🎯 Module 4 - Part 2: Screening Design Workshop

Design of Experiments & Formulation Optimization

Learning to efficiently screen multiple factors in pharmaceutical formulation development

🎯 Learning Objectives

By the end of this workshop, you will be able to:

📊 Introduction to Factor Screening 5 min

What is Factor Screening?

Factor screening is the systematic process of identifying which variables (factors) have significant effects on your response variables from a larger set of potential factors.

Why is it crucial in pharmaceutical development?

💊 Pharmaceutical Screening Example

Scenario: A pharmaceutical company is developing a new immediate-release tablet and needs to screen potential factors affecting dissolution rate.

Factors to screen:

  1. Binder type (HPMC vs PVP)
  2. Binder concentration (1-3%)
  3. Disintegrant type (Crosscarmellose vs Starch glycolate)
  4. Disintegrant concentration (2-8%)
  5. Lubricant concentration (0.5-1.5%)
  6. Compression force (5-15 kN)
  7. Granulation time (3-10 min)

Traditional approach: Testing all combinations = 2×3×2×4×3×3×4 = 1,728 experiments!

Screening approach: Fractional factorial = 8-16 experiments

🔬 Fractional Factorial Design Builder 20 min

Understanding Fractional Factorial Designs: 2^(k-p)

Let's think step-by-step about what this notation means:

🔍 Step-by-Step: Design Selection Process

Step 1: Determine Your Constraints

Decision Framework:
• Available budget: _____ experiments
• Number of factors (k): _____
• Time constraints: _____ days
• Required information: Main effects only OR interactions needed?

Step 2: Calculate Design Options

Common Fractional Factorial Designs:
• 2^(4-1) = 8 runs for 4 factors (half-fraction)
• 2^(5-1) = 16 runs for 5 factors (half-fraction)
• 2^(7-3) = 16 runs for 7 factors (1/8 fraction)
• 2^(8-4) = 16 runs for 8 factors (1/16 fraction)

Step 3: Choose Resolution Level

Resolution determines what effects you can estimate clearly:

Resolution III: Main effects confounded with 2-factor interactions

  • Use when: Only main effects are of interest (initial screening)
  • Example: A is aliased with B×C
  • Risk: If B×C interaction exists, it will inflate the A effect

Resolution IV: Main effects clear, 2-factor interactions confounded with each other

  • Use when: Main effects are priority, some interaction info acceptable
  • Example: A×B is aliased with C×D
  • Benefit: Main effects are unbiased estimates

Resolution V: Main effects and 2-factor interactions are clear

  • Use when: Both main effects and interactions are important
  • Cost: More experimental runs required
  • Benefit: Complete picture of factor impacts

💊 Worked Example: Tablet Hardness Screening

Scenario: Screen 5 factors affecting tablet hardness using a 2^(5-1) fractional factorial design (16 runs).

Factors and Levels:

Factor Low Level (-1) High Level (+1) Units
A: Binder % 2 4 %w/w
B: Compression Force 8 16 kN
C: Lubricant % 0.5 1.5 %w/w
D: Dwell Time 1 3 seconds
E: Granulation Wet Dry Method

🔍 Step-by-Step: Building the Design Matrix

Step 1: Choose the Generator

For 2^(5-1) design, we need one generator.
Common choice: E = A×B×C×D
This means column E is created by multiplying columns A, B, C, and D.

Step 2: Create the Basic 2^4 Matrix

Start with full factorial for first 4 factors (A, B, C, D):
Run 1: A=-1, B=-1, C=-1, D=-1
Run 2: A=+1, B=-1, C=-1, D=-1
Run 3: A=-1, B=+1, C=-1, D=-1
... (continue for all 16 combinations)

Step 3: Generate Column E

For each run, E = A×B×C×D
Run 1: E = (-1)×(-1)×(-1)×(-1) = +1
Run 2: E = (+1)×(-1)×(-1)×(-1) = -1
Run 3: E = (-1)×(+1)×(-1)×(-1) = -1
... (continue for all runs)
💻 Excel Implementation:
1. Create columns A through D with all 16 combinations
2. In column E, enter formula: =A2*B2*C2*D2
3. Copy down for all rows
4. Add randomization: =RAND() column, then sort by it

⚠️ Understanding Alias Structure

When E = A×B×C×D, the defining relation is I = A×B×C×D×E

Complete alias structure:

Interpretation: If you see a large "A effect," it could be due to factor A OR the 4-factor interaction B×C×D×E (unlikely but possible).

🎮 Interactive Challenge: Fold-Over Strategy

Problem: After running your 2^(5-1) design, you find that factors A and B appear significant, but you're concerned about potential A×B interaction being confounded.

Solution: Fold-Over Design

Step 1: Run the "mirror image" of your original design

Step 2: Change the signs of ALL factors in every run

Step 3: Combine data from both halves

Result: Main effects separated from 2-factor interactions!

🎲 Plackett-Burman Designer 10 min

When to Use Plackett-Burman (P-B) Designs

Plackett-Burman designs are perfect when:

🔍 Step-by-Step: P-B Design Construction

Step 1: Understand the Efficiency

P-B Design Efficiency:
• 11 factors in 12 runs (92% factor usage)
• 19 factors in 20 runs (95% factor usage)
• 23 factors in 24 runs (96% factor usage)

Compare to full factorial:
• 11 factors = 2^11 = 2,048 runs!
• P-B gives you main effects with just 12 runs

Step 2: Select Standard P-B Matrix

12-Run Plackett-Burman Base Row:

+ + - + + + - - - + -

This base row is cyclically shifted to create 11 rows, plus one row of all minus signs.

Step 3: Build Complete Design Matrix

Run A B C D E F G H I J K
1 + + - + + + - - - + -
2 + - + + + - - - + - +
3 - + + + - - - + - + +
... (continue cyclic shifts) ...
12 - - - - - - - - - - -

💊 Pharmaceutical P-B Example: Capsule Formulation

Scenario: Screen 11 factors affecting capsule disintegration time using 12-run P-B design.

Factors to screen:

  1. A: API particle size (Small vs Large)
  2. B: Diluent type (Lactose vs MCC)
  3. C: Diluent amount (20% vs 40%)
  4. D: Disintegrant type (Crosscarmellose vs Starch glycolate)
  5. E: Disintegrant % (2% vs 6%)
  6. F: Lubricant type (Mg stearate vs Stearic acid)
  7. G: Lubricant % (0.5% vs 1.5%)
  8. H: Mixing time (5 min vs 15 min)
  9. I: Capsule size (0 vs 1)
  10. J: Fill weight (300mg vs 500mg)
  11. K: Storage humidity (40% vs 75% RH)

🔍 Expected Results Interpretation

After running 12 experiments and measuring disintegration time:

Calculate main effects:
Effect_A = (Average of A_high runs) - (Average of A_low runs)

Example calculation:
If A_high average = 8.2 min and A_low average = 6.5 min
Effect_A = 8.2 - 6.5 = +1.7 min
(Larger particle size increases disintegration time)

⚠️ P-B Design Limitations

Complex confounding pattern: Unlike fractional factorials, P-B designs have complex alias structures where main effects are partially confounded with many interactions.

When to be cautious:

Best practice: Use P-B for initial screening, then follow up significant factors with fractional factorial or RSM designs.

💻 Excel Implementation for P-B Designs:
1. Download standard P-B matrices from NIST website
2. Assign your factors to columns A through K
3. Replace +1/-1 with your actual factor levels
4. Randomize run order using RAND() function
5. Calculate effects using AVERAGEIF() function

📊 Screening Data Analysis Suite 15 min

The Goal of Screening Analysis

Our mission: Separate the "vital few" factors that significantly affect our response from the "trivial many" that don't.

Two powerful visualization tools help us achieve this:

🔍 Step-by-Step: Pareto Chart Analysis

Step 1: Calculate All Effects

For each factor:
Effect = (Average response at high level) - (Average response at low level)

For interactions (fractional factorial only):
AB Effect = Average(Y when A and B have same sign) - Average(Y when A and B have opposite signs)

Step 2: Rank by Absolute Magnitude

Create table with factors ordered by |Effect| from largest to smallest:
Factor B: |Effect| = 3.2
Factor D: |Effect| = 2.8
Factor A: |Effect| = 1.9
Factor C: |Effect| = 0.6
Factor E: |Effect| = 0.3

Step 3: Apply Statistical Significance Line

Lenth's Method for significance threshold:

PSE = 1.5 × median(|effects|)
ME = 1.5 × PSE
SME = 2.5 × PSE

Where PSE = Pseudo Standard Error, ME = Margin of Error, SME = Simultaneous Margin of Error

💊 Worked Example: Tablet Dissolution Analysis

Scenario: Analyze results from 2^(5-1) screening design for tablet dissolution rate (% dissolved at 30 min).

🔍 Step-by-Step Analysis

Step 1: Raw Data Summary

Factor Average at Low Level Average at High Level Effect |Effect|
A: Binder % 82.3% 78.1% -4.2% 4.2%
B: Compression Force 85.2% 75.2% -10.0% 10.0%
C: Lubricant % 79.8% 80.6% +0.8% 0.8%
D: Dwell Time 84.1% 76.3% -7.8% 7.8%
E: Granulation 78.9% 81.5% +2.6% 2.6%

Step 2: Apply Lenth's Method

Absolute effects sorted: 10.0, 7.8, 4.2, 2.6, 0.8
Median = 4.2
PSE = 1.5 × 4.2 = 6.3
ME = 1.5 × 6.3 = 9.45
SME = 2.5 × 6.3 = 15.75

Step 3: Identify Significant Effects

Effects exceeding ME (9.45%):

  • Factor B (Compression Force): -10.0% (SIGNIFICANT)

Effects below threshold:

  • Factor D (Dwell Time): -7.8% (borderline)
  • Factor A (Binder %): -4.2% (not significant)
  • Factor E (Granulation): +2.6% (not significant)
  • Factor C (Lubricant %): +0.8% (noise)

Step 4: Pharmaceutical Interpretation

Compression Force (Factor B) is the dominant factor:

  • Higher compression force → Lower dissolution (75.2% vs 85.2%)
  • Mechanism: Increased tablet density reduces porosity and water penetration
  • Recommendation: Keep compression force at lower end of range
  • Critical Process Parameter (CPP): Yes, requires tight control

🔍 Step-by-Step: Half-Normal Plot Analysis

Step 1: Understand the Concept

The half-normal plot principle:

  • If all effects are just noise, they should follow a straight line when plotted against normal scores
  • Real effects will "fall off" this straight line
  • The more significant the effect, the further it deviates

Step 2: Calculate Normal Scores

For n effects, normal scores are calculated as:
Normal Score_i = NORM.S.INV((i - 0.5) / n)

For our 5 effects (ordered by absolute magnitude):
Effect 1 (10.0): NORM.S.INV(0.9) = 1.28
Effect 2 (7.8): NORM.S.INV(0.7) = 0.52
Effect 3 (4.2): NORM.S.INV(0.5) = 0.00
Effect 4 (2.6): NORM.S.INV(0.3) = -0.52
Effect 5 (0.8): NORM.S.INV(0.1) = -1.28

Step 3: Interpret the Plot

What to look for:

  • Straight line: Effects that follow the line are likely noise
  • Points above the line: Significant positive effects
  • Points below the line: Significant negative effects
  • Far from line: Very significant effects

🎯 Factor Selection for Optimization

The final step: Use screening results to select 2-4 factors for detailed optimization studies (RSM).

Selection Criteria:

  • Statistical significance: Effects above the threshold line
  • Practical significance: Effects large enough to matter clinically
  • Controllability: Factors you can actually control in manufacturing
  • Cost impact: Factors that significantly affect economics

For our tablet example:

Selected for optimization:

  • Compression Force (B): Clearly significant (-10.0%)
  • Dwell Time (D): Borderline significant (-7.8%)
  • Binder % (A): Moderate effect (-4.2%), but important for tablet integrity

Next step: Design a Response Surface Methodology (RSM) study with these 3 factors.

💻 Excel Analysis Tools:
1. Pareto Chart: Sort effects by magnitude, create bar chart with reference line
2. Half-Normal Plot: Use NORM.S.INV() for normal scores, create scatter plot
3. Effect Calculation: Use AVERAGEIF() to calculate high/low averages
4. Lenth's Method: Use MEDIAN() and simple multiplication for thresholds

🎯 Summary and Next Steps 5 min

Key Takeaways from Screening Designs

🚀 What's Next?

You've identified the critical factors - now let's optimize them!

In Part 3: Full Factorial Design Center, we'll learn how to:

🧠 Quick Knowledge Check

Before moving on, ask yourself:

  1. When would you choose a 2^(7-3) design over a 2^(7-1) design?
  2. Why might Plackett-Burman be better than fractional factorial for screening 15 factors?
  3. How do you know if an effect shown in a Pareto chart is actually significant?
  4. What's the main limitation of screening designs for understanding your process?

If you can answer these confidently, you're ready for Part 3!

🎯 Module 4 - Part 2 Complete!

You've mastered the art of efficient factor screening in pharmaceutical development.

Ready for Part 3: Full Factorial Design Center? →