f1 and f2 similarity factors MCQs With Answer

Introduction

For M.Pharm students in Modern Pharmaceutics (MPH 103T), mastering f1 (difference factor) and f2 (similarity factor) is essential for comparing dissolution profiles of test and reference products, particularly under SUPAC and bioequivalence frameworks. These model-independent metrics evaluate the closeness of cumulative percent dissolved over time. Typically, 12 units per product are tested at identical time points, and results are summarized as mean profiles. Regulatory benchmarks generally consider f1 between 0–15 and f2 between 50–100 as evidence of similarity, provided data quality criteria (e.g., variability limits) are met. The following MCQs deepen conceptual clarity, computation rules, regulatory conditions, and common pitfalls when using f1 and f2 in immediate- and modified-release formulations.

Q1. Which statement best describes the purpose of the f1 and f2 factors in dissolution profile comparison?

• They are model-dependent parameters fitted to the Weibull model
• They are compendial limits that replace Q-point specifications
• They are model-independent metrics to assess similarity between test and reference dissolution profiles
• They are variability indices used to set sample size

Correct Answer: They are model-independent metrics to assess similarity between test and reference dissolution profiles

Q2. What is the correct formula for the difference factor f1?

• f1 = [Σ(Rt − Tt) / ΣRt] × 100
• f1 = [Σ|Rt − Tt| / ΣRt] × 100
• f1 = 50 × log10{[1 + (1/n) Σ(Rt − Tt)2]−0.5 × 100}
• f1 = (Σ|Rt − Tt| / n) × 100

Correct Answer: f1 = [Σ|Rt − Tt| / ΣRt] × 100

Q3. What is the correct formula for the similarity factor f2?

• f2 = 50 × log10{[1 + (1/n) Σ(Rt − Tt)2]−0.5 × 100}
• f2 = 50 × ln{[1 + (1/n) Σ(Rt − Tt)]−0.5 × 100}
• f2 = 50 × log10{[1 + Σ(Rt − Tt)]−0.5 × 100}
• f2 = 100 − [Σ|Rt − Tt| / ΣRt] × 100

Correct Answer: f2 = 50 × log10{[1 + (1/n) Σ(Rt − Tt)2]−0.5 × 100}

Q4. Which acceptance ranges are generally used to declare similarity between two dissolution profiles?

• f1 between 0–25 and f2 between 40–70
• f1 between 0–15 and f2 between 50–100
• f1 between 10–20 and f2 between 60–120
• f1 between 0–10 and f2 between 40–60

Correct Answer: f1 between 0–15 and f2 between 50–100

Q5. How many units per product should typically be used to compute f2 under standard regulatory guidance?

• 6 units
• 8 units
• 12 units
• 24 units

Correct Answer: 12 units

Q6. Which statement about time points used in f2 calculation is correct?

• Include the zero time point to anchor the curve
• Use at least three common time points excluding t = 0
• Use all time points, including those after 100% dissolution
• Use only a single time point at Q

Correct Answer: Use at least three common time points excluding t = 0

Q7. What is the rule regarding time points where dissolution exceeds 85% when computing f2?

• Include all time points after 85% to improve power
• Exclude any time point above 85% for both products
• Include at most one time point greater than 85% dissolution
• Stop the test at 60% dissolution

Correct Answer: Include at most one time point greater than 85% dissolution

Q8. Which condition allows you to waive f2 comparison for immediate-release products?

• Rt and Tt differ by less than 5% at the first time point
• Both products reach at least 85% dissolution within 15 minutes under all conditions
• The test product shows higher assay than reference
• The paddle speed is 100 rpm

Correct Answer: Both products reach at least 85% dissolution within 15 minutes under all conditions

Q9. How are Rt and Tt defined in the f2 calculation?

• Medians of percent dissolved at each time point
• Means of percent dissolved at each time point across 12 units
• Individual unit values chosen at random
• Geometric means of individual unit data

Correct Answer: Means of percent dissolved at each time point across 12 units

Q10. Which variability criterion is typically recommended at each time point for valid f2 assessment?

• Percent CV ≤ 30% at all time points
• Percent CV ≤ 20% at early time points and ≤ 10% at other time points
• Percent CV ≤ 15% at all time points
• No variability limits are required

Correct Answer: Percent CV ≤ 20% at early time points and ≤ 10% at other time points

Q11. In the standard f2 computation, what weighting is applied to the time points?

• Weights proportional to time (wt = t)
• Equal weighting (1/n for each time point)
• Inverse variance weighting
• Higher weights for late time points

Correct Answer: Equal weighting (1/n for each time point)

Q12. What should be done if the sampling times differ between test and reference profiles?

• Compute f2 using all available points for each profile as is
• Discard the reference profile and repeat the study
• Use common time points or justify interpolation to a common set before calculating f2
• Include only the earliest time point

Correct Answer: Use common time points or justify interpolation to a common set before calculating f2

Q13. Which scenario most likely invalidates the use of a simple f2 comparison?

• Both profiles show low variability and 4–5 common time points
• One or more time points have variability beyond recommended CV limits
• The profiles are compared at identical time points
• The assay of both products is within 98–102%

Correct Answer: One or more time points have variability beyond recommended CV limits

Q14. Which of the following best describes the interpretation of f1 = 8 and f2 = 48?

• Similar, because f1 indicates similarity
• Similar, because f2 is near 50
• Not similar, because f2 is below 50
• Undetermined, because both indices must be ignored

Correct Answer: Not similar, because f2 is below 50

Q15. Which practice can artificially inflate the f2 value without improving early-time similarity?

• Reducing paddle speed to 50 rpm
• Adding many late plateau time points where both profiles are near 100%
• Using 6 units instead of 12 units
• Normalizing to percent label claim

Correct Answer: Adding many late plateau time points where both profiles are near 100%

Q16. What is the role of the reference profile in the f1 calculation?

• It is not used; only test data are required
• It provides the denominator as ΣRt to scale the absolute differences
• It determines the number of units to be tested
• It is used only at the first time point

Correct Answer: It provides the denominator as ΣRt to scale the absolute differences

Q17. Which of the following is a correct data-handling rule for f2 computation?

• Include the zero time point to ensure identical starting values
• Use percent dissolved of label claim at each time point
• Use raw milligrams dissolved without normalization
• Average medians from each unit

Correct Answer: Use percent dissolved of label claim at each time point

Q18. Under which condition can profiles be considered similar without formal f2 if only one apparatus condition is used?

• Both achieve more than 60% within 10 minutes
• Both achieve at least 85% within 15 minutes
• Test is faster by at least 10% at all points
• Reference profile has lower variability

Correct Answer: Both achieve at least 85% within 15 minutes

Q19. When f2 is not appropriate due to high variability, which approach is often recommended?

• Ignoring late time points and recomputing f1 only
• Bootstrap-based f2 using unit-level data or model-based multivariate methods
• Using only the fastest-dissolving six units
• Comparing only the Q-value time point

Correct Answer: Bootstrap-based f2 using unit-level data or model-based multivariate methods

Q20. Which statement about the minimum number and distribution of time points for f2 is most appropriate?

• Use exactly two time points to minimize variability
• Use at least three to five time points spanning early, middle, and late dissolution, with no more than one above 85%
• Use as many late time points as possible after 95% dissolution
• Use only the time points where Rt equals Tt

Correct Answer: Use at least three to five time points spanning early, middle, and late dissolution, with no more than one above 85%

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