Computer in pharmaceutical research and development-Mpharm(Pharmaceutics)

Statistics- Statistics is the science of collecting, organizing, presenting, analyzing and interpreting numerical data to assist in making more effective decisions.
 A statistics is a measure which is used to estimate the population parameter
 Parameters-It is used to describe the properties of an entire population.
Examples-Measures of central tendency Dispersion, Variance,  Standard Deviation (SD), Absolute Error, Mean Absolute Error (MAE), Eigen Value

1. COMPUTERS IN Pharmaceutical  research and  development Submitted To-  Dr. Rameshwar Dass (Associate Professor) Submitted By- Muskan (M-506) M.pharm. (2nd Sem) GURU GOBIND SINGH COLLEGE OF PHARMACY

2. STATISTICAL PARAMETERS Estimation Statistics - Statistics is the science of collecting, organizing, presenting, analyzing and interpreting numerical data to assist in making more effective decisions.  A statistics is a measure which is used to estimate the population parameter   Parameters -It is used to describe the properties of an entire population . Examples-Measures of central tendency Dispersion, Variance,  Standard Deviation (SD), Absolute Error, Mean Absolute Error (MAE), Eigen Value 2

3. 3 Measure of central tendency MEAN: The average of the data MEDIAN: The middle value of the data MODE: Most commonly occurring value Dispersion It is the extent to which a distribution is stretched or squeezed. Variance It measures how far a set of random numbers are spread out from the mean. Standard Deviation( σ) It is a measure used to quantify the amount of variation or dispersion of a set of data values. It is a numerical measure of the scatter of the data. Absolute Error (AE)  It is the magnitude of the difference between the exact value and the approximation Mean Absolute Error It is an average of the absolute errors. Eigen Value Eigenvalues are the special set of scalars associated with the system of linear equations. It is mostly used in matrix equations. 

4. STATISTICAL PARAMETERS ESTIMATION • It is required to minimize the impact of experimental errors or process parameters (Temp, pressure, concentration) which can be achieved by parameter estimation. Two types of estimation  1. Point estimation - Use of sample data to measure single value 2. Interval estimation – measure-  Upper value                                                           Lower value Interval estimation is better than point because it indicate range of precision.   Lower confidence limit (Lower value) and upper confidence limit (upper value) are present in confidence interval of interval estimation.

5. CONFIDENCE REGION 5 Confidence interval- It is a set of points in an n-dimensional space, often represented as an ellipsoid around a point which is an estimated solution to a problem, although other shapes can occur.  •   Confidence regions are multivariate extensions of univariate confidence intervals.  •    Confidence regions are sometimes called as interference regions.  •    The purpose of confidence interval is to estimate a parameter.  •    Confidence interval is often used to express the uncertainty in analytical result in pharmaceutical processes.  It has 3 elements:  A) Interval itself B) Confidence level (ex. 90,95 or 99%)  C) Parameter to be estimated (ex. population mean )

6. Non-linearity at the optimum  6 It is useful to study the degree of non-linearity of Statistical model in a neighborhood of forecast. If maximum non-linearity is excessive, for one or more parameters the confidence regions obtained by applying the results of classic theory not trusted.  In this case, alternative simulation procedures may be employed to provide empirical confidence regions.

7. Sensitivity analysis It is a technique to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions. It helps in analyzing how sensitive the output is, by the changes in one input while keeping the other inputs constant.  In the pharmaceutical manufacturing processes, sensitivity analysis has been used to quantify the individual effects and the interaction effects of the input factors, including critical design parameters, material properties, and operating conditions, for unit operations and integrated processes.  The results of sensitivity analysis can also be used to guide where the     models need to be further detailed, and to aid the development of           control strategies for qualified product.

8. 8 Principle : Sensitivity analysis works on simple principle i.e. change the model and observe the behavior.  Methods of sensitivity analysis  Modelling and simulation techniques Scenario management tools through Microsoft excel  There are mainly two approaches to analysing sensitivity Local Sensitivity Analysis  Global Sensitivity Analysis Sensitivity analysis

9. PRESENTATION TITLE 9 SENSITIVITY ANALYSIS Local SA  focus on the effects of uncertain inputs around one single point keeping the other parameters fixed Global SA  determine the influences of uncertain input factors over the whole input space. Screening method  e.g. Morris method  Morris method is an efficient way of screening a few important input factors (especially when large in no.) with small sampling cost. Regression-based method  e.g. PRCC method  PRCC is a measure of the strength of the linear relationship between two variables when all linear effects of other variables are removed. Variance-based method  e.g. Sobol's method Describes how the variance of output can be decomposed into terms depending on input factors and their interactions.

10. SENSITIVITY ANALYSIS PRESENTATION TITLE 10 Uses  They help in decision making. Testing the robustness of results of model in presence of uncertainty Reduction of uncertainty  Increased understanding of input and output variables in a model.  Searching for errors and their evaluation

11. Optimal design 11 Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.  Optimal designs allow parameters to be estimated without bias and with minimum variance A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design.

12. Methods of optimal Design 12 A-optimal design (average or trace)  It results in minimizing the trace (sum of eigenvalues) of inverse of information matrix by minimizing the average variance of the estimates of the regression coefficients. C-optimal design This criterion minimizes the variance of a best linear unbiased estimator of a predetermined linear combination of model parameters. D-optimal design (determinant)  It seeks to minimize the (X'X) 11, or equivalently maximize the determinant (product of eigenvalues) of the information matrix X'X of the design. E-optimal design (Eigen value)  It maximizes the minimum eigenvalue of the information matrix. T-optimal design  This criterion maximizes the trace of the information matrix.  G-optimal design It minimizes the maximum variance of the predicted values.  I-optimal design (integrated)  It seeks to minimize the average prediction variance over the design space.   V-optimal design (variance) It seeks to minimize the average prediction variance over a set of m specific points.

13. D-Optimal design 13 D-Optimal designs are one form of design provided by a computer algorithm. These type of computer aided designs are particularly useful when classical designs do not apply.  Unlike standard classical designs such as factorial and fractional factorials, D-optimal design matrices are usually not orthogonal and effect estimates are co-related. The reasons for using D-optimal designs instead of standard classical designs usually fall into 2-categories:  The standard factorial or fractional factorial designs requires too many runs for the amount of resources or time allowed for the experiment  The design space is constrained. i.e. the process space contains factor setting that are not feasible and or impossible to run.

14. Population modeling  14 Population modeling is an important tool in drug development. Population modeling is a complex process requiring robust underlying procedures for ensuring clean data, appropriate computing platforms, adequate resources and effective communication. Population modeling methods provide a framework for quantitating and explaining variability in drug exposure and response.  It is a tool to identify and describe the relationships between a subject's physiologic characteristics and observed drug exposure or response.  Population Modelling is a type of mathematical model that is applied to the study of population dynamics

15. Components of POPULATION MODELING  Structural models Functions that describe the time course of a measured response, and can be represented as algebraic or differential equations. Stochastic models Describe the variability or random effects in the observed data Covariate models  Describe the influence of factors such as demographics or disease on the individual time course of the response PRESENTATION TITLE 15

16. Methods for estimating population models naive pooled approach Fitting the combined data from all the individuals  Ignoring individual differences  two-stage approach. Fitting each individual's data separately   combining individual parameter estimates to generate mean (population) parameters  PRESENTATION TITLE 16

17. Thank you