INTRODUCTION
The guidance for industry on analytical procedures and method validation, provides
recommendations to applicants on submitting analytical procedures, validation
data and samples to support the documentation of the identity, strength, quality,
purity and potency of drugs and drug products. The FDA, EU, TGA and most of
other organizations requires that for development of any analytical procedure,
information must include data demonstrating accuracy, precision, linearity,
specificity, ruggedness, range, limit of detection and limit of quantitation
(FDA, 2000; EURACHEM Guide, 1998;
TGA, 2006; Thompson et al.,
2002). The USP, ICH Q2A and Q2B address almost all of these validation parameters,
although all the parameters are not needed for all types of methods by FDA,
USP as well as ICH (ICH Q2A, 1995; ICH
Q2B, 1996; Robinson and Lee, 1987). Any quantitative
analytical technique require experiments to be conducted to ensure consistent
results in concern of these parameters (Tahir et al.,
1999). Chromatographic methods are used primarily for determination of drugs
in biological fluids as well as pharmaceutical products but simple UVspectrophotometric
methods are suitable for daytoday analysis of aqueous solutions (Amini
et al., 2005). Where UVspectrophotometric analyses are more convenient
for frequent use, the methodology of relating response (absorbance) vs. predictor
(concentration) variables may introduce huge error in estimations. The relationship
between absorbance and concentration may be linear, quadratic or logarithmic,
hence, direct use of straight line equation y = α+βX should be avoided.
The prediction of relationship between variables may be started from a polynomic
equation which exhibits relationship between absorbance and concentration variables
as under:
This equation takes care of nonlinear behavior of absorbance with concentration
and can also get converted to various other equations (statistical or mathematical
models) on the basis of statistical significance of coefficients. The five different
types of models or equations, acceptable with FDA, which can originate from
this polynomic equations are:
• 
Model 1 

(2) 
• 
Model 2 

(3) 
• 
Model 3 

(4) 
• 
Model 4 

(5) 
• 
Model 5 

(6) 
where in each model, y and x are absorbance and concentration terms. The α,
β are coefficients of respective equations. The scheme for selection of
appropriate coefficients has been gives as Scheme 1.
Among these models or equations, model 1 and 2 are simple straight line equations
and models 4, 5 get transform to linear equations after log transformations.
The model 3 is a quadratic representation of relationship between absorbance
and concentration values. For accurate calibration of an instrument and generation
of standard curve, only model selection is not final criteria. The variance
in absorbance values is often heterogeneous at different concentration levels
which introduce error in relationship prediction. Therefore, smoothing of variances
is required that can be done by appropriate weight selection as per Scheme
2, starting with equation given below:
where, SD(y) and X are standard deviation of absorbance (response) and concentration
terms. The δ are coefficients as explained for polynomial equation. If
in any case, δ_{1} = δ_{2 }= 0, the SD (y) becomes
independent of concentration and variance is considered constant throughout
the concentration range. In such cases there is no need of weight or weight
becomes equal to unity. For cases where δ_{1}≠ δ_{2}≠
0, the choice of appropriate weight is decided on the basis of Sum of Square
(SS) values as given in Scheme 2. Where; SS (δ_{2}δ_{0},
δ_{1}) means SS due to inclusion of the δ_{2}X when
δ_{0 } and δ_{1}√X already exist in Eq.
7. Similarly SS (δ_{1 } δ_{0}, δ_{2})
indicates SS due to inclusion of the δ_{1}√X when δ_{0
} and δ_{2}X already exist in Eq. 7. So
on basis of Scheme 2, weight = 1/conc.^{2} and 1/conc.
can be selected to make variance homogeneous (Chow and Liu,
1995; Shahzad et al., 2003).
In this experiment, a UVvisible spectrophotometric method has been developed
to describe the processing of data in a way to relate absorbance and concentration
variables as per above theory. The model drug ofloxacin is a fluoroquinolone
category drug, freely soluble in water and measurable by UVspectroscopy. Ofloxacin
and other drugs that are rapidly and uniformly absorbed after oral administration
and have high oral bioavailability (∼100%) are good candidate for oral Extended
Release (ER) dosage forms. The ofloxacin ER tablet compositions of our previous
publication have been used to define various analytical parameters and absence
of interference from tablet excipients (Singh et al.,
2011).
MATERIALS AND METHODS
Materials, reagents and tablet composition: Ofloxacin (assay 99.8%) was provided by Ranbaxy, New Delhi, India. Hydroxypropyl methyl cellulose (3000 cps) and sodium alginate were purchased from S.D. Finechem. Ltd., Mumbai, India. Simulated Gastric Fluid (SGF) of pH 1.2 without enzymes, Simulated Intestinal Fluid (SIF) of pH 7.5 without enzymes and phosphate buffer of pH 6.2 were prepared as per USP standards. All the chemicals used were of AR grade.
The tablet composition “C” of our previous publication consists of
ofloxacin: HPMC: sodium alginate in 5:1:1 ratio (300 mg Ofloxacin, 60 mg HPMC,
60 mg sodium alginate) alongwith minor quantities of other assisting substances
like 3 mg magnesium stearate and 2 mg of talc (Singh et
al., 2011). Various other ofloxacin compositions (A1, A2, A3, B1, B2,
B3) were also prepared for assessing the specificity of the analytical method.
The compositions A1, A2, A3 were containing ofloxacin: HPMC in 2.5 : 1, 4 :
1, 5 : 1 ratios; while B1, B2, B3 were containing ofloxacin: sodium alginate
in 2.5 : 1, 4 : 1, 5 : 1 ratios. The amounts of ofloxacin and polymers in all
the compositions were used as per above ratios for an average of 425 mg final
tablet mixture.
Ofloxacin and ofloxacin composition solutions: The ofloxacin solutions were prepared by dissolving ofloxacin in SGF, buffer and SIF. Similarly, ofloxacin composition solutions were prepared by dissolving ofloxacin compositions A1, A2, A3, B1, B2, B3 and C in SGF, buffer and SIF. The solutions prepared were stock ofloxacin and stock ofloxacin composition solutions of 1 mg mL^{1} ofloxacin concentration.
Apparatus/ lab conditions: UVvisible spectrophotometer Beckman DU
640B, USA, Quartz cuvette of 1 cm path length were used for analysis. The pipettes
and volumetric flasks were certified class A apparatus, calibrated at 27°C.
The make of weighing balance was Afcoset ER 182A, Mumbai, India. All the measurements
were carried out at a lab temperature of 27±2°C.
Specificity of the method: Spiking experimental technique was used for
explaining specificity. The spiked samples of ofloxacin: HPMC, ofloxacin: sodium
alginate and ofloxacin: HPMC: sodium alginate were analyzed side by side with
unspiked samples to demonstrate effect on maximum absorbance wavelength (λ_{max})
(Amini et al., 2005). The unspiked samples of
concentration 5 μg mL^{1} were prepared from stock solutions of
ofloxacin (1 mg mL^{1}) after diluting with SGF, buffer and SIF. Similarly,
spiked samples of 5 μg mL^{1} concentration were prepared from
stock ofloxacin composition solutions with SGF, buffer and SIF. These standard
ofloxacin composition solutions were named A1, A2, A3, B1, B2, B3 and C as per
their original source of ofloxacin compositions. The samples were scanned in
the range of 200400 nm to determine λ_{max}. The absorbance scans
and absorbance values of these standard ofloxacin composition solutions were
compared with that of the standard ofloxacin solutions. The absence of interference
from polymers was decided on the basis of;( 1) absence of change (<5 nm)
in λ_{max} for standard ofloxacin solutions and standard ofloxacin
composition solutions in their respective media, and (2) less than 5.0% Relative
Standard Deviation (RSD) in absorbance values for standard ofloxacin solutions
and standard ofloxacin composition solutions.
Precision, range and stability of method: Ofloxacin stock solutions
and ofloxacin composition stock solutions were diluted with respective media
to get five concentrations between 28 μg mL^{1} range. Afresh
solutions of each concentration were prepared and analyzed at 0th, 4th and 8th
h of the day. The method was repeated for three consecutive days with preparation
of new solutions each day to address all the aspects of intra and interday
variations. The precision, range and stability of the method were established
on the basis of RSD values. In most of the cases the method is said to be precise
and stable if RSD is found to be <5.0% for response variable. In contrast,
the RSD values up to 10% has also been reported in literature for analysis of
ofloxacin in plasma and other biological fluids (Amini et
al., 2005).
Model selection and weight selection: The choice of appropriate model
or equation was done to describe actual relationship between absorbance and
concentration variables. The absorbance values were related to concentrations
as per polynomial regression in Microsoft Excel spreadsheet. Depending upon
coefficients (α, β) values obtained from regression statistics, the
polynomial equation was reduced to appropriate model as per Scheme
1. In most of the analytical methods, the relationship between absorbance
and concentration reduces to either model 1 or model 2. In rare cases the relationship
may lie among model 3, 4 or 5. The selection among higher models i.e., model
4 and 5, needs further assessment of Residual Sum of Square (RSS) values before
finalization of either model.
As for model selection, the weight selection was also decided on the basis
of coefficients (δ_{1 }and δ_{2}) values obtained
from regression analysis on standard deviation (SD(y)) vs. concentration in
Microsoft Excel spreadsheet. The selection of appropriate weights has been given
in Scheme 2. The maximum acceptance level for both model selection
and weight selection was kept at a plevel of 5.0%.
RESULTS AND DISCUSSION
Specificity of the method: As mentioned, the final compliance with specificity was done on basis of; a) insignificant change in λ_{max} of spiked and unspiked solutions and b) consistent value of absorbance for spiked and unspiked solutions. The λ_{max} of unspiked ofloxacin solutions was found to be 293±2, 286±3, 288±2 nm in SGF, buffer and SIF. The λ_{max} of spiked ofloxacin solutions, i.e., A1, A2, A3, B1, B2, B3 and C, were found to be lying within 292±3, 286±3, 287±4 nm in SGF, buffer and SIF (Table 1). The fluctuations were under the permissible limits and hence 293, 286 and 288 nm were considered as final λ_{max }values on an average basis for both ofloxacin solutions and ofloxacin composition solutions. The interference was also ruled out since data in Table 1 indicates that absorbance values of unspiked and spiked solutions remained within 5% RSD in all media. Therefore, the method remained specific w.r.t. ofloxacin even in the presence of excipients up to their maximum amounts utilized.
Precision, range and stability of method: Table 2
indicates that RSD of absorbance values (n = 9) at each concentration level
i.e., 2, 4, 5, 6 and 8 μg mL^{1} was <5.0%. As the solutions
were prepared three times, on three consecutive days and each sample was analyzed
thrice on its respective preparation day, so the inter and intraday variations
in the data remained under 5%, which reflects precision and stability of the
analytical method.
Table 1: 
Specificity and Interference data 

Av. Ab.: Average absorbance (n = 3), RSD: Relative standard
deviation 
Table 2: 
Precision, stability, range and weight data 

Av. Ab.: Average absorbance, SD: Standard deviation, RSD:
Relative standard deviation, Cal. Ab.: Calculated absorbance 
Table 3: 
Coefficients of polynomial and weight selection scheme 

Coeff.: Coefficients, SE: Standard error, ^{$}Actual
value is 0.000100, ^{#}Actual value is 0.000173 
The absorbance readings were lying between 0.20.8, so concentration range
of 28 μg mL^{1} can be considered as appropriate for the spectrophotometric
analysis of ofloxacin.
Model selection: As per Scheme 1, all five models
can be derived from single polynomial Eq. 1 on the basis of
values of different coefficients. The coefficient values were decided on the
basis of Standard Error (SE) and pvalues. The pvalue is the probability of
obtaining the estimated value of the coefficient if the actual coefficient is
zero. The smaller the pvalue, the more significant is the parameter and less
likeliness of the coefficient value to be equal to zero. The decision for considering
any coefficient equal to zero on basis of pvalue is applicable only when SE
value for that coefficient is smaller than coefficient’s own value. If
the SE is more than coefficient’s value then this indicates that coefficient
is showing more fluctuation and must be considered zero directly or independently
of the pvalue. In SGF (Table 3), value of α is 0.000
(not an absolute zero, rounded to three decimal places) and its SE is 0.002,
so error is more as compared to α value, hence its value was considered
equal to zero irrespective of the pvalue. For β_{1}, β_{2},
β_{3 }and β_{4} the SE values were less than coefficients
values, so, pvalues were considered for these coefficients. The pvalue <0.05
was found only for β_{1} hence β_{2}, β_{3}
and β_{4} were considered equal to zero and polynomial equation
reduced to y_{i} = β_{1}X_{i}+e_{i} (Model
2) equation. Therefore, model 2 was finalized for SGF case according to Scheme
1.
For buffer (Table 3), the β_{1} was significant as its SE was less than its own value and pvalue <0.05. The α was considered zero as its SE was more from its own value and β_{2}, β_{3} and β_{4} were not considered due to nonsignificant pvalues i.e., >0.05. Thus model 2 was finalized for buffer case.
For SIF (Table 3), the SE values were larger for β_{2},
β_{3} and β_{4} than coefficients own values and pvalue
was nonsignificant for β_{1}, so all of the coefficients were
considered equal to zero. But in this way absorbance became independent of concentration
term, which is not true in reality.

Scheme 1: 
Selection of Statistical Models for Standard Curves (α
is Intercept, β is Slope and e_{i} is Independent Variable) 

Scheme 2: 
Selection of Weight for Regression Model (Where SS (β_{2}
β_{0}, β_{1}) denotes Regression Sum of
Squares due to inclusion of the β_{2}X when β_{0}
and β_{1}X already exists in model) 
Such type of results appears mainly when data is related in a linear manner
but it is tried to fit to a higher polynomial relationships. The solution to
such a problem is starting with reduced polynomial equation i.e., y_{i}
= α+β_{1}X_{i}+β_{2}X_{i}^{2}+β_{3}X_{i}^{3}.
The new coefficient values for reduced equation have been given in parenthesis
in Table 3. Among the coefficients, β_{1} is
the only coefficient having high value than SE and significant pvalue. So,
in SIF, again model 2 was the final outcome explaining the relationship between
absorbance and concentration values.
Table 4: 
Regression sum of square values for weight selection scheme 

SS: Sum of square 
As the model 2 has been the model of choice in all pH conditions, the relationship between absorbance and concentrations can be declared linear and following y_{i} = β_{1}X_{i}+e_{i} (model 2) equation in all cases.
Weight selection: The Scheme 2 of weight selection
was applied on SD(y) and concentration values. The different coefficients (δ_{1}
and δ_{2}) were related to their levels of significance on basis
of the same methodology as used for model selection. The coefficient values,
SE and pvalues have been given in Table 3. As the values
of coefficients δ_{1} and δ_{2} were not equal to
zero i.e., δ_{1}≠δ_{2}≠0 in either of SGF, buffer
and SIF, so, selection of weights was done on the basis of SS values. In Table
4, it is clear that SS due to inclusion of δ_{2}X i.e., SS(δ_{2}δ_{0},
δ_{1}) was more as compared to SS due to the inclusion of δ_{1}√X
i.e., SS(δ_{1}δ_{0}, δ_{2}) in
all the cases, so the weight = 1/conc.^{2} was chosen for making variance
homogeneous.
CONCLUSION
In the present study a validated analytical procedure for ofloxacin determination in SGF, buffer and SIF has been developed. Classical regression methodology helped in prediction of best relationship between absorbance and concentration values alongwith balancing of variance heterogeneity. Further, the general statistical methodology also helped in screening of analytical method with respect to various validation parameters like specificity, precision, range, stability and inter/ intraday viability. Therefore, classical regression alongwith general statistics is beneficial in development of appropriate analytical method.