- *Corresponding Author:
- M. C. Gohel

Department of Pharmaceutics and Pharmaceutical Technology, L. M. College of Pharmacy, Navrangpura, Ahmedabad-380 009, India

**E-mail:**[email protected]

Date of Submission | 11 September 2006 |

Date of Revision | 9 January 2009 |

Date of Acceptance | 5 April 2009 |

Indian J. Pharm. Sci. 2009, 71 (2): 142-144 |

## Abstract

The objective of the present work was to propose a method for calculating weight in the Moore and Flanner Equation. The percentage coefficient of variation in reference and test formulations at each time point was considered for calculating weight. The literature reported data are used to demonstrate applicability of the method. The advantages and applications of new approach are narrated. The results show a drop in the value of similarity factor as compared to the approach proposed in earlier work. The scientists who need high accuracy in calculation may use this approach.

## Keywords

Similarity factor, Weight, Dissolution, Coefficient of Variation

Moore and Flanner proposed two new indices (f_{1} and f_{2}) to compare dissolution profiles of a test
and a reference formulations [1]. The concept of
similarity factor (f_{2}) has been endorsed by Food and
Drug Administration (FDA); therefore, it is widely
adopted in formulation and development and dossier
preparation. Earlier, we suggested three different
schemes for calculating weight to compute similarity
factor [2]. In the present work an additional scheme for calculating weight is proposed and its impact on
value of similarity factor is compared with the best
approach proposed in our earlier work [2]. The equation
of similarity factor proposed by Moore and Flanner is
represented in Eqn. 1 [1],

where, f_{2} is similarity factor, n is the number of
observations, wt is optional weight, R_{t} is average
percentage drug dissolved from reference formulation
and T_{t} is average percentage drug dissolved from test formulation. Generally, an average of twelve
observations is used for calculating f_{2}. The weight
factor (w_{t}) is usually considered as unity.

FDA states that in the instances where within batch
variability is more than 15% coefficient of variation
(CV), a multivariate model independent procedure is
more suitable for dissolution profile comparison. It is
further stated in the guidance document that to allow
use of mean data, the percent coefficient of variation
(%CV) should not be more than 20% at the earlier
time points, and at the other time points %CV should
not be more than 10% [3]. These values are considered
as maximum allowable %CV in the present work.
One of the objectives of the proposed work was to
incorporate these conditions in calculation of f2. The
new scheme for calculating weight shows impact
of within sample variability on f_{2} value. Weight
(w_{t}) is calculated using Eqn. 2, w_{t}=1+{(%CVof R_{t})/
(MCV_{E/L})}+{(%CV of T_{t})/(MCV_{E/L})}--(2), where,
w_{t} is weight, %CV of R_{t} and %CV of T_{t} are the
percentage coefficient of variation of reference and
test products respectively. MCV_{E/L} is the maximum
allowable %CV. MCV_{E/L} was 20 for earlier time point
(30 min) and it was 10 for later time points (above
30 min). Co-efficient of variation was calculated using
the Eqn. 3. If the %CV of Rt and %CV of T_{t} is equal
to zero, w_{t} is equal to one. %CV=(standard deviation
/mean)×100--(3).

In our earlier publication, we stated that the approach 3 was the best amongst other approaches for calculating weight. In approach 3, reference product (12 units) and test product (12 units) were used to generate 144 values of absolute differences between a reference and a test formulation at the four sampling time points (30, 60, 90 and 180 min). Standard deviation (SD) of the 144 values was calculated. The twelve units of test formulation will show different dissolution profiles and this variability is referred to as between samples variability. The weight was calculated from the Eqn.: (1+standard deviation/ maximum allowed standard deviation). The maximum allowed standard deviation was arbitrarily chosen as 10 to allow within samples as well as variability between samples. In was arbitrarily decided to give weight equal to one when standard deviation is zero.

The value of similarity factor (f2) is 100 when the difference between reference and test formulation is zero and weight (wt) is unity. Previously, we reported that as the value of weight (wt) increases, a decrease in the value of similarity factor is anticipated [2]. In the present work, two ratio terms are included in Eqn. 2 to cause a drop in similarity factor as variability increases.

To demonstrate the utility of new weight approach,
the dissolution data reported by Shah et al. were
used [4]. The average value of cumulative percentage
drug dissolved for reference (R) and (T) formulations
are shown in **Table 1**. The standard deviation and
average of dissolution data of reference and test
formulations were calculated at each sampling time.
The results are shown in **Table 2**.

Reference | Test 1 (n = 12) | Test 2 (n = 12) | ||||||
---|---|---|---|---|---|---|---|---|

Time (min) | Average | SD | Time (min) | Average | SD | Time (min) | Average | SD |

30 | 34.92 | 2.26 | 30 | 40.34 | 4.10 | 30 | 49.33 | 2.32 |

60 | 59.60 | 3.85 | 60 | 67.15 | 6.34 | 60 | 65.33 | 5.02 |

90 | 79.27 | 5.12 | 90 | 87.01 | 4.76 | 90 | 86.75 | 3.52 |

180 | 95.08 | 6.14 | 180 | 97.73 | 1.48 | 180 | 102.83 | 1.72 |

f_{2} = 60.04 |
f_{2} = 51.08 |

Test 3 (n = 12) | Test 4 (n = 12) | Test 5 (n = 12) | ||||||
---|---|---|---|---|---|---|---|---|

Time (min) | Average | SD | Time (min) | Average | SD | Time (min) | Average | SD |

30 | 25.80 | 2.36 | 30 | 15.08 | 5.78 | 30 | 43.39 | 1.29 |

60 | 50.64 | 4.46 | 60 | 59.50 | 3.07 | 60 | 77.96 | 1.43 |

90 | 67.00 | 6.14 | 90 | 79.27 | 4.32 | 90 | 86.33 | 2.80 |

180 | 88.60 | 8.12 | 180 | 95.08 | 2.68 | 180 | 95.58 | 1.99 |

f_{2} = 51.19 |
f_{2} = 50.07 |
f_{2} = 48.05 |

SD = standard deviation, f_{2} = similarity factor

**Table 1:** Dissolution data for calculating f_{2}values[4]

Time(min) | R | T | SDR | SDT | CVR | CVT | wt |
---|---|---|---|---|---|---|---|

30 | 34.92 | 40.34 | 2.26 | 4.10 | 6.47 | 10.16 | 1.83 |

60 | 59.50 | 67.15 | 3.85 | 6.34 | 6.47 | 9.44 | 2.59 |

90 | 79.27 | 87.01 | 5.12 | 4.76 | 6.45 | 5.47 | 2.19 |

180 | 95.08 | 97.73 | 6.14 | 1.48 | 6.45 | 1.51 | 1.79 |

R = reference, T = Test , SDR = standard deviation of R_{t}, SDT = standard deviation of T_{t}, CVR = percentage coefficient of variation of R_{t}, CVT = percentage coefficient variation of T_{t}, w_{t} = 1 + (%CV of R_{t}/MCV_{E/L}) + (% CV of T_{t}/MCV_{E/L})

**Table 2:** Sample calculation for weight (wt) for test formulation1

**Table 3** displays the value of similarity factor
calculated using the new approach (f_{2-m}) and approach
3 (f_{2-m3}) of our earlier publication. The results show
that the value of f_{2-m} was lower than the value of f_{2-m3} in all the cases (test 1 to test 5). The new approach
appears to be more sensitive than the approach 3
proposed in our publication since within sample
variability is incorporated in the new approach. If the average value of reference and test at all the time
point is similar then it is irrational to compute weight
for calculating similarity factor because the product
of weight (w_{t}) and (R_{t}-T_{t}) will be zero. Therefore f_{2} is equal to 100.

Test formulations | f_{2-m} |
f_{2-m3} |
f_{2} |
---|---|---|---|

1 | 51.34 | 54.68 | 60.04 |

2 | 45.01 | 46.88 | 51.08 |

3 | 41.86 | 48.30 | 51.19 |

4 | 37.38 | 46.46 | 50.07 |

5 | 42.05 | 44.98 | 48.05 |

f_{2-m} = Similarity factor calculated using new approach, f_{2-m3} = Similarity factor
calculated using approach 3, f_{2} = Similarity factor calculated using conventional
method (w_{t} = 1)

**Table 3:** Similarity factors for different test formulations

In the new scheme of weight (w_{t}) calculation, no
parameter was decided on an arbitrary ground.
The new approach appears to be more realistic as
compared to approach 3. Another advantage of the
new method is simple calculation steps than approach
3. Equal stress is given to variability in reference and
test formulation in the new approach. The maximum
allowable %CV is also considered in the proposed
method. It considers within samples (12 units of
reference and 12 units of test) as well as between
samples (reference and test formulations) variability
because of utilization of standard deviation and
averages of reference and test formulations at each
time points for calculating weight. The use of new
method is recommended in deciding equivalence of
test product with innovators product. The approach
may also find application in selection of a bio-batch.
The use of new approach may become a strong point in Abbreviated New Drug Application (ANDA)
submission. If the value of f_{2-m} is greater than 50
than we may safely conclude that products show
similar dissolution. The positive and negative points
of the new approach will emerge out when various
researchers will try the approach with their data sets.

## References

- Moore JW, Flanner HH. Mathematical comparison of dissolution profiles. Pharma Tech 1996;20:64-74.
- Gohel MC, Sarvaiya KG, Mehta NR, Soni CD, Vyas VU, Dave RK. Assessment of similarity factor using different weighting approaches. Diss Tech 2005;12:22-37.
- Guidance for industry: Dissolution testing of immediate release solid oral dosage forms. US Food and Drug Administration, Rockville, MD, USA, 1997.
- Shah VP, Tsong Y, Sathe P, Liu JP.
*In vitro*dissolution profile comparison statistics and analysis of the similarity factor, f2. Pharma Res 1998;15:889-95.