This document discusses sensitivity analysis in drug development. Sensitivity analysis determines how changes in independent variables impact dependent variables. It allows decision-makers to identify areas for improvement. The document outlines methods of sensitivity analysis including local analysis of derivatives and global analysis using Monte Carlo techniques. Sensitivity analysis is useful for assessing risk, aiding decision making, and identifying errors in models. It provides insight into how sensitive outcomes are to changes in parameter values.

1. SUBJECT: COMPUTER AIDED DRUG DEVELOPMENT
SUBMITTED BY: SUBMITTED TO
PAWAN DHAMALA Prof K MAHALINGAN
2nd SEM M. Pharm Department of Pharmaceutics
Introduction of Non linear Pharmcokinetics

2. CONTENT
 Introduction of Non linear Pharmokinetics
 Detection of Non-linearity
 Estimation of Km and Vmax
 Sensitivity Analysis
 Sensitivity Analysis Advantages
 Sensitivity Analysis Disadvantages
 Sensitivity Analysis Formula
 Methods of Sensitivity Analysis
 Uses of Sensitivity Analysis
 Conclusion

3. INTRODUCTION
 The rate process of drug’s ADME are depend upon carrier or enzyme that are substrate
specific, have definite capacities and are susceptible to saturation at a high drug
concentration.
 In such cases, an essentially first-order kinetics transform into a mixture of first-order and
zero-order rate processes and the pharmacokinetics parameters are changed with the size
of the administered dose.
 Pharmacokinetics of such drugs are said to be dose-dependent. Terms synonymous with it
are mixed-order, nonlinear and capacity-limited kinetics.

4. Detection of non-linearity
There are several tests to detect non-linearity in pharmacokinetics but the simplest ones
are:
First test: Determination of steady state plasma concentration at different doses.
Second test: Determination of some important pharmacokinetic parameters such as
fraction bioavailabity, elimination half life or total systemic clearance at different
doses of drug. Any change in these parameters in indicative to non-linearity which are
usually constant.

5. Estimation of Km and Vmax
• In enzymatics kinetic work, the classic Michaelis-Menten equation:
V=Vmax.C ---- (1)
KM+C
Where, V=reaction rate,
C=substrate conc. Both are used to determine Vmax & Km.
The velocity of the reaction(V) at various concentration levels of drug(c) are determined
either by in-vitro experiments or in-vivo experiments at constant enzyme levels.

6. Method 1

8. Sensitivity Analysis
• The technique used to determine how independent variable values will impact a
particular dependent variable under a given set of assumptions is defined
as sensitivity analysis.
• It’s usage will depend on one or more input variables within the specific
boundaries, such as the effect that changes in interest rates will have on a bond’s
price.
• It is extensively used by economists and financial analyst.
• This technique is used within specific boundaries that depend on one or more
input variables.

9. Sensitivity Analysis Advantages
• The advantages of sensitivity analysis are numerous. Because it’s an in-depth
study of all the variables.
• It allows decision-makers to see exactly where they can make improvements.
• Sensitivity analysis is also fairly simple to understand. The numerical
outcomes do not favour any particular variables.

10. Sensitivity Analysis Disadvantages
Following are the disadvantages of this analysis:
• Sensitivity analysis is based on historical data & management assumptions. If
these assumptions itself are wrong, the whole analysis will be wrong and the
future forecast will not be accurate.
• It is not Relative in Nature.
• It does not reflects the effects of diversification.
• It ignores the interaction among the variables.

11. Sensitivity Analysis Formula
• The formula for sensitivity analysis is basically a financial model in excel
where the analyst is required to identify the key variables for the output
formula.
• Then the output based on different combinations of the independent variables.
• Mathematically, the dependent output formula is represented as,
Z = X2 + Y2
Example:
• Let us take the example of a simple output formula, which is stated as the
summation of the square of two independent variables X and Y.

12. • In this case, let us assume the range of X as 2, 4, 6, 8, and 10, while that of Y
as 1, 3, 5, 7, 9, 11, and 13. Based on the above-mentioned technique, all the
combinations of the two independent variables will be calculated to assess the
sensitivity of the output.
• For instance, if X = 3 (Cell B2) and Y = 7 (Cell B3), then Z = 32 + 72 = 58
(Cell B4).

13. Methods of Sensitivity Analysis
1. Local Sensitivity Analysis
2. Global Sensitivity Analysis
1. Local sensitivity analysis is derivative based (numerical or analytical). The term
local indicates that the derivatives are taken at a single point. This method is for simple cost
functions, but not feasible for complex models, like models with discontinuities do not always
have derivatives.
 Mathematically, the sensitivity of the cost function with respect to certain parameters is
equal to the partial derivative of the cost function with respect to those parameters.

14. 2. Global sensitivity analysis is the second approach to sensitivity analysis, using
Monte Carlo techniques. This approach uses a global set of samples to explore the
design space.
The various techniques widely applied include:
• Differential Sensitivity analysis
• One at a time sensitivity measures
• Factorial Analysis method
• Correlation Analysis method
• Regression Analysis method
• Subjective Sensitivity analysis

15. Differential Sensitivity Analysis:
• It is also referred to the direct method. It involves solving simple partial derivatives to
temporal sensitivity analysis.
• Although this method is computationally efficient, solving equations is intensive task to
handle.
• Differential analysis of parameter sensitivity is based on partial differentiation of the model in
aggregated form. It can be thought of as the propagation of uncertainties.

16. One at a Time Sensitivity Measures:
• It is the most fundamental method with partial differentiation, in which
parameters values are taken one at a time.
• It is also called as local analysis as it is an indicator only for the addressed point
estimates and not the entire distribution.

17. Factorial Analysis:
• It involves the selection of given number of samples for a specific
parameter and then running the model for the combinations.
• The outcome is then used to carry out parameter sensitivity.
Correlation Analysis:
• It helps in defining the relation between independent and dependent
variables.

18. Subjective Sensitivity Analysis:
• In this method the individual parameters are analysed. This is a subjective
method, simple, qualitative and an easy method to rule out input
parameters.
• It helps in assessing the risk of strategy, identifying and analysing the
dependent of the output on the input values.

19. Regression Analysis:
• It is a comprehensive method used to get responses for complex models.
• The generalized form of a simple regression equation is:
Y = 𝑏0 + 𝐾 𝐵𝑘 𝑍𝑘,
• Where each Zk is a predictor variable and a function of (X1 ..... Xn) and each
bk is a regression coefficient.

20. Uses of Sensitivity Analysis
• The key application of sensitivity analysis is to indicate the sensitivity of
simulation to uncertainties in the input values of the model.
• They help in decision making
• It helps in assessing the riskiness of a strategy.
• Helps in taking informed and appropriate decisions
• Aids searching for errors in the model
• Helps in identifying how dependent the output is a particular input value.

21. Conclusion
• Sensitivity analysis is one of the tools that help decision makers with more
than a solution to a problem.
• It provides an appropriate insight into the problems associated with the model
under reference.
• Finally the decision maker gets a decent idea about how sensitive is the
optimum solution chosen by him to any changes in the input values of one or
more parameters.

22. REFERENCE
• https://www.slideshare.net/non-linear-kinetics
• https://www.edupristine.com/blog/all-about-sensitivity-analysis
• http://cleartax.in/g/terms/sensitivity-analysis
• http://www.Investopedia.com/terms/s/sensitivityanalysis.asp
• http://gocardless.com/guides/posts/what-is-sensitivity-analysis/