Statistics and modeling in in vitro release studies

Transcription

1 Statistics and modeling in in vitro release studies J-M. Cardot Biopharmaceutical Department University of Auvergne, 28 place H. Dunant Clermont-Fd France First Disso India May 2013 SPDS Mumbai 3-4 May 2013 JMC - 1 Introduction SPDS Mumbai 3-4 May 2013 JMC - 2

2 API Formulation and process General scheme in vivo What you see in vivo is the slowest phenomenon Often called absorption by the pharmacokineticists Release Dissolution Absorption DDF Free API Dissolved API Absorbed drug In vivo dissolution Can be simulated in vitro API characteristics Formulation Production Etc. Distribution Elimination Pharmacokinetics Pharmacodynamics Safety Drug in blood Efficacy Safety Drug in fluids tissues SPDS Mumbai 3-4 May 2013 JMC - 3 In vitro dissolution Formulation type: IR, MR, type of MR, etc Dissolution apparatus Formula: composition, grade of excipients, quantity of API and excipients, etc Dissolution media Dissolution parameter Process parameters: mixing, granulation, drying, tabletting, coating Dissolution results: percentage dissolved vs time API: source, quality, purity, salt, etc. API: solubility, dissolution rate, particle size, crystal shape, polymorphism, pka, etc. SPDS Mumbai 3-4 May 2013 JMC - 4

3 Value of dissolution Function of formulation and BCS and phase SR always interesting Function of BCS for IR Class 3 less interesting Class 4 variable Class 1 and 2 important Dissolution function of solubility and dissolution rate SPDS Mumbai 3-4 May 2013 JMC - 5 Dissolution curves 100 % Dissolved Slow Reference Rapid Time (h) SPDS Mumbai 3-4 May 2013 JMC - 6

4 First Describe the curve Simple parameters read on the curve T10 or 20% T50% T80 or 90% Calulated parameters MDT: Mean dissolution time DE: dissolution efficiency SPDS Mumbai 3-4 May 2013 JMC - 7 A method must not be: However Over discriminant : show differences in vitro that did not exist in vivo Under discriminant : show nothing Comparison and differences must have a significance Know how of predictivity of dissolution only after in vivo results SPDS Mumbai 3-4 May 2013 JMC - 8

5 Modeling of curves SPDS Mumbai 3-4 May 2013 JMC - 9 Two major classes Mechanistic models: Higuchi, Korsmeyer-Peppas Hixson-Crowell Empirical models: Hill Weibull Makoid-Banakar And sometine logit, probit, simple exponential SPDS Mumbai 3-4 May 2013 JMC - 10

6 Mechanistic models in vitro dissolution Fitting equation to explain drug release and dissolution dc dt Modified Noyes-Whitney Equation: A. (Cs-C) D h Surface A - Particle size, Wettability Thickness boundary layer - Flow rate - Agitation Diffusivity D - Molecular size - Dissolution medium - Viscosity Concentration gradient - Solubility - ph - Cristal structure SPDS Mumbai 3-4 May 2013 JMC - 11 Mechanistic models in vitro dissolution Fitting equation to explain drug release and dissolution Many different dissolution models available in commercial software M 1/3 0 M Hixson-Crowell 1/3 Q D 2A C s C s t kt 1/ 2 Higuchi Mass transport Qt/Q = Kt n Korsmeyer Peppas SPDS Mumbai 3-4 May 2013 JMC - 12

7 Empirical models No need of release behavior Only describe the curve Two of them based on MDT (that can be studied alone) Problem if dissolution does not reach 100 % Insufficient sampling points SPDS Mumbai 3-4 May 2013 JMC - 13 Hill D(t) = F inf t b Empirical models MDT b t b Weibull D(t) = F inf 1 e Makoid-Banakar t Tmax D(t) = F Max t > Tmax D(t) = F Max t Tmax t MDT b b e b 1 t Tmax Finf / Fmax = amount released at time infinity / at Max (plateau starting at Tmax) MDT = mean dissolution time b = slope factor SPDS Mumbai 3-4 May 2013 JMC - 14

8 Modeling in vitro dissolution Specific softwares To simulate drug absorption and factors affecting drug release and absorption Gastroplus DDDplus Simcyp Intellipharm PKCR PKSIM STELLA Phoenix Kinet DS DD Solver And so on SPDS Mumbai 3-4 May 2013 JMC - 15 Interest Based on the results can simulate the in vivo possible impacts, that suppose Either a good know how of all parameters Or an IVIVC That the behaviour is technology dependent and not formulation and/or API dependent SPDS Mumbai 3-4 May 2013 JMC - 16

9 Comparison of curves described in guidelines SPDS Mumbai 3-4 May 2013 JMC - 17 Two Pharmaceutical Products Reference Possible Differences Drug particle size,.. Excipients Manufacturing process Equipment Site of manufacture Batch size. Test Is dissolutions equivalent? If yes are the two products equivalent Adapted from J. WELING, CBG MEB, Budapest 2007 SPDS Mumbai 3-4 May 2013 JMC - 18

10 Comparison problem? Often internal hurdle in the companies: F1/F2 is the standard at FDA and F2 at EMEA other approaches are not appreciated. Note for guidance for example: EMEA NOTE FOR GUIDANCE ON THE INVESTIGATION OF BIOAVAILABILITY AND BIOEQUIVALENCE CPMP/EWP/QWP/ 1401 / 98/Rev1 Guidance for Industry SUPAC-MR: Modified Release Solid Oral Dosage Forms Center for Drug Evaluation and Research (CDER) September 1997 Basic papers: Pradeep M. Sathe, Yi Tsong, Vinod P. Shah; in vitro dissolution profile comparison: statistics and analysis, model dependent approach; Pharmaceutical Research, 1996, 13, 12 Yi Tsong, T. Hammerstrom, Pradeep Sathe, Vinod P. Shah; Statistical Assessment of mean differences between two dissolution data sets, Drug Information Journal, 1996, 30, pp SPDS Mumbai 3-4 May 2013 JMC - 19 What is Model Independent F1/F2 F 1 : relative error between curves FDA F 2 : similarity function EMEA FDA f Each f1 < 15 % 2 n Rt Tt t 1 f1 100 n Rt t n log 1 ( R t T t ) 100 n t 1 SIMILARITY Final f2 > 50 % SPDS Mumbai 3-4 May 2013 JMC - 20

11 Profiles comparison Conditions 12 units of each formulation Use of mean values Only 1 sample over 85% At least 3 points Not allowed to discard points Starts at the first sample CV see region difference Not applicable to fast release (> 85% in 15 min) SPDS Mumbai 3-4 May 2013 JMC Example 1 % Dissolved f1 f Time (h) Ref Test test SPDS Mumbai 3-4 May 2013 JMC - 22

12 70 Example 2 % Dissolved f1 f Time (h) Ref Test SPDS Mumbai 3-4 May 2013 JMC Example 3 shape dif f1 f % Dissolved Time (h) Ref Test SPDS Mumbai 3-4 May 2013 JMC - 24

13 Remarks F1/F2 Mean and CV are a simple factors but smooth outlier presence Not a good method for «fast» profiles (if >85 <15 min not applicable) A small difference in a time (especially first time) give bad results => program the sample in accordance, problem of EC (see after) F1 might be too conservative not needed in EU and J. Increasing the number of sample is not always the best choice SPDS Mumbai 3-4 May 2013 JMC - 25 Lag time Region differences F1/F2 EU-US no correction J: correction by the time to have 5% dissolved (interpolated) if existing for the reference product Sampling EU/US At least 3 samples Only one sample % D > 85% J (fct of the case) >85% between 15 and 30 min: sample 15, 30, 45 min > 85% (or 80 for SR) >30 min Ta: time for 85% (or 80) dissolved, sampling: Ta/4, Ta/2, 3/4Ta and Ta <85% (80% for SR), Ta:time for 85% (or 80) of the amount dissolved in a prescribed time, sampling Ta/4, Ta/2, 3/4Ta and Ta SPDS Mumbai 3-4 May 2013 JMC - 26

14 Variability of data F2 EU-US: 1st point < 20%, other < 10%, J: depends Similarity EU-US > 50 J: numerous cases and fct of the case but as a mean idea Ref > 85% in less than 15min error <15% no f2 Ref >85% (or 80 SR) between min error <15% or f2>45 Ref <85(or 80)% in 30 min Disso >85 (or 80)% points between 40-85% error 15% or F2>42 Disso >50% but <85(or 80)% error <12% or f2>46 Disso <50% error <9% or f2>53 SPDS Mumbai 3-4 May 2013 JMC - 27 Remark for EC in EMA: Omperazole in Q&A! Concluding similarity if dissolution of more than 85% is obtained within 15 minutes is not applicable for gastroresistant formulations. The comparison of dissolution profiles should be performed even if dissolution is more than 85% before 15 min in either products or strengths. A tight sampling schedule is recommended after the product has been investigated for 2 h in media mimicking the gastric environment (ph 1.2 or 4.5) since profile comparison (e.g. using the f2 calculation) is required. SPDS Mumbai 3-4 May 2013 JMC - 28

15 Model Independent Multivariate Confidence Region Procedure Close to Mahalanobis distance introduced by P. C. Mahalanobis in 1936 Based on variance/covariance matrixes Usefull if within batch variation CV > 15% Not informative: smooth the overall difference of the overall curves n could lead to the same same Mahalanobis distance Assumption that the dissolution data are multivariate normally distributed SPDS Mumbai 3-4 May 2013 JMC - 29 Steps Model Independent Multivariate Confidence Region Procedure 1. Determine the similarity limits in terms of multivariate statistical distance (MSD) based on interbatch differences from reference. 2. Estimate the MSD between the test and reference mean dissolutions. 3. Estimate 90% confidence interval of true MSD between test and reference batches. 4. Compare the upper limit of the confidence interval with the similarity limit. SPDS Mumbai 3-4 May 2013 JMC - 30

16 Model comparison Model with no more than three parameters. Select the most appropriate model common for all reference. Calculate the MSD on model parameters between test and reference batches. Estimate the 90% confidence region of the true difference between the two batches. Compare the limits of the confidence region with the similarity region. If the confidence region is within the limits of the similarity region => OK SPDS Mumbai 3-4 May 2013 JMC - 31 Remarks Accommodate non-identical sampling schemes How to select an appropriate model => C² test? Often Akaike Information Criterion (AIC), the Model Selection Criterion (MSC), or the coefficient of determination (COD) used no model can be empirically fitted to all types of dissolution curves, Weibull model prefered MSD is calculated under the assumption that the model parameters are multivariate normally distributed Other tests could be used to compare equations SPDS Mumbai 3-4 May 2013 JMC - 32

17 Dissolution and statistical tool All processes implies in Pharmacy are multivariate with interactions between variables Process analytical technology: PAT refers to a collection of analytic methods which can be used to ensure adherence of a product to quality specifications and is based on multivariate approaches PAT principles are used to find correlation between dissolution results and process parameters: multivariate analysis (Multiple regression, Principal Component Analysis (PCA) or Partial Least Squares Regression (PLS)) SPDS Mumbai 3-4 May 2013 JMC - 33 And PCA? Two variables are strongly (positively) correlated when there is a small angle between the lines connecting them with the origin. If the two variables considered are two responses one can conclude that these responses are correlated, If it is a factor and a response it means that the factor has a positive effect on the response. When the factor has a negative effect on a response the angle between the lines connecting them with the origin is close to 180 Y. Van der Heyden et al. / Analytica Chimica Acta 2002, SPDS Mumbai 3-4 May 2013 JMC - 34

18 Strengh and wekness Strength All historical data (batches) are used and compared to new data. Trends could potentially be identified earlier. This could help improvement of process consistency after scale up and post approval changes. They can handle the large amount of data including data produced in continuous process during dissolution (on line spectro or optic fibre). Weakness Statistical approach Not easy to set up and interpret the data Some hypothesis are underlined : linearity, etc Establish a relationship did not imply a causality Does not contain criteria to decide if batches are good or similar or not SPDS Mumbai 3-4 May 2013 JMC - 35 Conclusion SPDS Mumbai 3-4 May 2013 JMC - 36

19 Know what you study Formulation kdd Disintegration Release kr Dissolution ks Solubilized Drug SPDS Mumbai 3-4 May 2013 JMC - 37 Conclusion Setting in vitro dissolution test is complicated Analyzing dissolution data is First to have a look on the apparatus during dissolution Second to examine the curve Third to apply simple tools And then try to investigate more sophisticated tool The type of analysis is dependent of the step Development QC Always try to understand what you are doing and why SPDS Mumbai 3-4 May 2013 JMC - 38