Similarity factor (f2)

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Similarity factor (f2) Caluclation

Similarity factor (f2) is a "logarithmic reciprocal square root transformation of one plus the mean squared (the average sum of squares) differences of drug percent dissolved between the test and the reference products"

There had been an introduction on similarity factor in the last blog

Various contents of this book page include

1. Definition of similarity factor 1,2

The FDA and EMEA defined similarity factor as a "logarithmic reciprocal square root transformation of one plus the mean squared (the average sum of squares) differences of drug percent dissolved between the test and the reference products"

In other words, the similarity factor ( f2) is a logarithmic transformation of the sum-squared error of differences between the test Tt and reference products Rtover all time points.It represents closeness of two comparitive formulations. Generally similarity factor in the range of 50-100 is acceptable according to US FDA.

2. Equation for calculation of similarity factor 1, 2, 3

f2 = 50 + log {[1+ (1/n) ?t=1 * n (Rt-Tt)2]-0.5 *100}.............(eq. 1)

Rtand Ttare the cumulative percentage dissolved at each of the selected n time points of the reference and test product respectively

3. Calculation of similarity factor

The following sheet depicts the calculation of similarity factor

Similarity factor Calculation Sheet ( Excel Sheet)

4. Purpose, Significance, applications of similarity factor 3

The primary purpose of f2 is to compare the closeness of two products under consideration.
4.1. Significance and applications of similarity factor
The wide application of similarity factor signifies it as an efficient tool for comparison of dissolution profiles.Similarity factor finds its main application as

  • Response or dependent variable usually for optimization purposes, e.g. to compare manufacturing processes for establishing experimental conditions maximizing similarity between formulations.
  • Part of a decision criterion to establish similarity of two formulations. The regulatory suggestion "decide similarity if (the sample) f2 exceeds 50" is applied in a literal sense.

5. Challenges for considering similarity factor as a tool for comparison of dissolution profiles2, 4, 5

  • This method is more appropriate when more than three or four dissolution time points are available.
  • The dissolution treatment is effective in the presence of at least 12 individual dosage units
  • This method is applied only when the average difference between reference and test is less than 100.Normalization of the data may be required if the average difference between reference and test is higher than 100.
  • The f2 may become invariant with respect to the location change and the consequence of failure to take into account the shape of the curve and the unequal spacing between sampling time points lead to errors.
  • It is difficult to formulate a statistical hypothesis for the assessment of dissolution similarity since f2 is only a sample statistic that further complicates to evaluate false positive and false negative rates of decisions for approval of drug products based on f2 .
  • It may be too liberal in concluding similarity between dissolution profiles.
  • In addition, the range of f2 is from minus infinity to 100 and is not symmetric about zero. From these evidences it may be stated that f2 is convenience criterion and not a criterion based on scientific facts.

Nevertheless, with a slight modification in the statistical analysis, similarity factor would definitely serves as an efficient tool for reliable comparison of dissolution profiles.

"This book page doesn't include any plagiarized material"

Related Articles

1) Mathematical approach for the assessment of similarity factor using a new scheme for calculating weight .

2) An alternative method to the evaluation of similarity factor in dissolution testing by P. Costa,International Journal of Pharmaceutics Volume 220, Issues 1-2, 4 June 2001, Pages 77-83 3) In Vitro Dissolution Profile Comparison--Statistics and Analysis of the Similarity Factor, f2 Vinod Shah, Yi Tsong , Pradeep Sathe , and Jen-Pei Liu, Pharmaceutical ResearchVol. 15 Number 6, Jun 1998.

1. Yuksel N, Kanik AE, Baykara T, Comparison of in vitro dissolution profiles by ANOVA-based, model-dependent and -independent methods, Int J Pharm, 209, 2000, 57-67.
2. Costa P & Jose MSL, Modeling and comparison of dissolution profiles, Eur J Pharm Sci, 13, 2001, 123-133.
3. Ocana J, Frutos G & Sanchez O P, Using the similarity factor f2 in practice: A critical revision and suggestions for its standard error estimation, Chemometrics and Intelligent Laboratory Systems, 99, 2009, 49-56.
4. Costa P, An alternative method to the evaluation of similarity factor in dissolution testing, Int J Pharm, 220, 2001, 77-83.
5. O Hara T, Dunne A, Butler J & Devane J, A review of methods used to compare dissolution profile data, Pharmaceutical Science & Technology Today, 1(5), 1998, 214-223.

EMEA: Human Medicines Evaluation Unit of The European Agency for the Evaluation of Medicinal Products

About the Author

TK Indira's picture
Author: TK Indira

Indu Roy is post graduate in pharmacy and working as Research Officer, Formulation-IPR Department at Mylan Laboratories Limited (A subsidiary of Mylan Inc) .
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A.R.Khan's picture

I read your page but i could not get it where exactly one can apply this . So, i called my friend in UK who is working in Formulation Development of a multitnational company . What i understand from our discussion , Similarity Factory caluclation is used in following situations (but not limited to ), 1) When a product batch is scaled up in batch size or scaled down in batch size, then new batch dissolution profile is compared with old batch dissolution profile . 2)When a production manufacturing site is changed, dissolution profile of the batch maufactured at the new manufcturing is comapared with a batch from old manufactured site ie..similarity factor and that should be in certain range..other wise USA FDA will not approve new site unless you do "bio" studies... He explained couple other examples like similarity factor comparision of Submission batch (R&D bactch details submitted to FDA) vs First 3 validation batches ...So, if you could update Section 4 with "practcal applications examples", that would be help ful to learners like me. Hope you will help me in learning this "concept" in simple way with "real life examples".
TK Indira's picture

Dear khan sir, Thank you for your comment. Well coming to the query,similarity factor is a dissolution comparative factor. Therefore applications of similarity factor is inter related with applications of dissolution. Therefore similarity factor is calculated in instances wherever the dissolution is taken as a primary constraint. In brief, -It is used in instances of SUPAC changes (the examples you mentioned under comes under this category). SUPAC stands for scale up and post approval changes, it a documented format submitted in instances of any changes in components and composition(example change of binder and its concentration), changes in manufacturing equipment(example change of manufacturer), changes in manufacturing site(example shift from one block to other block), changes in batch size(example increase or decrease of batch size, in other words it is said to be scale up or scale down process), changes in analytical testing laboratory(example shift of analytical lab), changes in packaging site(example shift of site from ameerpet to panjagutta). Therefore all the above changes requires dissolution document to be submitted based on level of change (level 1-slight changes that would not have much effect on final product quality, safety, efficacy, level 2-minor changes that may have an impact on final product quality,safety, efficacy and level 3-major changes that will definitely have an impact on final product quality, safety and efficacy. Therefore in all these instances there is a need to prove that there was no much impact of SUPAC and that the generic product is still in compliance with innovator product with similarity factor being unchanged and within limits. Apart from SUPAC changes it may also be helpful to calculate similarity factor in instances of stability studies where ICH guidelines stresses on in vitro dissolution data.Here we need to prove that the product is stable throughout its shelf life and that the generic product is similar to innovator product. For further reference please check I tried to brief you out. still any queries? you are most welcome.

T.K. Indira.

-- "Our greatest glory is not in never falling, but in rising every time we fall..." Team 'Char'minar.

Prof. J. Vijaya Ratna's picture

Dear Indira You have given the information on similarity factor in a very concise manner, well done. To Khan Sir's query, I would like to add this, that we in Pharmaceutics research use the similarity factor quite a lot. For example, when a student formulates a controlled release tablet for a drug, say aceclofenac, he will compare it with a standard controlled release tablet of aceclofenac, by carrying out the dissolutions of both tablets and calculating the similarity factor. I have this feeling that the similarity factor and the dissimilarity factor are the pharmaceutical technologist's way of carrying out t tests or testing of hypothesis. The t test is used by statisticians to find out whether an observed difference between two samples is significant or not at a particular probability level. So what do you say, Indira to my feeling? Are they similar techniques or not? Vijaya Ratna

A.R.Khan's picture

I appreciate your reply . I guess examples makes easy to understand and helps to remember well. If everyone can include those examples or practical applications in these book pages that helps a lot .
TK Indira's picture

Thank you for your comment. In my opinion calculation of similarity or difference factors are like a tool for comparison of dissolution profiles and how far the formulated preparation matches the innovator product under the formulated conditions like use of different excipients, or change of dosage form from tablet to capsule or development of a novel drug delivery system etc. But, that comparison may be biased sometimes, therefore the statistical approach has been applied to sort out the errors of sampling, sampling methods etc. Student t test is a parametric test used to compare any parameter(either weight variation or in vitro dissolution profile etc) and find out whether the hypothesis is significant at fixed % of error or not and based on the results the significance can be stated when the observed values and null hypothesis are un equal (if i assume dissolution of two products are equal and if i get the higher dissolution profile for one product then that product is said to be significant).Therefore, t test may be used intern to compare the significance of in vitro dissolution profile and not limited to that and can be used to compare ANY parameter like weight variation, hardness, two compare in vivo data (AUC),the activity of any two anti hypertensive drugs, comparison of actives with placebo etc. t test is purely a statistical method of application and may be applied even to find the significance of similarity factor at fixed level of error. While the similarity factor or difference factors are meant only for dissolution parameter comparison and they make use of some statistical approaches to neutralize the errors, bias etc(like use of standard deviation, variance, parametric and non-parametric methods etc). Am not sure how far i reached you, but i would like to extend further discussion. I welcome you for any clarifications in this regard.

T.K. Indira.

-- "Our greatest glory is not in never falling, but in rising every time we fall..." Team 'Char'minar.

Prof. J. Vijaya Ratna's picture

Indira Your interpretation is correct and you brought out the differences between t test and similarity/ disimilarity factor very well. What I said, I am feeling is, when you look at similarity/ disimilarity calculations, you remember the t test. T test and these calculations do a similar sort of job. I understand what Khan Sir is saying and I will try to put in this page one or two examples from our work, preferably, published work. Vijaya Ratna
TK Indira's picture

Dear mam, Nice to hear that from you. Looking forward for your write up.That would definitely help to sort out the understanding difficulty. And you said it right that "T test and these calculations do a similar sort of job".

T.K. Indira.

-- "Our greatest glory is not in never falling, but in rising every time we fall..." Team 'Char'minar.

Nilkanth Bapurao Chapole's picture

Dear Indira. Can you help me to understand below 1. Why is the log transformation used in f2 calculation. 2. Why is 50 and 1+ in formula 3. Is there any significance level considered in f2 calculation. 4. How can it be possible to perform t test in dissolved profile comparison, where in multiple time points to be compared collectively. It will help me if you can illustrate application of the test for disso comparison.
Ph. Bhagavan P S RPh's picture

I submit my pranams to all of you for putting forth such a wonderful topic and I feel educated.

Pardon me and correct me if I am wrong, as I am an old timer.

I had heard of a term called 'BIO-EQUIVALENCE" for the product for which standards are not available but can be compared with an existing approved product, that is at the end user level could be considered Therapeutic equivalence. (Commercially called 'Me-too-product')

Here I understand that there is a need for ;Pharma-equivalence' with respect to all the parameters that you have mentioned to bring out a product of set acceptable standard.


Good to learn and it is interesting.

May your tribe cherish and flourish

Thank you and Good wishes to all

Bhagavan P.S. B Pharm

Rtd. Dy Dir.(Pharmacy),Govt of Karnataka, India

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