Statistically Justifiable Visible Residue Limits - Pharmaceutical Technology

Latest Issue
PharmTech

Latest Issue
PharmTech Europe

Statistically Justifiable Visible Residue Limits
Current methods for establishing visible residue limits (VRLs) are not statistically justifiable. The author proposes a method for estimating VRLs based on logistic regression.


Pharmaceutical Technology
Volume 34, Issue 3, pp. 58-71

Although the relationship between observed probability of detection and the residue concentration is nonlinear, a generalized linear modeling technique can be applied to these data. The logistic-regression technique fits the observed data with a linear model, the parameters for which are estimated using the maximum likelihood technique. Next, logistic regression transforms this linear model into a nonlinear logistic curve also known as an S-shaped or sigmoid curve. Logistic regression can therefore be seen as the conversion of a linear model into a nonlinear model that is naturally suited to the description of a binary response variable (13). The link function, commonly known as logit (the logarithm of odds), is used for converting the linear model to nonlinear logistic model and vice versa.




The logistic regression model is represented by the following equation (13):

in which P(Y =1) represents the predicted probability of response being equal to 1 (i.e., the predicted probability of detection); e is the exponent function; β0, β1, β2, ... βk are coefficients estimated from the data (obtained using the method of maximum likelihood); x 1, x 2, ... x k are independent variables; and k is the number of independent variables.




The term β0 + β1 x 1 + β2 x 2 ... + βk x k is the logit function and is defined as a natural logarithm of odds (e.g., the probability that an observer detects the residue divided by the probability that he or she does not detect it). Odds are expressed by the following equation:

For the data presented in Table III, which involves only one independent variable (i.e., residue concentration), logit = β0 + β1 x 1. Once a meaningful relationship is defined between spiked residue concentration and probability of detection, VRL could easily be obtained from the regression model.


ADVERTISEMENT

blog comments powered by Disqus
LCGC E-mail Newsletters

Subscribe: Click to learn more about the newsletter
| Weekly
| Monthly
|Monthly
| Weekly

Survey
FDASIA was signed into law two years ago. Where has the most progress been made in implementation?
Reducing drug shortages
Breakthrough designations
Protecting the supply chain
Expedited reviews of drug submissions
More stakeholder involvement
Reducing drug shortages
32%
Breakthrough designations
11%
Protecting the supply chain
37%
Expedited reviews of drug submissions
11%
More stakeholder involvement
11%
View Results
Jim Miller Outsourcing Outlook Jim Miller Health Systems Raise the Bar on Reimbursing New Drugs
Cynthia Challener, PhD Ingredients Insider Cynthia ChallenerThe Mainstreaming of Continuous Flow API Synthesis
Jill Wechsler Regulatory Watch Jill Wechsler Industry Seeks Clearer Standards for Track and Trace
Siegfried Schmitt Ask the Expert Siegfried SchmittData Integrity
Sandoz Wins Biosimilar Filing Race
NIH Translational Research Partnership Yields Promising Therapy
Clusters set to benefit from improved funding climate but IP rights are even more critical
Supplier Audit Program Marks Progress
FDA, Drug Companies Struggle with Compassionate Use Requests
Source: Pharmaceutical Technology,
Click here