Clinical Chemistry Chapter 3

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Clinical ChemistryChapter 3

• Quality Control and Statistics

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Introduction

• What is normal or OK
• What makes something weird , abnormal or
  deviant and something to worry about?
• When does a laboratory test result become weird
  or abnormal ?
• At some point we have to draw a line in the
  sand on this side of the line youre normal
  on the other side of the line youre
  abnormal. Where and how do we draw the line ?
• In the laboratory, we have to be concerned with
  these issues because we have to give meaning to
  our observations or test results Are they
  normal or abnormal ?
• Statistics is used to draw lines in the sand
  for patient specimens, control specimens and
  calibrators
• If the results are normal we re comfortable
  about them and dont worry
• But if theyre abnormal, were uncomfortable and
  we fear that there is something wrong with the
  patient or the test procedure .

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• To answer these questions we need a little
  statistics
• There are two main ideas we need to concern
  ourselves with
• Central tendency
  
  ( how numerical values can be expressed as a
  central value )
• Dispersal about the central value
  ( how spread
  out are the numbers ? )
• Using these two main ideas we can begin to
  understand how basic statistics are used in
  clinical chemistry to define normal values and
  when our instruments are ( or are not )
  generating expected numerical results

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Key Terms

• Accuracy
• Control specimen
• Delta check
• Dispersion
• Histogram
• Precision
• Quality Assurance
• Quality Control
• Random error
• Reference method
• Shift
• Standard specimen
• Trend

• Standard Deviation ( SD )
• Coefficient of Variation ( CV )
• Mean
• Average
• Mode
• Median
• Gaussian Curve
• Westgard Rules
• Pre analytic
• Post analytic
• Range
• Levy Jennings Chart
• Z - Score

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• Objectives
• Define the Key Terms
• Discuss how statistics is used to determine
  normal values and establish QC ranges
• Given numerical observations, calculate the
• Mean, Mode, Median, Range, SD and CV
• Recognize random error, shifts and trends on
  Quality Control Charts
• Discuss common Westgard Control Rules

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• Statistical Concepts
• There are lies, dammed lies and statistics.
  (
  Quotation of 19th century British Prime Minister
  Benjamin Disreili )
• Statistics is a branch of mathematics that
  collects, analyzes, summarizes and presents
  information about observations.
• In the clinical lab, these observations are
  usually numerical test results
• A statistical analysis of lab test data can help
  us to define normal ranges for patients ( normal
  and abnormal ) and acceptable ranges for control
  specimens ( in and out of control )
• Descriptive statistics information about one
  group of observation
• Inferential statistics ways to compare
  different groups of observations

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• Common Descriptive techniques
• Mean Average value (expression
  of central tendency )
• Median Middle observation
  (expression of central tendency )
• Mode Most frequent observation (expression of
  central tendency )
• Observations can be grouped together into smaller
  groups. The frequency of each smaller group can
  be expressed graphically as a bar-chart or
  histogram
• Standard Deviation ( SD ) mathematical
  expression of the dispersion of the observations
  how spread out the observations are from each
  other
• Coefficient of Variation ( CV ) A way of
  expressing the Standard Deviation in terms of the
  average value of the observations that were used
  in its calculation

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• Accuracy versus Precision
• Accuracy Observations that are close to the
  true or correct value
• Precision Observations that are reproducible
  or repeatable
• The laboratory must produce results that are both
  accurate and reproducible

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Right on target !
Close enough ?
Keep your day job
In the laboratory we need to report tests with
accuracy and precision, but how accurate do we
need to be? Its not possible to hit the
bulls-eye every time. So how close is close
enough?
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3 possible testing outcomes - Hitting the target
x
x
x
Lacks precision and accuracy
x
x
Has good precision but poor accuracy
x
x
x
x
x
x
x
Good precision and good accuracy A lab must
report the correct results all the time !!!
x
x
x
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Formulas for Statistical Terms
Mean Median List all the
observations in order of magnitude and pick
the observation thats in the middle
Odd of observations
Middle observation Even of
observations Average of the 2 middle
values Mode The observation that
occurs most frequently
There may be more than one, or none at all All
three of these are expressions of a central
observation, but they dont say anything about
the observations as a whole Are they close
together? Although we can look at all the
individual observations, the mean, median and
modes by themselves do not give us any indication
about the dispersion of the observations
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Formulas for Statistical Terms
Standard Deviation
n the number of observations (how many
numerical values ) S the sum of in
this case, the sum of all the
the mean value
X the value of each individual
observation this means that the
value of will have
to be calculated for every value of
x The Standard Deviation is an expression of
dispersion the greater the SD, the more
spread out the observations are
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• Discussion of the Standard Deviation (SD)
• As the name suggests, it is a measurement of
  deviation
• More specifically, it can measure deviation in
  terms of an individual observation or a group of
  observations
• In both cases, the deviation is measured in
  terms of how far away the observation(s) are from
  the mean value
• The SD is a measurement of dispersion
• We use the SD to draw our lines in the sand
• For most considerations, laboratories will define
  normal or acceptable results as being within
  2.0 SD from the mean value
• If results are greater than 2.0 SD from the
  mean, then we say they are abnormal or out of
  control
• This means that they are unlike the other
  observations and they may be the results of
  faulty laboratory testing

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Calculation of the Standard Deviation
Data 10.0 10.1 10.2 10.3 10.4
Mean 10.2
( x x ) (x x )2
S ( x x )2 10.0 10.2 -
0.2 0.04 0.10 10.1 10.2 -
0.1 0.01 10.2 10.2 0.0 0.00 10.3 10.2
0.1 0.01 10.4 10.2 0.2 0.04
PS , Most calculators have statistical modes
that will easily do this for you
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Example of the Standard Deviation
Establishment of Normal Values A minimum of 20
observations should be sampled in order to obtain
valid results ( but Ill use just 6 to save time
) Lets determine the normal range for fasting
plasma glucose using 6 people Johns glucose
98 mg/dl Average 109 mg/dl Pauls
glucose 100 mg/dl SD 20.0
mg/dl Georges glucose 105 mg/dl 2 SD
40.0 mg/dl Ringos glucose 150
mg/dl Micks glucose 102 mg/dl Erics
glucose 101 mg/dl That means that
the normal range for this group is from 109 40,
or 69 - 149 which is 2.0 SD from the
mean Ringo is considered abnormal if we use this
commonly accepted criteria to define normal and
abnormal By the way, the CV for this group of
observations is about 18 - a fairly big
dispersal about the mean
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Example of Control Specimens
Every test in the laboratory requires that
control specimens be performed on a regular
basis to ensure the testing process is producing
accurate results. Running controls is a check
on the lab techs technique, reagents and
instrumentation. Suppose you are running the
glucose normal control and you get the
following results Glucose 100 mg/dl
Is this acceptable? To answer this question you
need to known what the previously established
acceptable range for this control specimen is (
done like the normal range ) Lets say the
acceptable range for this control specimen is
Mean 104 mg/dl SD 5
mg/dl That means that 2.0 SD 10
mg/gl The acceptable range for this control is
104 10 94 - 104 mg/dl In other words, 94
104 mg/dl is considered to be acceptable
dispersion. So, your control value of 100 mg/dl
is well within the acceptable range. Everything
seems to be working OK !!!
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• How can you find out how many Standard Deviations
  (SD) any one observation is from the mean?
• This is sometimes called the Z Score
• Its simply a way of expressing an observation in
  terms of how far away it is from the mean i (
  using 1 SD as a unit of measurement )
• Lets use our previous example
• What is the Z Score of Georges fasting plasma
  glucose?

Average 109 mg/dl Z Score
Patient - Mean SD 20 mg/dl
SD George
105 mg/dl
Georges glucose value was 0.2 SD below the mean
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Example of a Levy Jennings chart
A Levy Jennings chart is a graph that plots QC
values in terms of how many Standard Deviations
each value is from the mean
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But what if your control specimen is out of
control?

• Out of control means that there is too much
  dispersion in your result compared with the rest
  of the results its weird
• This suggests that something is wrong with the
  process that generated that observation
• Patient test results cannot be reported to
  physicians when there is something wrong with
  the testing process that is generating inaccurate
  reports
• Remember No information is better than wrong
  information
• Things that can go wrong and what to do
• Instrumentation malfunction ( fix the machine )
• Reagents deteriorated, contaminated, improperly
  prepared or simply used up ( get new
  reagents)
• Tech error ( identify error and repeat the test )
• Control specimen is deteriorated or improperly
  prepared ( get new control )

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Formulas for Statistical Terms
Coefficient of Variation (CV)
The CV allows us to compare different sets of
observations relative to their means Why the CV?
Whats wrong with the SD? Each SD is a
reflection only of the data that produced it, and
not other groups of observations. You cant use
the SD to compare different groups of data
because they are measuring different observations
- you cant compare apples to oranges. The CV
can turn all groups of observations into a
percentage of their relative means - everything
gets turned into oranges.
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• Example of the usefulness of the CV
• Which of the 2 following data sets is the more
  precise, or has the least dispersion?
• Set A SD 1.0
• Set B SD 2.0
• Simple, right? It seems to be Set A because it
  has the lower SD
• Remember, however, that we dont know what was
  measured . Heres some more information
• The mean for Set A 10 The SD
  is 1/10 of the mean
• The mean for Set B 1000 The SD is
  1/500 of the mean

In spite of having a larger SD, Set B is actually
far more precise in terms of the relative size of
its observations
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Establishment of Reference Ranges

• Each lab must establish its own reference ranges
• Factors affecting reference ranges
• Age
• Sex
• Diet
• Medications
• Physical activity
• Pregnancy
• Personal habits ( smoking, alcohol )
• Geographic location ( altitude )
• Body weight
• Laboratory instrumentation ( methodologies )
• Laboratory reagents

Normal ranges ( reference ranges ) are defined
as being within 2 Standard Deviations from the
mean
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Review of Statistical Calculations
Given the following plasma potassium
concentrations ( meq/l ) from 7 different
patients, calculate the mean, median, mode, SD
and CV 5.1 4.2 3.8 4.2 4.6
4.5 4.0 Answers below - Howd you
do?? Mean 4.3 Median
4.2 Mode 4.2 SD
0.4 CV 9.3

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Statistics Top 10

• Mean Arithmetic average value measurement of
  central tendency
• Median Middle observation arrange
  observations first
• Mode Most frequent observation ( if any ) ..,
  maybe more than 1
• SD Measure of dispersion how spread out
  observations are
• CV SD as a of the mean compares different
  data groups
• Z-score Converts observation into its distance
  from the mean in SDs
• Accuracy Closeness to the true or correct result
• Precision Reproducibility
• 2.0 SD Common acceptable dispersion range
• Levy Jennings Chart Graph of QC data in
  terms of SDs from the mean