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A Step in the Right Direction? t he development of USP chapter <1210>. Charles Y. Tan, PhD USP Statistics Expert Committee. Outline. Introduction of <1210> Key topics Accuracy and Precision Linearity LOD , LOQ , range Summary. USP <1210>. United States Pharmacopeia

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a step in the right direction t he development of usp chapter 1210

A Step in the Right Direction? the development of USP chapter <1210>

Charles Y. Tan, PhD

USP Statistics Expert Committee

outline
Outline
  • Introduction of <1210>
  • Key topics
    • Accuracy and Precision
    • Linearity
    • LOD, LOQ, range
  • Summary
usp 1210
USP <1210>
  • United States Pharmacopeia
  • General Chapters
  • <1210> Statistical Tools for Method Validation
  • Current status: a draft is published in Pharmacopeial Forum40(5) [Sept-Oct 2014]
  • Seek public comments
purpose of 1210
Purpose of <1210>
  • A companion chapter to <1225> Validation of Compendial Procedures
    • USP <1225> and ICHQ2(R1)
    • USP <1033> Biological Assay Validation
  • Statistical tools
    • TOST, statistical equivalence
    • Statistical power, experimental design
    • tolerance intervals, prediction intervals
    • Risk assessment, Bayesian analysis
    • AIC for calibration model selection
recent framework
Recent Framework
  • Life cycle perspective
    • procedure design
    • performance qualification / validation
    • ongoing performance verification
  • ATP: Analytical Target Profile
    • Pre-specified acceptance criteria
    • Assume established
  • Validation: confirmatory step
    • Statistical interpretation of “validation”
p erformance characteristics
Performance Characteristics
  • Different statistical treatments
  • Tier 1: accuracy and precision
    • Statistical “proof” ATP is met
    • Equivalence test / TOST
    • Sample size / power, DOE
  • Tier 2: linearity, LOD
    • Relaxed evidential standard, estimation
    • Sample size / power optional
key topics
Key topics

USP General Chapter <1210>

Statistical Tools for Method Validation

accuracy and precision
Accuracy and Precision
  • Separate 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 condition
Experimental Condition
  • Yij = μ + Ci + Eij
  • Ci: experimental condition
    • combination of ruggedness factors: analyst, equipment, or day
    • DOE: experience the full domain of operating conditions
    • As independent as possible
  • Eij: replication within each condition
  • One-way analysis (w/ random factor): why?
separate assessment
Separate Assessment
  • Closed form formulas:
    • Accuracy: classic confidence interval for bias
    • Precision: confidence interval for total variability under one-way layout (Graybill and Wang)
  • Power and sample size calculation
  • Statement 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 precision
Combine Accuracy and Precision
  • Statement 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 λgiven in ATP
    • Pr (-λ≤ deviation from truth ≤ λ|data)
scale of analysis
Scale of Analysis
  • Pooling variances is central to stat analysis
    • Variance estimates with df=2 are highly unstable
    • Need to pool across samples, levels
  • Variance at mass or concentration scale/unit
    • Increase with level
  • Solutions:
    • Normalize with constants, eg. Label claim
      • Normalizing by observed averages makes stat analysis too complicated
    • Log transformation
    • %NSD and %RSD
linearity
Linearity
  • Internal performance characteristic
    • External view: accuracy and precision
    • Transparency => credibility
  • Appropriateness of standard curve fitting
    • A model
    • A range
  • Better than the alternatives (all models are approximations)
    • Proportional: model: Y = β1X + ε
    • Straight line: Y = β0 + β1X + ε
    • Quadratic model: Y = β0 + β1X + β2X2 + ε
current practices
Current Practices
  • Pearson correlation coefficient
    • Anscombe's quartet
  • Lack-of-fit F test
    • independent replicate
  • Mandel’s F-test, the quality coefficient, and the Mark–Workman test
  • Test 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
two new proposals
Two New Proposals
  • Equivalence test, TOST, in concentration units
    • Define maximum allowable bias due to calibration in ATP
    • Construct 90% confidence interval for the bias comparing the proposed model to a slightly more flexible model
    • Closed form formula, complex
    • Evidential standard: could be high, depend on allowable bias
  • Akaike Information Criterion, AICc
    • Compare the AICc of the proposed model to a slightly more flexible model (smaller wins)
    • Very simple calculations
    • Evidential standard: most likely among candidates
different burden of proof
Different Burden of Proof
  • Hypothesis Testing: Neyman-Pearson
    • Frame the issue: null versus alternative hypotheses
    • Goal: reject the null hypothesis
    • Null hypothesis: protected regardless of amount of data
    • Decision standard: beyond reasonable doubt
    • Legal analogy: criminal trial
  • Information Criteria: Kullback-Leibler
    • Frame the issue: a set of candidate models
    • Goal: find the best approximation to the truth
    • Best: most parsimonious model given the data at hand
    • Decision standard: most likely among candidates
    • Legal analogy: civil trial
  • Stepping-stone or tactical questions: information criteria are apt alternatives to hypothesis tests
range and loq
Range and LOQ
  • Range
    • suitable level of precision and accuracy
    • Both upper and lower limits
  • LOQ (LLOQ)
    • acceptable precision and accuracy
    • lower limit
  • LOQ versus LOD
    • Only one is needed for each use
    • LOQ for quantitative tests
    • LOD for qualitative limit tests
  • LOQ calculation in ICHQ2: candidate starting values
summary
Summary
  • A draft of USP <1210> is published, seeking public comments
    • A step in the right direction?
  • More than a bag of tools
  • Implement modern validation concepts with a statistical structural
  • More tools development needed
  • More statisticians involvement needed in pharmacopeia and ICH development