# Similarity factor (f2)

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**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

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** 1. Definition of similarity factor **^{1,2}

^{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 ( f_{2}) is a logarithmic transformation of the sum-squared error of differences between the test T_{t }and reference products R_{t}_{}over 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.

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** 2. Equation for calculation of similarity factor** ^{1, 2, 3 }

f_{2} = 50 + log {[1+ (1/n) ?_{t=1} * n (R_{t}-T_{t})^{2}]^{-0.5} *100}.............(eq. 1)

R_{t}_{}and T_{t}_{}are the cumulative percentage dissolved at each of the selected n time points of the reference and test product respectively

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** 3. Calculation of similarity factor**

**The following sheet depicts the calculation of similarity factor**

Similarity factor Calculation Sheet ( Excel Sheet)

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**4. Purpose, Significance, applications of similarity factor **^{3 }

^{3 }

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** ** 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

*4.1. Significance and applications*

*of similarity factor*

- 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.

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** 5. Challenges for considering similarity factor as a tool for comparison of dissolution profiles**^{2}^{, 4, 5 }

^{2}

^{, 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"**

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**Related Articles**

**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.

*References***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.

**Abbreviation**

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

## Comments

A.R.Khan

Sat, 10/02/2010 - 01:28

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## Similarity factor for beginners

TK Indira

Sat, 10/02/2010 - 07:00

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## Similarity factor and SUPAC changes

T.K. Indira. http://www.pharmainfo.net/tkindira

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

Sat, 10/02/2010 - 17:16

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## Pharmaceutics research and the similarity factor

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

http://www.pharmainfo.net/vijayaratna

www.drvijayaratna.in

A.R.Khan

Sat, 10/02/2010 - 17:40

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## Thanks Madam

TK Indira

Sat, 10/02/2010 - 18:50

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## Calculation of similarity

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. http://www.pharmainfo.net/tkindira

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

Sun, 10/03/2010 - 04:10

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## Difference betwee test and similarity/ dissimilarity factor

http://www.pharmainfo.net/vijayaratna

www.drvijayaratna.in

TK Indira

Sun, 10/03/2010 - 10:33

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## T test and Similarity factor calculations

"T test and these calculations do a similar sort of job".T.K. Indira. http://www.pharmainfo.net/tkindira

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

Mon, 05/25/2015 - 18:48

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## need to understand the logic behind f2 formula

Ph. Bhagavan P S RPh

Mon, 05/25/2015 - 20:29

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## Similarirty concept

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.

Great

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