Using Plackett Burman partial factorial designs for method ...

1 Using Plackett Burman partial factorial designs for method robustness testingBy D. A. DurdenCanadian Food Inspection AgencyCalgary Laboratory3650 36 St NWCalgary , ABReproducibility of a method {Ruggedness{RobustnessRuggedness of a method { the degree of reproducibility of test results obtained by the analysis of the samesamples under a variety normaltest conditions USPR uggedness test conditionszDifferent{laboratories{analys ts{instruments{reagent lots{analysis days{elapsed assay times{assay temperatureszFactors are external to the methodzShould show a lack of influencezICH intermediate precision Robustness of a method a measure of its capacity to remain unaffected by small but deliberate variations in method parameters and provides an indication of its reliability during normal use.}}}}}}}}}}

2 USP, ICHF actors are internal to the methodShould show a lack of influenceTypical robustness parameters{HPLCzMobile phase compositionzNumber, type, and proportion of organic solventszBuffer composition and concentrationzpH of the mobile phasezDifferent column lots (same brand and model)zTemperaturezFlow ratezWavelengthzGradient; slope and lengthExperimental design {The scientists approachzUnivariate{Change a single variable at a timezTime consuming, inefficientzInteractions may not be detectedExperimental design 2{The statisticians approachzMultivariate{Change many variables at a timezMore efficientzMay allow observation of interactionszSome main effects may be obscuredMultivariate approaches{ComparativezCompare totally different methods solvent vs SPE extraction vs other methods{Response surface modellingzMinimize or maximize a response{Regression modellingzQuantify response variable to input variables{ScreeningzIdentify which factors are important or significantMultivariate screening approaches{Full factorial 2k{Fractional factorialz2k-pzPlackett BurmanFull factorial {Each factor is set at two levels, high (+) or low (-).}}}}}}}}}}}}

3 {For k factors the number of experiments is 2k{The number of experiments increases rapidly{Satisfactory for up to 5 factorsFactors kNumber of runs 2k2438416532664712882569512 Full factorial design {Full factorial {Main effectszEffect A = (y2 + y4 + y6 + y8)/4 -(y1 + y3 + y5 + y7)/4z=differences of averagesz= average y(+) average y(-){All effects are clear confounding by - ----++++2+-Y1Y2Y3Y4Y5Y6Y73- +4++5- -6+-7- +8++Y8 Fractional factorial 2k-p{Same layout as full factorial {Select 1/2pof the experiments{For p = 1 run half of experiments: 1,4,6,7.{Effect = average y(+) average y (-){Effect A = (y2 + y6)/2 (y1 + y7)/2{Main effects may be confounded by interactionsABC1------++++2+-Y1Y2Y3Y4Y5Y 6Y73- +4++5- -6+-7-+8++Y8 Box, , Hunter, , & Hunter, (1978) Statistics for Experimenters.}}}}}}}}}}}}

4 An introduction to design , Data Analysis, and Model Building, John Wiley and Sons, NYPlackett- Burman designs {A two level fractional factorial design {Experiments numbers n are in multiples of 4{ n = 8, 12, 20, 24, 28, 32 etc{Factors k <= n 1{For k < n-1 use dummy factors{Most commonly used are n=8 and n=12{ Plackett , , & Burman , (1946) Biometrika33, 305-325P-B usefulness{LimitationszMain effects may be aliased by two way interactionszChoice of layout by Plackett and Burman was set to minimize these{Thusz these designs are very useful for economically detecting large main effects, assuming all interactions are negligiblewhen compared with the few important main effects 11 Factor 12 experiment P-B layoutFactors ExperimentABCDEFGHIJK response1++-+++---+-y12- ++ - +++ - - - +y23+ - ++ - +++ - - -y34-+-++-+++--y45--+-++-+++-y56---+-++- +++y67+---+-++-++y78++---+-++-+y89+++--- +-++-y910-+++---+-++y1011+-+++---+-+y111 2-------- - - -y12 Weightings0-102-8-18-28-16-48-210 DummyD2D1D3D4 Vander Heyden, Y.}}}}}}}}}

5 , Nijhuis, A., Smeyers-Verbeke, J., Vandeginste, , & Massart, (2001) J Pharm Biomed Anal 24, 723-753 Analysis of P-B results{Youden test{Test for any overall significant effects{Vander Heyden 1{Comparison of individual effects to method Std Dev{Vander Heyden 2{Comparison to the dummy factors{Waters and Dovetoglou{Analysis of varianceBasic calculation - Differences{From previous{Factor A for 12 experiment P-B{Also called standard errors6)(6)(121065421198731 YYYYYYYYYYYYDA+++++ +++++=Youden test{Compare SD differences to within batch method precision{SD replicates calculated from the Normal samples.{Must be significantly larger than sqrt 2 SEnnormalsSDt > =22 Vander Heyden 1{Individual differences are compared to the SE replicatesnnormalsSDSE=SEtABSDi >See.}}}}}}}}}}}}}}}

6 Barwick, , & Ellison, (2000) Development and Harmonization of Measurement Uncertainty Principles Part (d): Protocol for uncertainty evaluation from validation data. in VAMT echnical Report No. LGC/VAM/1998/088 Eq Heyden 2{Comparison of the differences of the factors to the differences of the dummy factors. NB ABS values againDDdummyit >Waters and Dovetoglou{Comparison of the Yi (+) to the Yi (-) Using analysis of variance.{ Using NCSS calculated as multiple linear regression Using the +1, -1 coefficients{Also calculated in Excel following Spence et. , , Cotton, , Underwood, , & Duncan, (1990) Elementary Statistics, Prentice HallAnalysis of fluoroquinolones in egg: method summary{5g homogenized egg are spiked with standards, recovery spikes and IS and allowed to co-mingle 15 min{15 ml ACN containing 2% acetic acid added and shaken{2 g NaCL added{Centrifuged 15 min at 3200 rcf and ACN poured off{10 mL hexane added to the ACN and shaken, and then aspirated{Dried on N-Evap at 55 C{Redissolved in pH 3 buffer{SPE Oasis conditioned with MeOH, water, 2% NaCL, pH3 phosphate{Loaded{Eashed with 30% MeOH inwater{Eluted with ACN:MeOH = 80.}}}}}}}}}}}}}}}

7 20 (v/v){Dried{Redissolved in formic acid{Filtered into vials{Analysed by LC-MS-MSFluoroquinolones Factors Exp 1 Factor+Normal-ABCDEFGHIJKCo-mingle time (min)101520 Extraction volume of ACN141516% acetic acid in time (min)101520N-Evap temperature ( C)505560 Buffer time (x 15 sec)123 Dum 1---Dum 2---Dum 3---Dum 4---Sample sequence for LC-MS-MS analysisMethod Blank + 1 Normal eNormal 10 bMethod Blank + 2 Normal fNormal 10 cMethod Blank + 3 Expt 2 Normal 10 dMethod Blank + 4 Expt 4 Normal 10 eMMCC ppbExpt 5 Normal 10 fMMCC ppbExpt 6 method Blank + 1 MMCC 2 ppbExpt 10 method Blank + 2 MMCC 5 ppbExpt 12 method Blank + 3 MMCC 20 ppbExpt 1 method Blank + 4 MMCC 50 ppbExpt 3 MMCC ppbMethod Blank + 1 Expt 7 MMCC ppbNormal aExpt 8 MMCC 2 ppbNormal bExpt 9 MMCC 5 ppbNormal cExpt 11 MMCC 20 ppbNormal dNormal 10 aMMCC 50 ppbDifferences tVol% Aceticin ACNC entrifugeTimeN-EvaptempBuffer pHVortexTimeDum 1 Dum 2 Dum 3 Dum tests for fluoroquinolonesvs SE normalsCompoundSignificance levelCiproDano 314p< < < < <}}}}

8 Heyden 1individual differences vs SE normalsFactorABCDEFGCo-mingleExt vol% aceticCentrifuge timeN-EvaptempBuffer pHVortex timeCiprofloxacin**Danofloxacin**Enroflo xacin**SarafloxacinNorfloxacin**Lomeflox acin** p< , ** p< Heyden 2vs dummy factorsFactorABCDEFGCo-mingleExt vol% aceticCentrifuge timeN-EvaptempBuffer pHVortex timeCiprofloxacin**DanofloxacinEnrofloxa cin**Sarafloxacin**Norfloxacin**Lomeflox acin** p< , ** p< and Dovetoglouby AnovaFactorABCDEFGCo-mingleExt vol% aceticCentrifuge timeN-EvaptempBuffer pHVortex timeCiprofloxacin**DanofloxacinEnrofloxa cin**Sarafloxacin**NorfloxacinLomefloxac in* p< , ** p< of all methods Exp 1 FactorABCDEFGCo-mingleExt vol% aceticCentrifuge timeN-EvaptempBuffer pHVortex timeCiprofloxacin** (abc)** (b)Danofloxacin* (a)** (a)Enrofloxacin** (abc)Sarafloxacin** (bc)** (bc)** (bc)Norfloxacin** (a) * (b)**(a) *(b)Lomefloxacin** (a) * (b)* p< , ** p< vs SD, b vs dummy, c by AnovaConclusions of Exp 1{Significant effects were:zcaused by the % of acetic acid in the extraction solvent (ACN).}

9 Zcaused by the buffer pH{ButzThe changes used were somewhat greater than one would expect in making solutions{Therefore repeat with smaller changeszAdd different other factorsFluoroquinolones Factors - Exp 2 Factor+Normal-ABCDEFGHIJKE xtraction volume of ACN141516 Percent acetic acid in of of hexane (mL)91011 Dum 2---Dum 1---Dum 3---Buffer volume (mL)91011 Wash volume (mL) volume (mL)678 Summary of all methods Exp 2 FactorABCDEFGCo-mingleExt vol% aceticCentrifuge timeN-EvaptempBuffer pHVortex timeCiprofloxacinDanofloxacinEnrofloxaci nSarafloxacinNorfloxacinLomefloxacinNo significant effects were observedConclusions{All three methods of evaluating the Plackett Burman design detect the main effects of robustness changes.{A 12 experiment P-B layout is ideal for 7 to 8 factors as can include dummy factors{A 12 experiment P-B layout is feasible to run in one day{Total number of extractions is about 28-30 Acknowledgements{Tanya MacPherson{Dr Jian Wang{Fred Butterworth{Dugane Quon{Lesley Rhys-Williams{CFIASome referencesBox, , Hunter, , & Hunter, (1978) Statistics for Experimenters.}}}}}}}}}}}}

10 An introduction to design , Data Analysis, and Model Building, John Wiley and Sons, NY{ Plackett , , & Burman , (1946) Biometrika 33, 305-325{Vander Heyden, Y., Nijhuis, A., Smeyers-Verbeke, J., Vandeginste, , & Massart, (2001) J PharmBiomed Anal 24, 723-753{Barwick, , & Ellison, (2000) Development and Harmonization of Measurement Uncertainty Principles Part (d): Protocol for uncertainty evaluation from validation data. in VAM Technical Report No. LGC/VAM/1998/088{Spence, , Cotton, , Underwood, , & Duncan, (1990) Elementary Statistics, Prentice Hall{Waters, , & Dovletoglou, A. (2003) Journal of Liquid Chromatography & Related Technologies 26, 2975 - 2985}}}}}