Presentation on theme: "Joseph G Pigeon Villanova University"— Presentation transcript:
1Joseph G Pigeon Villanova University Complex Experimental Design and Simple Data Analysis: A Pharmaceutical ExampleJoseph G PigeonVillanova University
2IntroductionDesigns with restricted randomization have multiple error measuresPharmaceutical example where the split plot structure is even more complexWhole plot structure in two dimensionsCorrelation structure in two dimensionsCaveatsLimited understanding of the biology involvedNo originality of statistical methods claimed
3Split Plot Designs Originated in agricultural experiments where Levels of some factors are applied to whole plotsLevels of other factors are applied to sub plotsSeparate randomizations to whole plots and sub plotsTwo types of experimental unitsTwo types of error measuresCorrelation among the observations
4Split Plot Designs Also common in industrial experiments when Complete randomization does not occurSome factor levels may be impractical, inconvenient or too costly to changeThis restriction on randomization results in some whole plot factors and some sub plot factorsData analysis needs to account for this restricted randomization or split plot structure
5Split Plot Example Consider a paper manufacturer who wants to study Effects of 3 pulp preparation methodsEffects of 4 temperaturesResponse is tensile strengthPilot plant is capable of 12 runs per dayOne replicate on each of three days
7Split Plot ExampleInitially, we might consider this to be a 4 x 3 factorial in a randomized block designIf true, then the order of experimentation within a block should have been completely randomizedHowever, this was not feasible; data were not collected this wayThe multiplication sign in 4 x 3 had to be replaced with an x.
8Split Plot Example Experiment was conducted as follows: A batch of pulp was produced by one of the three methodsThe batch was divided into four samplesEach sample was cooked at one of the four temperaturesSplit plot design withPulp preparation method as whole plot treatmentTemperature as sub (split) plot treatment
10Split Plot ExampleSubplot error is less than whole plot error (typical)
11Split Plot Example Lessons We must carefully consider how the data were collected and incorporate all randomization restrictions into the analysisWhole plot effects measured against whole plot errorSub plot effects measured against sub plot error
12Description of Example – MQPA Assay Multivalent Q-PCR based Potency AssayUsed to assign potencies (independently) to each of five reassortants of a pentavalent vaccineRelies on the quantitation of viral nucleic acid generated in 24 hoursTwo major componentsBiological component (infection of the standard and sample viruses)Biochemical component (quantitative PCR reaction where PCR = Polymerase Chain Reaction)
14Description of Example- Biological Component Vero cell maintenance and set upSerial dilution of known standard and unknown sample are incubated with trypsinInfected in 4 replicate wells of Vero cell monolayers seeded in a 96 well plateInfection proceeds for 24 hours and then halted with the addition of a detergent and storage at –70C
15Description of Example- Biochemical Component Lysate is thawed and dilutedPreparation of a “master mix”Preparation of Q-PCR plate (master mix + diluted lysates)Configuration of the Q-PCR detection systemPotency is determined by parallel line analysis of standard and test samplesSpecific interest is on optimization of the PCR portion of the assay
16PCR Optimization Design Discussions with Biologists identified 13 factors8 factors associated with preparation of master mix5 factors associated with configuration of PCR detection system (instrument)Discussions with Biologists identified 3 responsesLowest cycle time (range: 1 – 40)Least variability between replicatesValid amplification plot (range: 0 – 4)Completion of experiments and analysis immediately!
18PCR Optimization Design Considerations Interactions not expected to existExperiments performed in a 96 well plateEach plate can accommodate at most 15 master mix combinations12 run PB deign for 8 factorsThe exponent 2 ^ (5-1) would not copy from word. I left two parentheses to mark the spot.
19PCR Optimization Design Considerations Time constraints imply at most 16 plates (instrument settings)25-1 fractional factorial for 5 factors (5 = 1234)Concern about using only 12 of 28 combinationsHalf of the plates use a 12 run PB design (123 = 45 = +1)Half of the plates use the foldover PB design (123 = 45 = 1)
20Plackett-Burman Design Factors: Replicates: Design: 12Runs: Center pts (total): 0Data Matrix (randomized)Run A B C D E F G H
21Half Fraction Design Factors: 5 Base Design: 5, 16 Resolution: V Runs: Replicates: Fraction: 1/2Blocks: none Center pts (total):Design Generators: E = ABCDRow StdOrder RunOrder A B C D E
22PCR Optimization Design Layout Each represents a 12 run PB design16 × 12 = 192 observations
30PCR Optimization Results Fractional Factorial Fit: ctgmEstimated Effects and Coefficients for ctgm (coded units)Term Effect Coef SE Coef T PConstantinstrinstrinstrinstrinstrinstr1*instrinstr1*instrinstr1*instrinstr1*instrinstr2*instrinstr2*instrinstr2*instrinstr3*instrinstr3*instrinstr4*instr
46PCR Optimization Summary No complex models – all simple analyses5 factors were found to be significant (mm3, mm7, mm8, instr3 and instr4)These factors were further studied using response surface experimentsScientists seem quite happy with the results of the PCR optimization experiments
47Concluding RemarksMany industrial experiments do have a split or strip plot structure which means multiple and possibly complex error measuresArises from the conduct of an experiment and/or any restrictions on the randomizationWe need to incorporate these considerations into a proper analysis and interpretation of experimental data
48Concluding RemarksExperimental designs with balance, symmetry and orthogonality permit simple but effective graphical analyses (even with some missing data)Much can be learned from simple analyses following suitable experimental designAll models are wrong, but some models are usefulAll models are wrong, but some models are more wrong than others