Post on 31-Dec-2015
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A Step in the Right Direction? the development of USP chapter <1210>
Charles Y. Tan, PhDUSP Statistics Expert Committee
OutlineIntroduction of <1210>Key topics
Accuracy and PrecisionLinearityLOD, LOQ, range
Summary
USP <1210>United States PharmacopeiaGeneral Chapters<1210> Statistical Tools for Method
ValidationCurrent status: a draft is published in
Pharmacopeial Forum 40(5) [Sept-Oct 2014]Seek public comments
Purpose of <1210>A companion chapter to <1225> Validation of
Compendial ProceduresUSP <1225> and ICH Q2(R1)USP <1033> Biological Assay Validation
Statistical toolsTOST, statistical equivalenceStatistical power, experimental designtolerance intervals, prediction intervalsRisk assessment, Bayesian analysisAIC for calibration model selection
Recent FrameworkLife cycle perspective
procedure designperformance qualification / validationongoing performance verification
ATP: Analytical Target ProfilePre-specified acceptance criteriaAssume established
Validation: confirmatory stepStatistical interpretation of “validation”
Performance Characteristics Different statistical treatmentsTier 1: accuracy and precision
Statistical “proof” ATP is metEquivalence test / TOSTSample size / power, DOE
Tier 2: linearity, LODRelaxed evidential standard, estimationSample size / power optional
Key topicsUSP General Chapter <1210>Statistical Tools for Method Validation
Accuracy and PrecisionSeparate Assessment Of Accuracy And Precision
Confidence interval within acceptance criteria from ATP
Combined Validation Of Accuracy And Precision γ-expectation tolerance interval: 100γ%
prediction interval for a future observation,Pr (-λ ≤ Y ≤ λ) ≥ γ
γ-content tolerance interval: 100γ% confidence of all future observations
Bayesian tolerance interval
Experimental ConditionYij = μ + Ci + EijCi: experimental condition
combination of ruggedness factors: analyst, equipment, or day
DOE: experience the full domain of operating conditions
As independent as possibleEij: replication within each conditionOne-way analysis (w/ random factor): why?
Separate AssessmentClosed form formulas:
Accuracy: classic confidence interval for biasPrecision: confidence interval for total variability
under one-way layout (Graybill and Wang)Power and sample size calculationStatement of the parameters: bias, variance
Eg. CI of bias: [-0.4%, 1.1%], within ±5% (ATP)Eg. CI of total variability: ≤2.4%, within 3% (ATP)
Implicit risk level: 95% confidence intervals
Combine Accuracy and PrecisionStatement of observation(s)
Closed form formulas, but a bit more complicate 99%-expectation tolerance interval: eg. [-4.3%, 5.0%]
within ±10% (ATP) 99%-content tolerance interval: eg. [-5.9%, 6.6%]
within ±15% (ATP)Bayesian tolerance interval
“the aid of an experienced statistician is recommended”
Simpler Alternative: directly assess the risk with the λ given in ATPPr (-λ ≤ deviation from truth ≤ λ|data)
Scale of AnalysisPooling variances is central to stat analysis
Variance estimates with df=2 are highly unstableNeed to pool across samples, levels
Variance at mass or concentration scale/unitIncrease with level
Solutions: Normalize with constants, eg. Label claim
Normalizing by observed averages makes stat analysis too complicated
Log transformation%NSD and %RSD
LinearityInternal performance characteristic
External view: accuracy and precisionTransparency => credibility
Appropriateness of standard curve fittingA modelA range
Better than the alternatives (all models are approximations)Proportional: model: Y = β1X + εStraight line: Y = β0 + β1X + εQuadratic model: Y = β0 + β1X + β2X2 + ε
Current PracticesPearson correlation coefficient
Anscombe's quartetLack-of-fit F test
independent replicate Mandel’s F-test, the quality coefficient, and the Mark–
Workman testTest of significance
Evidential standard: low since it gives the benefit of doubt to the model you want
Good precision may be “penalized” with a high false rejection rate
Poor precision is “rewarded” with false confirmation of the simpler and more convenient model
Anscombe's Quartet
Two New ProposalsEquivalence test, TOST, in concentration units
Define maximum allowable bias due to calibration in ATPConstruct 90% confidence interval for the bias
comparing the proposed model to a slightly more flexible model
Closed form formula, complexEvidential standard: could be high, depend on allowable
biasAkaike Information Criterion, AICc
Compare the AICc of the proposed model to a slightly more flexible model (smaller wins)
Very simple calculationsEvidential standard: most likely among candidates
Different Burden of ProofHypothesis Testing: Neyman-Pearson
Frame the issue: null versus alternative hypothesesGoal: reject the null hypothesisNull hypothesis: protected regardless of amount of dataDecision standard: beyond reasonable doubtLegal analogy: criminal trial
Information Criteria: Kullback-LeiblerFrame the issue: a set of candidate modelsGoal: find the best approximation to the truthBest: most parsimonious model given the data at handDecision standard: most likely among candidatesLegal analogy: civil trial
Stepping-stone or tactical questions: information criteria are apt alternatives to hypothesis tests
IUPAC/ISO LOD (RC and RD)
IUPAC/ISO LOD
LOD: Using Prediction Bounds
Range and LOQRange
suitable level of precision and accuracyBoth upper and lower limits
LOQ (LLOQ)acceptable precision and accuracylower limit
LOQ versus LODOnly one is needed for each useLOQ for quantitative tests LOD for qualitative limit tests
LOQ calculation in ICH Q2: candidate starting values
SummaryA draft of USP <1210> is published, seeking
public commentsA step in the right direction?
More than a bag of toolsImplement modern validation concepts with a
statistical structuralMore tools development neededMore statisticians involvement needed in
pharmacopeia and ICH development