Applications of factorial design in drug development MCQs With Answer

Factorial design is a powerful Design of Experiments (DoE) tool widely used in drug development for screening and optimizing formulation and process variables. B.Pharm students should grasp full and fractional factorials, interaction effects, main effects, resolution, blocking, replication, and interpretation using ANOVA and Pareto charts. Key applications include formulation optimization, robustness testing, stability studies, process parameter screening, and implementing Quality by Design (QbD) to identify Critical Quality Attributes (CQAs) and Critical Process Parameters (CPPs). Practical use of factorial experiments improves experimental efficiency, reduces resource use, and strengthens product understanding for regulatory submissions. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. Which primary advantage does a factorial design offer in pharmaceutical formulation studies?

• Ability to study one factor at a time
• Identification of both main effects and interactions between factors
• Guaranteed reduction of experimental error to zero
• Elimination of the need for statistical analysis

Correct Answer: Identification of both main effects and interactions between factors

Q2. In a 2^3 full factorial design, how many experimental runs are required?

• 3
• 6
• 8
• 9

Correct Answer: 8

Q3. What is the purpose of using fractional factorial designs in drug development?

• To measure only interactions and ignore main effects
• To reduce the number of runs while estimating key effects
• To replace replication and blocking
• To remove the need for randomization

Correct Answer: To reduce the number of runs while estimating key effects

Q4. Which term describes confounding where an interaction is indistinguishable from a main effect?

• Aliasing
• Blocking
• Replication
• Centering

Correct Answer: Aliasing

Q5. In factorial experiments, what does “resolution” refer to?

• The signal-to-noise ratio of analytical methods
• The degree to which effects are confounded with each other
• The number of center points used
• The visual sharpness of Pareto charts

Correct Answer: The degree to which effects are confounded with each other

Q6. Which statistical method is most commonly used to analyze factorial design results in formulation optimization?

• Chi-square test
• ANOVA (Analysis of Variance)
• Kaplan-Meier analysis
• Pearson correlation

Correct Answer: ANOVA (Analysis of Variance)

Q7. What is a primary reason to include center points in factorial designs?

• To estimate pure error and detect curvature in the response
• To increase the number of interactions estimated
• To force linear models to fit nonlinear data
• To eliminate the need for randomization

Correct Answer: To estimate pure error and detect curvature in the response

Q8. Which design is typically used after factorial screening to explore response surfaces for optimization?

• Fractional factorial design
• Central Composite Design (CCD)
• Completely randomized design
• Latin square design

Correct Answer: Central Composite Design (CCD)

Q9. In the context of QbD, factorial design helps identify which critical elements?

• Critical Quality Attributes (CQAs) and Critical Process Parameters (CPPs)
• Only regulatory submission dates
• Market pricing strategies
• Patent expiration timelines

Correct Answer: Critical Quality Attributes (CQAs) and Critical Process Parameters (CPPs)

Q10. When performing a 2^4 full factorial study, how many two-factor interactions exist?

• 4
• 6
• 8
• 16

Correct Answer: 6

Q11. Which plot helps visualize the magnitude and significance of effects from a factorial study?

• Kaplan-Meier plot
• Pareto chart
• Scatter matrix without labels
• Box plot of residuals only

Correct Answer: Pareto chart

Q12. In a fractional factorial design, what is the trade-off most commonly encountered?

• More runs but less information
• Greater power with no increase in runs
• Reduced runs but some effects become aliased
• No need for replication

Correct Answer: Reduced runs but some effects become aliased

Q13. Which factor type is typically considered a “noise” factor in robustness testing using factorial design?

• Controlled formulation variable intentionally changed
• Environmental humidity that varies during manufacturing
• Primary active ingredient concentration set by design
• Pre-planned process parameter

Correct Answer: Environmental humidity that varies during manufacturing

Q14. Blocking in factorial experiments is used primarily to:

• Increase confounding between factors
• Control known nuisance variability and improve precision
• Eliminate main effects
• Double the number of runs

Correct Answer: Control known nuisance variability and improve precision

Q15. Which of the following best describes an interaction effect?

• When two factors independently affect the response without influence
• When the effect of one factor depends on the level of another factor
• When all factors have equal magnitude
• When a factor has no measurable effect

Correct Answer: When the effect of one factor depends on the level of another factor

Q16. How does replication contribute to factorial experiments in drug development?

• It increases confounding
• It allows estimation of experimental error and increases precision
• It reduces degrees of freedom for error
• It changes factor levels

Correct Answer: It allows estimation of experimental error and increases precision

Q17. Which software feature is most helpful for designing and analyzing factorial experiments?

• Automatic chemical structure prediction
• DoE module with ANOVA, model fitting and diagnostics
• Only plotting chromatograms
• Text editing capabilities

Correct Answer: DoE module with ANOVA, model fitting and diagnostics

Q18. What is an alias structure in fractional factorials used to describe?

• The randomization order of runs
• Which effects are confounded with each other
• The sequence of stability samples
• The scaling of factor units

Correct Answer: Which effects are confounded with each other

Q19. Which design is preferable when initial screening must consider many factors with minimal runs?

• Full 2^k factorial
• Fractional factorial (e.g., 2^(k-p))
• Central Composite Design
• One-factor-at-a-time (OFAT)

Correct Answer: Fractional factorial (e.g., 2^(k-p))

Q20. In interpreting ANOVA from a factorial experiment, a small p-value for an interaction term indicates:

• The interaction term explains little variation in the response
• The interaction term is not statistically significant
• The interaction between factors is statistically significant
• The model is invalid and should be discarded

Correct Answer: The interaction between factors is statistically significant

Q21. Which response-surface design is efficient for three-level optimization without axial points?

• Central Composite Design (CCD)
• Box-Behnken Design
• Full factorial 3^k
• Completely randomized design

Correct Answer: Box-Behnken Design

Q22. For a formulation with suspected nonlinearity, which strategy improves model accuracy?

• Only use two-level factorial points
• Add center points and consider quadratic terms in modeling
• Avoid replication to maximize factor combinations
• Remove interactions from the model

Correct Answer: Add center points and consider quadratic terms in modeling

Q23. Which is a common practical constraint when applying factorial designs to drug development?

• Unlimited material and time are always available
• Regulatory agencies prohibit factorial experiments
• Limited material, time, or cost can restrict the number of runs
• Factorial designs always eliminate need for stability testing

Correct Answer: Limited material, time, or cost can restrict the number of runs

Q24. What does “screening” refer to in the context of factorial design?

• Assessing stability under ICH conditions
• Identifying the most important factors from many candidates
• Final product release testing
• Regulatory dossier submission

Correct Answer: Identifying the most important factors from many candidates

Q25. When evaluating residuals after fitting a factorial model, which assumption is important?

• Residuals should follow a uniform distribution
• Residuals should exhibit no systematic patterns and approximate normality
• Residuals must be exactly zero for a good model
• Residuals should increase with factor levels

Correct Answer: Residuals should exhibit no systematic patterns and approximate normality

Q26. How can factorial design support scale-up from lab to pilot manufacturing?

• By identifying scale-dependent CPPs and interactions that affect CQAs
• By replacing process validation entirely
• By ensuring identical equipment geometry
• By eliminating the need for in-process controls

Correct Answer: By identifying scale-dependent CPPs and interactions that affect CQAs

Q27. In designing a robustness study using factorial design, what is typically varied?

• Only the active pharmaceutical ingredient
• Critical factors likely to vary in routine manufacturing, such as temperature or mixing speed
• Regulatory requirements
• Marketing strategies

Correct Answer: Critical factors likely to vary in routine manufacturing, such as temperature or mixing speed

Q28. What is the role of randomization in factorial experiments?

• To intentionally introduce bias
• To ensure the order of runs minimizes systematic bias from uncontrolled variables
• To maximize confounding effects
• To guarantee normality of responses

Correct Answer: To ensure the order of runs minimizes systematic bias from uncontrolled variables

Q29. Which metric helps prioritize factors after a screening factorial experiment?

• Effect size and statistical significance combined with practical relevance
• Only factor names alphabetically
• Total number of experiments performed
• Cost of raw materials only

Correct Answer: Effect size and statistical significance combined with practical relevance

Q30. How do factorial designs contribute to regulatory submissions for drug products?

• By providing structured evidence of factor effects, interactions, and control strategy consistent with QbD principles
• By eliminating the need for any analytical validation
• By guaranteeing approval without stability data
• By replacing clinical trials

Correct Answer: By providing structured evidence of factor effects, interactions, and control strategy consistent with QbD principles

Download