ppt

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2. 
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 Problem statement, research
questions, purposes, benefits
 Theory, assumptions, background
literature Variables and hypotheses
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Operational definitions and measurement
Research design and methodology
Instrumentation, sampling
Data analysis
Conclusions, interpretations, recommendations

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A sample is “a smaller (but hopefully
representative) collection of units from a
population used to determine truths about that
population” (Field, 2005)
Why sample?
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Resources (time, money) and workload
Gives results with known accuracy that can be
calculated mathematically
 The sampling frame is the list from which the
potential respondents are drawn
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Registrar’s office
Class rosters
Must assess sampling frame errors
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4.  What is your population of interest?
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To whom do you want to generalize your
results?
All doctors
School children
Indians
Women aged 15-45 years
Other
Can you sample the entire population?
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5. 
3 factors that influence sample
representative- ness
 Sampling procedure
 Sample size
 Participation (response)
 When might you sample the entire population?
 When your population is very small
 When you have extensive resources
 When you don’t expect a very high response
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6. 8
SAMPLING BREAKDOWN

7. 9
TARGET POPULATION
STUDY POPULATION
SAMPLE

8. Probability (Random) Samples
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 Simple random sample
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Systematic random sample
Stratified random sample
Multistage sample
Multiphase sample
Cluster sample
 Non-Probability Samples
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Convenience sample
Purposive sample
Quota 10

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The sampling process comprises several stages:
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Defining the population of concern
Specifying a sampling frame, a set of items or
events possible to measure
Specifying a sampling method for selecting
items or events from the frame
Determining the sample size
Implementing the sampling plan
Sampling and data collecting
Reviewing the sampling process

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A population can be defined as
including all people or items with
the characteristic one wishes to
understand.
 Because there is very rarely enough time or
money to gather information from everyone
or everything in a population, the goal
becomes finding a representative sample (or
subset) of that population.

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A probability sampling scheme is one in which every
unit in the population has a chance (greater than
zero) of being selected in the sample, and this
probability can be accurately determined.
 . When every element in the population does have the
same probability of selection, this is known as an
'equal probability of selection' (EPS) design. Such
designs are also referred to as 'self-weighting'
because all sampled units are given the same weight.

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Probability sampling includes:
Simple Random Sampling,
Systematic Sampling,
Stratified Random Sampling,
Cluster Sampling
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Multistage Sampling.
Multiphase sampling

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Any sampling method where some elements of population have no
chance of selection (these are sometimes referred to as 'out of
coverage'/'undercovered'), or where the probability of selection can't
be accurately determined. It involves the selection of elements based
on assumptions regarding the population of interest, which forms the
criteria for selection. Hence, because the selection of elements is
nonrandom, nonprobability sampling not allows the estimation of
sampling errors..
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Example: We visit every household in a given street, and interview the
first person to answer the door. In any household with more than one
occupant, this is a nonprobability sample, because some people are
more likely to answer the door (e.g. an unemployed person who spends
most of their time at home is more likely to answer than an employed
housemate who might be at work when the interviewer calls) and it's
not practical to calculate these probabilities.

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Nonprobability Sampling includes:
Accidental Sampling, Quota Sampling and
Purposive Sampling. In addition,
nonresponse effects may turn any
probability design into a nonprobability
design if the characteristics of
nonresponse are not well understood, since
nonresponse effectively modifies each
element's probability of being sampled.

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Applicable when population is
small, homogeneous & readily
available
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All subsets of the frame are given an equal
probability. Each element of the frame thus
has an equal probability of selection.
It provides for greatest number of possible
samples. This is done by assigning a number
to each unit in the sampling frame.
A table of random number or lottery system
is used to determine which units are to be
selected. 19

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Estimates are easy to calculate.
Simple random sampling is always
an EPS design, but not all EPS
designs are simple random
sampling.
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Disadvantages
If sampling frame large, this method impracticable.
Minority subgroups of interest in population may not be
present in sample in sufficient numbers for study.

17. Optimization Concept:
 The term Optimize is defined as to make perfect , effective , or as functional
as possible.
 It is the process of finding the best way of using the existing resources while
taking in to the account of all the factors that influences decisions in any
experiment
 Traditionally, optimization in pharmaceuticals refer to changing one variable
at a time, so to obtain solution of a problematic formulation.
 Modern pharmaceutical optimization involves systematic design of
experiments (DoE) to improve formulation irregularities.
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18. ⚫Optimization is used in pharmacy relative to
formulation and processing .
⚫It is the process of finding the best way of using the
existing resources while taking in to the account of all
the factors that influences decisions in any
experiment.
⚫Final product not only meets the requirements from
the bioavailability but also from the practical mass
production criteria. .
In development projects , one generally
experiments by a series of logical steps, carefully
controlling the variables & changing one at a
time, until a satisfactory system is obtained
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19. ⚫Target processing parameters – ranges for each
excipients & processing factors .
Questions optimization requires:
• How we can make Formulation perfect ?
⚫What should be characteristics?
⚫ What should be the conditions?

20. Why is Optimization necessary?
OPTIMIZATION
Safety &
Reducing
error
Reproducib
ility
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Save
Time
Primary objective may not be to optimize absolutely but to compromise
effectively & thereby produce the best formulation under a given set of
restrictions .
Reducing
cost

21. Formulation and Processing
Clinical Chemistry
Medicinal Chemistry
High Performance Liquid Chromatographic
Analysis
Formulation of Culture Medium in Virological
Studies.
Study of Pharmacokinetic Parameters.
APPLICATIONS:
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22. Terms Used
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o FACTOR: It is an assigned variable such as concentration , Temperature
etc..,
Quantitative: Numerical factor assigned to it
Ex- Concentration- 1%, 2%,3% etc.
Qualitative: Which are not numerical
Ex- Polymer grade, humidity condition etc.
o LEVELS: Levels of a factor are the values or designations assigned to
the factor.
o RESPONSE: It is an outcome of the experiment.
• It is the effect to evaluate.
Ex- Disintegration time.

23. Terms Used
o EFFECT: It is the change in response caused by
varying the levels
 It gives the relationship between various factors
& levels.
o INTERACTION: It gives the overall effect of two
or more variables
Ex- Combined effect of lubricant and glidant on
hardness of the tablet
FACTOR LEVELS
Temperature 300 , 500
Concentration 1%, 2%
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24. Advantages
o Yield the “Best Solution” within the domain of study.
o Require fewer experiments to achieve an optimum
formulation.
o Can trace and rectify problem in a remarkably easier
manner.

26. Softwares for Optimization
⚫ Design Expert 7.1.3
⚫ SYSTAT Sigma Stat 3.11
⚫ CYTEL East 3.1
⚫ Minitab
⚫ Matrex
⚫ Omega
⚫ Compact 21-Apr-15 O

27. PARAMETERS
CONSTRAINED
PROBLEM TYPE
UNCONSTRAINED
VARIABLES DEPENDENT
INDEPENDENT
Optimization Parameters
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28. Problem Types
Unconstrained
• In unconstrained optimization problems there are no restrictions.
• For a given pharmaceutical system one might wish to make the hardest
tablet possible.
• The making of the hardest tablet is the unconstrained optimization problem.
Constrained
• The constrained problem involved in it, is to make the hardest tablet possible,
but it must disintegrate in less than 15 minutes.
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29. Variables
• Independent variables : The independent variables are under the control of
the formulator. These might include the compression force or the die cavity
filling or the mixing time.
• Dependent variables : The dependent variables are the responses or the
characteristics that are developed due to the independent variables. The
more the variables that are present in the system the more the
complications that are involved in the optimization.

30. Example of Variables

31. ⚫Once the relationship between the variable
and the response is known, it gives the
response surface as represented in the Fig. 1.
Surface is to be evaluated to get the
independent variables, X1 and X2, which
gave the response, Y.Any number of
variables can be considered, it is impossible
to represent graphically, but mathematically it
can be evaluated.
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33. Factorial Design (FD)
⚫ Factorial experiment is an experiment whose
design consist of two or more factor each with
different possible values or “levels”.
⚫FD technique introduced by “Fisher” in 1926.
⚫Factorial design applied in optimization
techniques.
⚫Factors : Factors can be “Quantitative” (numerical
number) or they are qualitative. They may be
names rather than numbers like Method 1, site B,
or present or absent .

34. ⚫Factorial design depends on independent
variables for development of new formulation .
⚫Factorial design also depends on Levels as well
as Coding
⚫There are three types of levels : 1) LOW
2)INTERMEDIATE 3) HIGH
⚫Simultaneously CODING takes place for Levels :
1) for LOW = (-1)
2)For intermediate = (0)
3) for HIGH =(+1)
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35. ⚫FD is for the evaluation of multiple factors
simultaneously.
⚫2 3 means 2 is level while 3 is factor .
⚫ Factorial Design is divided into two types
1. Full Factorial Design
2.Fractional factorial design
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36. 1.Full Factorial
Design
⚫A design in which every setting of every factor
appears with setting of every other factor is full
factorial design.
⚫Simplest design to create, but extremely
inefficient.
⚫If there is k factor , each at Z level , a Full FD has
ZK
Number of runs (N)
N = y x Where, y = number of levels, x = number of
factors E.g.- 3 factors, 2 levels each, N = 23 = 8
runs
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37. ⚫Factorial Design : 22 , 23 , 32 , 33
⚫22 FD = 2 Factors , 2 Levels = 4 runs
⚫23 FD = 3 Factors , 2 Levels = 8 runs
⚫32 FD = 2 Factors , 3 Levels = 9 runs
⚫33 FD = 3 factors , 3 Levels = 27 runs

38. TWO Levels Full FD :
⚫ 2 factors : X1 and X2 (Independent variables)
⚫ 2 levels : Low and High
⚫Coding : (-1) , (+1)
Three level Full FD :
In three level factorial design ,
• 3 factors: X1, X2 and X3
• 3 levels are use ,
1) low (-1)
2) intermediate (0)
3) high (+1)
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39. FRACTIONAL FACTORIAL
DESIGN
⚫In Full FD , as a number of factor or level
increases , the number of experiment required
exceeds to unmanageable levels .
⚫In such cases , the number of experiments can
be reduced systemically and resulting design is
called as Fractional factorial design (FFD).
⚫Applied if no. of factor are more than 5 .
⚫Means “less than full”
⚫Levels combinations are chosen to provide
sufficient information to determine the factor
effect
⚫ More efficient

40. Types of Fractional Factorial Design
⚫Homogeneous fractional
⚫ Mixed level fractional
⚫ Plackett-Burman
Homogenous fractional
Useful when large number of factors must be
screened
Mixed level fractional
Useful when variety of factors need to be
evaluated for main effects and higher level
interactions can be assumed to be negligible.
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41. Response surface methodology, or RSM
 Collection of mathematical and statistical techniques
 Useful for the modeling and analysis of problems
 Response of interest is influenced by several variables
 The objective is to optimize the response.
 Temperature (x₁) and pressure (x₂) & yield (y)
 The levels of temperature (x₁) and pressure (x₂) maximize the yield (y) of a process
 The process yield is a function of the levels of temperature and pressure, say
y = f (x₁, x₂) + 𝜖
For example
Region of Interest
Region of Operability