1. A Bayesian approach to the Comparison of NIR vs HPLC analytical methods in Continuous Manufacturing Process Validation Studies
Areti Manola1, Jyh-Ming Shoung1, Steven Novick2,
Tara Scherder3, Gilfredo Navarro1, Eric Sanchez1,
Stan Altan1
1Janssen R&D, 2MedImmune, 3Arlenda
NCB2015 Conference
Villanova University
October 15, 2015

2. Outline Overview of Continuous Manufacture Quantitative stakeholders:
Process Engineers, Chemometricians, Statisticians
Process Performance Qualification
Verification of HPLC – NIR calibration
Study Design
Method Comparability/Equivalence
Relative Performance Index
Comparison of ratios of probabilities
Bayesian approach
Case Study
Summary 

3. Recent Industry Announcements

4. Engineering Definition of Continuous Manufacturing vs Batch Manufacturing
FDA Perspective on Continuous Manufacturing, Sharmista Chatterjee, Ph.D.
IFPAC Annual Meeting Baltimore, January , 2012

5. Example of Continuous Manufacturing with On-line Monitoring
FDA Perspective on Continuous Manufacturing, Sharmista Chatterjee, Ph.D.
IFPAC Annual Meeting Baltimore, January , 2012

6. Ideal Future Vision of CM

7. Traditional Release Approach
Real Time
Release Approach
Traditional Release Approach

8. Advantages of Continuous Manufacture
Scientific/Engineering
Operational/Business
Integration of QbD concepts
Cohesive development, quality and technical operations
Application of new methodologies, technologies and equipment
Improved process capability
Real time understanding of process integrating process engineering, chemometrics and statistical considerations
Reduces costs
Streamlined facility lay-out
Reduction of raw materials and intermediates inventories
Flexibility in supply size
Payoff
Reduction of overall drug substance and drug product development time
Improve time to market
Assures supply of high quality product

9. Process Engineering Aspects
Unit Operations Model: Mixer
Residence Time Distribution Model
Detector
(i.e., PAT tools)
Pulse of Tracer
(i.e., API)
RTD models are used to determine:
Disturbance dissipation along process
Raw material traceability
Scale up requirements
Critical process parameters (CPPs)
Data (DEM predicted particle velocities)
Outputs
Powder properties
Unit responses:
Flow Rate
Mixing (RTD)
Unit: Mixer

10. Chemometric Aspects
Process Analytical Technology (PAT)
Near Infra Red (NIR) calibration modeling for PAT during Process Design
PAT PLS = assess comparability to HPLC method
Gage R&R designs relating HPLC to NIR during development and subsequently during process validation

11. Statistical Aspects Verification of HPLC – NIR calibration
Process Validation
Stage 1 Process Design – DoE, data analysis and interpretation
Stage 2 Process Performance Qualification
Statistical sampling protocols for Large n sampling plans
IPC sampling
Verification of HPLC – NIR calibration
Stability protocol and sampling designs
Definition of sampling frequency and sample size
Stage 3 Continued Process Verification (PV) - Process Capability

12. Verification of HPLC – NIR calibration
Calibration model is developed during Process Design, Gage R&R to assess equivalence
Blocked design is 3 concentrations, at target tablet weight, tablets are the blocks leading to essentially a paired comparison design
During the stages of PV, the calibration model will be tested in production
Equivalence measures will be calculated
Schuirmann’s test
We propose a Relative Performance Index using a Bayesian approach to the assessment of an individual analytical determination falling within a prespecified limit of the true value for comparing NIR vs HPLC

13. Relative Performance Index
Assuming the HPLC is the gold standard method, the probability of a single analytical determination y from HPLC (or NIR) falling within some interval  of the true value µ is calculated as follows:
where (•) is the CDF of standard normal distribution.
The Relative Performance Index is defined as follows:

14. Method Comparison using the Relative Performance Index
Given delta, Bias and Method Variability
OC Curves of probability of falling within delta of true value
Rel_Pfm across delta of true value
Criterion for equivalence
Pr(Rel_Pfm≥1)≥PC, where PC is a desired probability level

15. Case Study - Data Description
A single CM batch was sampled as follows:
20 locations chosen equispaced throughout the CM run
3 tablets per location
Tested by both NIR and HPLC methods

16. Statistical Model Variance component model : where
Yj(i),k = assay of jth tablet (j=1,2,3) from ith (i=1,2,…,20) location from kth (k=HPLC, NIR) method,
Mk = overall mean from kth method,
Li = random effect of ith location: ~ N(0, L2)
Tj(i) = random effect of jth tablet from ith location: ~ N(0, T2)
j(i),k = residual error from kth method: ~ N(0, k2), k = 1, 2
Preliminary analysis showed no location effect, therefore the random effect of location was dropped from final model.

17. REML Parameter Estimates
Effect
Parameter
Estimate (se)
95% Confidence Interval
Lower
Upper
Fixed
HPLC
(0.10)
99.81
100.32
NIR
(0.05)
100.08
100.29
Bias* (NIR-HPLC)
0.17 (0.09)
-0.02
0.36
Random
(SD)
Tablet
0.35
0.26
0.53
Residual (HPLC)
0.70
0.58
0.86
Residual (NIR)
0.20
0.11
1.04
*The 90% confidence interval for Bias = (0.01, 0.33)

18. JAGS – Posterior Samples
A Bayesian simulation of the posterior distribution and credible intervals based on the previous model was done using JAGS with vague priors:
Mean[HPLC], Mean[NIR] ~ N( Mean=100, SD=10 )
SD_Tablet ~ U(0, 5)
SD_HPLC, SD_NIR ~ U(0, 5)
60,000 posterior samples:
Number of chains=3
Burn-in = 20000
No. of sample = 20000
thin=25

19. JAGS – Parameter Estimates and Credible Intervals
Effect
Parameter
Mean (Median)
95% Credible Interval
Lower
Upper
Fixed
HPLC
(100.02)
99.81
100.22
NIR
(100.19)
100.08
100.29
Bias* (NIR-HPLC)
0.17 (0.17)
-0.02
0.36
Random
(SD scale)
Tablet
0.36 (0.36)
0.21
0.47
Residual (HPLC)
0.72 (0.71)
0.59
0.89
Residual (NIR)
0.19 (0.20)
0.02
0.37
*The 90% credible interval for Bias = (0.01, 0.33)

20. Normal Density Plots of HPLC and NIR centered on the true mean Given Estimated mean bias and median of sigmas for HPLC and NIR methods

21. OC Curves of Probability of Falling within delta of True Value Given Estimated mean bias and median of sigmas for HPLC and NIR methods

22. Relative Performance Index across delta values Given Estimated mean bias and median of sigmas for HPLC and NIR methods

23. Summary of Posterior Distribution (JAGS) of Relative Performance Index with Various deltas
Mean
Median
Maximum
Minimum
Pr(Rel_Pfm ≥ 1)
0.05
2.21
2.01
24.06
0.00
0.819
0.10
2.25
2.05
12.13
0.849
0.15
2.29
2.11
8.46
0.890
0.20
2.31
2.15
6.64
0.929
0.25
2.28
2.17
5.78
0.959
0.30
4.91
0.980
0.35
2.10
4.24
0.991
0.40
2.02
3.72
0.996
0.45
1.90
1.91
3.33
0.999
0.50
1.79
1.80
3.01
0.55
1.70
2.75
0.86
>0.999
0.60
1.61
2.54
0.89
0.65
1.53
2.36
0.92
0.70
1.47
1.46
0.95
0.75
1.41
1.40
2.08
0.97
0.80
1.35
1.34
1.97
0.99
0.85
1.31
1.30
1.87
1.01
1.000
0.90
1.26
1.02
1.23
1.22
1.71
1.00
1.20
1.19
1.64

24. Comparison of Schuirmann’s Test and Relative Performance Index for Method Comparison
Criterion
delta= 0.25
delta = 0.50
Schuirmann’s
90%Credible Interval of Bias
90%CI =
(0.01, 0.33)
Fail
Pass
Relative Performance Index
Pr(RPI ≥ 1) ≥ 80%
Pr(RPI ≥ 1) = 0.96
Pr(RPI ≥ 1) = 1.0

25. Summary
CM is being actively encouraged by the FDA; companies are now engaged in weighing its costs/benefits
CM offers many scientific and business advantages, major quantitative stakeholders are process engineers, chemometrician, statisticians working together to ensure quality
Equivalence of NIR to gold standard HPLC can be established through a Relative Performance Index evaluated through Bayesian calculations
Made possible because Tablet dispersion can be removed orthogonally given the paired comparison design
Provides a natural interpretation of method performance