAC- and unfold-PlSrnethod with respect to their predict ive perforrnance is not c1ear.Unfold-PLS is perhaps rnore f lexible, but PARAFAC uses a lower numbero f  degrees  o f  f reedom to  es t imate  the  node l  parameters .  Va l ida t ioncri teria to assess the performance of both three-way methods shouldb e  t e s t e d .347

Multivariate calibration of reversed-phase chromatographic systems

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Multivariate calibration of reversed-phase chromatographic systems

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