Issues in Non-Clinical Statistics Stan Altan Chemistry, Manufacturing & Control Statistical Applications Team Department of Non-Clinical Statistics 1
Outline Introduction Regulatory Considerations Impacting Statistical Practices in Non-Clinical Development (Two Issues) Stability Analysis Issues and Controversies Equivalence Approach to Bioassay Potency Testing Issues in the Statistical Analysis of a Non- standard Design (The N-1 Design) Excipient Compatibility Studies Wrap-up 2
Pharmaceutical Product Development: Discovery through Launch Lead Compound Discovery Opt Selection Non-Clinical Formulation Safety /Pre-Clinical Development Assessment Clinical Research and Commercialization Phase IIa Phase I First Proof of Phase IIb Phase III in humans biological activity in humans Registration NDA/MAA Approval & Launch Submission 3
Information Needed for Formulation Development Project Active Pharmaceutical Ingredient (API) • fundamental physical and chemical properties of the drug molecule and other derived properties : pKa,solubility,melting point,hygroscopicity • Chemical stability through degradation studies Oral absorption potential of API evaluated based on the API aqueous solubility throughout the pH range of the GI Tract and the permeability of the compound in an in-situ rat intestinal loop or CaCo-2 model. Polymorphism, particle size and surface characteristics 4
Biopharmaceutics Classification System BCS Class I: High Solubility & High Permeability BCS Class II: Low Solubility & High Permeability Solubility > 1 mg/mL; Permeability > 6 x 10 -5 cm/s Solubility < 1 mg/mL; Permeability > 6 x 10 -5 cm/s BCS Class III: High Solubility & Low Permeability BCS Class IV: Low Solubility & Low Permeability Solubility > 1 mg/mL; Permeability < 6 x 10 -5 cm/s Solubility < 1 mg/mL; Permeability < 6 x 10 -5 cm/s CLASS BOUNDARIES • HIGHLY SOLUBLE when the highest dose strength is soluble in < 250 ml water over a pH range of 1 to 7.5. • HIGHLY PERMEABLE when the extent of absorption in humans is determined to be > 90% of an administered dose, based on mass- balance or in comparison to an intravenous reference dose. • RAPIDLY DISSOLVING when > 85% of the labeled amount of drug substance dissolves within 30 minutes using USP apparatus I or II in a volume of < 900 ml buffer solutions. 5
Stability Analysis : Issues and Controversies Introduction Objectives of a Stability Study Kinetic Models Design of Stability Studies Stability Models Fixed and Mixed effects Case Study Bayesian Approach 6
Introduction Stability is defined as the capacity of a drug substance or a drug product to remain within specifications established to ensure its identity, strength, quality, and purity throughout the retest period or expiration dating period 7
Introduction Purpose of Stability Testing To provide evidence on how the quality of a drug substance or drug product varies with time under the influence of a variety of environmental factors (such as temperature, humidity, light, package) To establish a re-test period for the drug substance or an expiration date (shelf life) for the drug product To recommend storage conditions Control focused on lot mean 8
Kinetic Models (API) (Underlying Mechanism) Orders 0,1,2 ( 0 ) C ( t ) C k t 0 0 k t ( 1 ) C ( t ) C e 1 0 1 1 ( 2 ) ( ) C t k t 2 C 0 where C 0 is the assay value at time 0 When k 1 and k 2 are small, ( 1 ) ( 2 ) 2 C ( t ) C C k t and C ( t ) C C k t 0 0 1 0 0 2 9
Basic Design Randomly select containers/dosage units at time of manufacture, minimum of 3 batches, stored at specified conditions related to zones I,II,III,IV requirements At specified times 0,1,3,6,9,12,18,24,36,48,60 months, randomly select dosage units and perform assay on composite samples Basic Factors : Batch, Strength, Storage Condition, Time, Package Additional Factors: Position, Drug Substance Lot, Supplier, Manufacturing Site, ... 10
Development Stability Study Description of Data Assay measurements at 0, 1, 3, 6, 9,12 months 3 Batches held at 25C/60%RH and 30C/65%RH and 40C/75%RH storage conditions, 3 package configurations Specification limits: 90 – 110% Label Claim (w/w) 11
Expiration Date Regression Model (Fixed Terms) y A b t e ij i ij ij If b i < 0, the expiration date (T ED ) at condition i is the solution to the equation (roots of a quadratic) LSL A b T t Var ( A b T ) i ED ( , df ) i ED LSL = lower specification limit , t ( ,df ) is the ( 1- ) th quantile of the t-distribution with df degrees of freedom. 12
Expiration Date Intersection of specification limit with lower 1- sided 95% confidence bound on the batch mean Scatterplot of Observed Assay, True Concentration, Lower CL vs Time 104 Variable Obs_Assay True_Conc 102 LCLM Concentration % Label Pred 100 98 96 94 92 90 90 0 1 3 6 9 12 18 24 Time (Months) Shelf Life 13
Regulatory Model ICH Q1E ( n b Batches, n c Conditions) Models 1,2,3 (Fixed Terms) Fit individually by Batch and Condition 1. (n b * n c models) Fit by Batch, include all Conditions (fit 2. n b constrained intercept models) Fit all Batches and Conditions (fit 1 3. model, constrained batch intercepts, with/without constrained slopes) 14
Regulatory Models (ICH Q1E) Model Specification Type Number Form Number Number Fixed Variance Parameters Parameters Fixed 1 2*n b *n c n b *n c y A B T ijk ij ij ijk ijk 2 n b *n c +n b n b y A B T ijk i ij ijk ijk 3a y A B T n b *n c +n b 1 ijk i ij ijk ijk 3b y A B T n c +n b 1 ijk i j ijk ijk Index i=Batch, j=Condition, k=Time 15
Issues with Regulatory Models Pooling across batches of drug Product Intercepts and Slopes at p=0.25 Unrealistic to assume batch potencies are identical at release (time or manufacture), batches are going to be ‘different’, so why test for equality? Residual error term used for pooling across Intercepts – Why should this be the criterion for poolability? Multiple error terms possible if models 1,2 chosen P=0.25 ignores levels of process and analytical variability Cannot power a stability study design – emphasis is on estimation of degradation rates Ignores the fact that the Chemistry is independent of batch, same API, rate constant is property of the molecule 16
Issues with Regulatory Models Are the regulatory guidelines reflective of current technology and statistical practice? This is the right time to question the pooling paradigm Equivalence approach not a way out Are we stuck in a Hypothesis Testing /Equivalence Testing rut? 17
Pooling across batches Mechanistic basis exists to forego pooling tests (constrained models) Assume a fixed common temperature-condition specific slope based on kinetic considerations Assume different batch-specific Intercepts Main requirement is to estimate the parameters and account for incipient variation in such a way that control over the lot mean is assured. 18
Mixed Model If one can assume that drug product batches arise from a fixed manufacturing process, then one can regard the batches as the primary independent statistical units. Statistical model needs to estimate : Process Mean at time of Manufacture Rate parameter Variance Structure Process (Lot-Lot) Analytical Variation Measurement error, Extraneous sources 19
Mixed Effects Model The mixed effects model provides a coherent modeling framework in a compact way consistent with the manufacturing process Acknowledges all sources of variation, simple but flexible variance structure Consistent with the basic philosophy that batch is the conditionally independent primary statistical unit (subject specific effects) A natural representation of a batch process, direct lead- in to process simulations, bootstrapping, post commercialization studies Easily extended to multiple fixed factors under study Main objection – small number of batches 20
Mixed Effects Model Models 4, 5 (Mixed Models, with 1 or 2 Random Terms) Random Term in the Intercept 4. Random Terms in Intercept and Slopes 5. Correlation not likely for API, may be for others 21
Mixed Effects Model Model Specification Type Number Form Number Number Fixed Variance Parameters Parameters Mixed 4 n c +1 2 y ( ) B T ijk 0 i j ijk ijk 5 n c +1 3 y ( ) B T ijk 0 i j i ijk ijk Index i=Batch, j=Condition, k=Time 22
Case study: Data Listing Condition Month Batch B1 Batch B2 Batch B3 25C-60RH 0 99.7 99.0 99.4 25C-60RH 1 100.0 99.4 100.5 25C-60RH 3 99.1 99.2 99.7 25C-60RH 6 98.8 99.5 99.7 25C-60RH 9 98.7 98.7 99.4 25C-60RH 12 98.7 98.6 99.3 30C-65RH 1 100.4 99.9 101.7 30C-65RH 3 99.6 99.4 100.0 30C-65RH 6 99.3 99.5 99.6 30C-65RH 9 98.2 98.2 98.9 30C-65RH 12 98.0 97.4 98.5 23
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