statistics and errors in pharmaceutical calculations

7/29/2019 statistics and errors in pharmaceutical calculations

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PHARMACEUTICAL ANALYSIS

ERRORS

ANDSTATISTICAL VALIDATION


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PRESENTED BY:

RITIKA BHATIAM.PHARMA-II SEM

GUIDED BY:

MR. RAKESH MARWAHA

ASSISTANT PROFESSOR

DEPTT. OF PHARMACY

M.D.U ROHTAK


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INTRODUCTION

Statistics are concerned with the presentation,

organization, and summarization of data.

In this presentation we are going to discuss:

1. Errors

2. Statistical Validation


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ERRORS IN

PHARMACEUTICAL

INDUSTRY


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INTRODUCTION

The terminology ERROR refers to the differencein the numerical values between the measuredvalue and the true value.

It has become universally accepted in methodsof comparison that percentage composition of astandard sample provided and certified by NISTor BPCRS or European Pharmacopoeia must be

regarded and treated as absolutely correct, pureand authentic while evaluating a new analyticalprocedure.


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CLASSIFICATION OF ERRORS


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DETERMINATE (SYSTEMATIC) ERROR

These are the errors that posses a definite

value together with a reasonable assignable

cause. These errors are avoidable and can be

measured and accounted for convenience.


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TYPES OF DETERMINATE ERRORS

They are caused due to personal equation of an analyst & haveno bearing either on the prescribed procedure or methodologyinvolved.

PERSONALERRORS

These are caused due to faulty and uncalibrated instrumentsINSTRUMENTAL

ERRORS

These errors that are introduced by individual reagents. E.g.,impurities inherently present in reagent, unwanted introductionof foreign substances by action of reagent on porcelain orglassware.

REAGENTERRORS


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They are rather independent of themagnitude of measured amount andturn out be less significant as

magnitude enhances.

CONSTANTERRORS

The absolute value of this kind of error

changes with the size of the sample insuch a way that the relative errorremains constant.

PROPORTIONALERRORS

Both improper sampling andincompleteness of a reaction oftenlead to serious errors

ERRORS DUE TOMETHODOLOGY


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The additive errors are independent of

quantum of substances actuallypresent in assay.

ADDITIVEERRORS

These errors are usually caused by

environmental conditions over whichthe observer has no control

They cannot be eliminated butnecessary corrections may be applied

EXTERNALERRORS


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INDETERMINATE (RANDOM) ERROR

These cannot be pin-pointed to any specific

well defined reasons. They are usually

manifested due to the minute variations

which take place in several successivemeasurement performed by the same

analyst, using utmost care, under almost

identical experiment parameters.


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Random fluctuations

Recognition ofspecific defiant value

which are beyondanyone's control

Random variation Random scattering

SALIENTFEATURES


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ACCURACY

PRECISION


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ACCURACY It is the measure of

degree of closeness

PRECISION Its defined as the

agreement amongst

a cluster ofexperimental results.

Under similar

conditions the resultsare reproducible


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GRAPH

PROBABILITY

DENSITY

Accuracy

Precision VALUE

R

Accuracy indicates proximity of measurement results to the true value

Precision is the reproducibility of measurement

R=reference


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MINIMIZING SYSTEMATIC ERRORS

Instruments and apparatus commonly used in for analyticalpurposes must be calibrated duly and necessary correctionsmust be incorporated to the original measurement.

Calibration ofinstruments, apparatus& applying necessary

corrections

It comprises of performing altogether separate estimationunder almost identical experimental parameters with aquantity of standard substance that comprises of same wt.of component as in unknown sample.

Performing a parallelcontrol determination

It may be established by performing a separate parallelestimation without the sample under same experimentalconditions.

Blank determination


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The accuracy of results may be cross checked byperforming another analysis of the samesubstance by different method.

Cross checking ofresults by

different methods

of analysis

Small qty. of component is added to sample

which is subject to analysis for total amount ofcomponent present.

Gives recovery of quantum added component

Method of std.addition

A fixed quantity of reference std. or internal std.is added to a series of unknown concentrationof material to be assayed.

In chromatographic and spectroscopic

determinations.

Method ofinternal standards


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STATISTICAL VALIDATION


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INTRODUCTION

The data generated may show fluctuations &may be random in nature . The powerful &effective technique is employed to render such

random results into a set pattern. Suchtechnique is called STATISTICS.

The specific statistical treatment of thecalibration data, aided by preprogrammable

calculators and micro-computers, yielded a fairlyaccurate and more presentable determination ofthe graphs.


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STATISTICAL TREATMENT OF FINITE

SAMPLES

MEDIAN

MODE

MEAN


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MEAN

It is the average of a series of results.

X = x1+x2+x3+xn = Xi

N NThis is the arithmetic mean

X= x

NMean is the measure of central tendency.


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Themedian isthat half

of datapoints fallabove itand halfbelow it

MEDIAN

The mode

is mostfrequentoccurring

category

MODE


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THE MEAN MODE AND MEDIAN ARE

MEASURE OF CENTRAL TENDENCY


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MEASURE OF DISPERSION

A measure of dispersion refers to how closelythe data cluster around the measure of

central tendency.


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RANGE

1.The range is the difference between the

highest and the lowest value.

2.Because of problems with range such as

instability from one sample to other or new

subjects are added, another term called

interquartile range or midspread is used.

3.Interquartile=QL-QU


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INDEX OF DISPERSION

D =K(N2-fi2)

N2(K-1)

Where, K-no. of categoriesfi-no. of rating in each category

N-total no. of rating


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MEAN

DEVIATION

The sum of

deviation of any

set of nos.

around it mean

is 0.

Meandeviation=

X-X

N

VARIANCE

Variance is the

measure of avg.

deviation of

individual values

divided by N

S2=x2/N

STANDARD

DEVIATION

Its square root

of variance

Constantaddition toevery no.

doesnt change&hence S.D


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SKEWNESS & KURTOSIS

Skew refers to the symmetry of thecurve

CURVE A

CURVE B

Curve A: skewed right(+ve skew) Curve B: skewed left (-ve skew)


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Curve A

Curve B

Curve C

The 3 curves in the above graph are symmetric (skew=0) but they differ w.r.t flat orPeaked they are, this is called Kurtosis.


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CURVE A

Bell

shaped(normaldistribution)

MESOKURTICDISTRIBUTION

CURVE B

Peaked

LEPTOKURTICDISTRIBUTION

CURVE C

Flatter

PLATYKURTICDISTRIBUTION


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BOX PLOT

Its one of the most powerful

graphing techniques. It was

introduced by John Turkey


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GRAPHS

Mean, mode, median

Mean, mode, median in symmetric distribution.


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mode

median

mean

Mean, mode, median in skewed distribution


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SIGNIFICANT FIGURES

All digits that are certain plus which

contains some uncertainty are

significant figures


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COMPUTIONAL RULES

Addition & subtraction

+16.48+9.375+118.9-3.5450

+16.48+9.38+118.9-3.55=141.21=141.2

Multiplication & division

2.64X3.126x0.8524X32.9453

2.64X3.126X0.852X32.95=231.675=231.68{ 5 significant

figures}

Rounding numbers

8.62=8.6

9.38=9.4

If the last digit is 5,always round the

preceding digit tonearest even no ,eg8.75= 8.6


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STANDARD DEVIATION &STANDARD

ERROR

SEm = S.D = s

(Sample size) N

The S.D reflects how close individual scores

cluster around their mean

S.E shows how close mean scores from

repeated samples may be to true mean

Z = (X- U)

S.E


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COMPARISION OF RESULTS

Statistically, it may be possible to ascertain

whether the analytical procedure adopted

has accurate or precise or if its superior to

one of two methods.


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TWO METHODS FOR COMPARISON

STUDENT t-TEST ANOVA


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DEGREE OF FREEDOM

Its the no. of individual observationwhich can be allowed to vary under

conditions that mean(X) and SD

ones determined, beheld constant


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STUDENT t-TEST

This test focus on the distribution of differencesbetween the two groups, so that we test anotherhypothesis.

Under null hypothesis its presumed that the

difference arising from a distribution of differenceswith a mean of zero& SD is related original distribution. Its used tocompare the mean obtained from sample having

certain sample value and have to express certaindegree of confidence insignificance of comparison.

t= (X1-U)N/S


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ANOVA

The test uses ratio variances of two sets of

result to determine if SD are significantly

different

F= S12/S22

S1 &S2- SD of two sets of results.

Used to compare the results obtained from

two different labs or from two different

analytical procedures


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METHOD OF LEAST SQUARE

It has been noticed that experimental points

rarely fall exactly upon straight line by virtue

of indeterminate errors caused by

instrumental readings. Its tedious to obtainthe best straight line for a std. plot, based on

observed point so that the error is brought

down to least possible extent. At this stagemethod of least squares is used.


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REGRESSION LINE

Its the straight line passing through the data

that minimizes the sum of the square

differences between original data and fitted

points. The best fitted line is regression line.

SS(regression)=(y-Y)2

Where SS-sum of square, y-no. that results

from plugging the X value of individualregression


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SAMPLE SIZE

The sample sixe withdrawn from a

heterogeneous material is guided by

V=K/n

V-sampling variance, n-actual no. of sampling

increments, K-constant


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CONCLUSION

Statistical analysis is a widely used method in

pharma industry. Apart from pharma

industry its widely employed in form of

biostats, medicinal statistics, chemometrics,epidemology etc. Its also used in various

analysis for NDD.


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REFERENCE

Geoffrey R. Norman, David L. Streiner, Biostatistics,the bare essential II edition. Published by BC DeckersInc, Hamliton, 2000.

Ashutosh Kar Pharmaceutical drug analysis II

edition. Published by New Age InternationalPublishers, New Delhi 2008. pg 71-87

A.L Nagar, R.K Das Basic Statistics II edition.Published by Oxford University Press, New Delhi2000. pg 1-6, 30-56

Sanford Bolton, Charles Bon PharmaceuticalStatistics, practical and clinical applications IVedition. Published by Marcel Dekker, New York, 2004.


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THANK YOU

statistics and errors in pharmaceutical calculations

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