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Medical Laboratory Technology: Volume 1
StatiSticaL QuaLity controL of Quantitative Data
It is dicult to apply statistical tools in evaluating data which are of a qualitative or subjective
nature. Quantitative laboratory data must be subjected to rigorous ‘quality control’
procedures in order to obtain dependable information for clinical diagnosis. The commonly
followed procedure of quality control in handling quantitative data will be discussed in this
section. Before we focus on the quality control procedures of laboratory ndings, it may be
worthwhile to explain some of the commonly used terms in quality control.
Commonly used terms in quality control
Control: Controls are solutions that contain the same constituents as the patient sample.
The control sera must be analysed with patient sample using identical methods, test
conditions and reagents. At least two levels of controls should be used and these have to be
run at least daily. Records of the control assay must be documented for any future inspection.
Standard solution: It is a carefully made solution of the test substance whose concentration
is known.
Calibration and Standards: A standard or reference material is a substance that has an exact
known composition and that, when accurately weighed or measured can produce a solution
of exact concentration.
Calibration refers to process of checking, standardizing, adjusting a method or equipment
so that it yields accurate results.
Precision: Precision refers to reproducibility of results or the closeness of obtained results to
each other.
Accuracy: Accuracy refers to closeness of the result to the true value.
Dependability: A combination of precision and accuracy that implies reproducibility and
accuracy (close to the true value).
baSic StatiSticS
Quality Control programs use Statistics, the branch of Mathematics that deals with
collection, classication, analysis and interpretation of numerical data. The entire collection
of observations is called a population, while a group of specimens realized from this bigger
domain is called a sample.
A few common statistical measures used in Quality Control (QC) are mean, standard deviation, coecient of variation and tolerance range.
Mean
The arithmetic mean, often simply called the ‘mean’, is a measure of central tendency of the
dataset and denoted by X—. It is calculated by summing up value of each observation, divided
by the number of observations. In mathematical notations,
where Σ is the summation symbol, Xi = individual observation and n is the number of
observations. For example, the arithmetic mean of six values: 34, 27, 45, 55, 22 and 34 is
obtained as
X
36 167.
6
Good Laboratory Practices and Statistical Quality Control
()XX
n
1
ii
in1
2
SD =
6 8575 47089
0568
CV(%
SD
219
Standard deviation (SD)
It is a commonly used measure of dispersion of the data and is measured by variability from
the mean. It is dened as
SD =
i
n
1
2
i
where Σ = summation sign; Xi = individual observation; X = mean and n = number of
observations.
This can be simplied for easy calculation, often referred to as the calculator method for
determining standard deviation:
2
n
2
i
1
1
()
nn
2
X
= square of the sum of all values;
i
1
in
where,
SD =
n
2
= sum of squares of individual values;
X
i
i
1
n
nX X
i
1
and n = number of observations. Using the calculator method for the dataset above, we note
n
2
X
8575
i
i
1
that
and
X
47089
i
65
. Substituting in the formula, we get
12
.
These two methods can give slightly dierent numerical results; however, the numerical
dierence is expected to be minimal for datasets with at least 20 observations.
Coefficient of variation
For some purposes, the standard deviation is expressed as a percentage of the mean value.
This is called the coecient of variation (CV) or relative standard deviation (RSD); the laer
is a beer term. Coecient of variation is calculated as follows:
) = 100
Mean
Tolerance range
It is the acceptable range of variation in quality control. This is equivalent to ±2SD.
Use of Standard Deviation in Laboratory
It is expected that the data for most situations in a laboratory will be from a bell-shaped curve, also
called normal distribution or Gaussian distribution (Figure 7.1). This curve is symmetric about
the mean, with half of the values greater than the mean and half less than the mean (Figure 7.1a).
Frequency of values closer to the mean is higher than that away from it.
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Medical Laboratory Technology: Volume 1
Figure 7.1 Normal distribution curve showing (a) frequency distribution around the mean, (b)
proportion of population falling between mean and ± 1s (SD), ±2s (SD) and ±3s (SD)
Normal distribution can be divided into percent divisions in terms of its mean and standard
deviation. If s refers to its standard deviation, then we note that 68.2% of the values are expected
to lie between x ± s; 95.4% between x ± 2s; and 99.8% between x ± 3s (Figure 7.1b). As only 0.4% of
the values are expected to be greater than x + 3s or less than x –3s, special aention should be paid
to values exceeding these thresholds and double checked to ensure that they are not due to any
systematic errors. Values outside x ± 3s threshold are called outliers.
Clinical laboratories must establish allowable standard deviation for each analysis method.
A common choice is two-standard deviation limit, often called condence limit. As noted
before, it is expected that 95.4% of the values lies between this condence limit.
Preparation of Quality Control Chart
Quality Control (QC) charts or Levey–Jennings charts demonstrate a method’s precision and
allow problems to be easily detected. This will be further illustrated with the help of an example.
Good Laboratory Practices and Statistical Quality Control
221
Suppose for a particular method, the mean is 75 and the standard deviation is 8. In
Figure 7.2, thus, mean line is 75 and lines on either side of the mean line denote ±2s. For each
day, the control serum is ploed (Figure 7.3).
A trend is observed when a series of control values consistently increase or decrease
(moves away from the mean in the same direction) for consecutive days (Figure 7.4).
It is a signal of a systematic error that the laboratory technician should further investigate and locate the root cause. Some of the common sources of such an error are the
instrument, the technique, the reagents or the control serum. Once the source is located,
a new lot of control serum can be analysed. If the error is still present, it may call for
recalibrationof instruments.
Control serum is expected to randomly uctuate above and below the mean (Figure 7.3).
When the control serum stays either above or below the mean for several consecutive days,
but at a constant level, a shift is observed (Figure 7.4). This may signal a systematic error and
should be investigated for root cause.
Figure 7.2 Quality control (QC) chart of glucose analysis prepared from Table 7.6
Step 1: Repeated analyses of control serum
The goal of repeated analyses with the control serum is to establish accuracy and degree of
variation (CV) which depends on the type of test and analytical skill. The analysis of control
serum for a specic test (e.g., glucose) should be performed for at least 20 times. The control
222
Medical Laboratory Technology: Volume 1
serum used in repeated analyses is preserved in the freezing compartment of the refrigerator
(in small vials) for ‘daily analysis’ of control and for ploing the quality control (QC) chart
(Table 7.6 and Figure 7.3).
Figure 7.3 Quality control chart for daily plotting. An acceptable quality control chart should indicate equal
distribution of points on both sides of the mean and the points should stay within the tolerance
range (±2SD). Note the out of range plots shown by arrows.
Step 2: Calculation of standard deviation and coecient of variation
From the data obtained in Step 1, determine mean, SD and CV. The SD provides the tolerance
range (±2SD). Table 7.5 provides an example, but for convenience, only 10 observations are
shown. The following calculations are used to determine the mean and tolerance range for
the data in Table 7.5.
Good Laboratory Practices and Statistical Quality Control
SD by calculator
556440 555025 00
39
.
CV (%
39
.
.%
223
Figure 7.4 Quality control chart showing shift (a) to one side of the mean, and (b) trend of unidirectional
For the above example:
This expression of CV, an indicator of precision, should desirably be less than 5%.
move. Both should be investigated. A shift is usually due to defect in control and trend is due
to deterioration of chemical.
method =
10 9
)=100
74 5
.
523
.
224
Table 7.5 Determination of mean and tolerance range of control serum
Medical Laboratory Technology: Volume 1
Serum glucose
Observation
1 78.1 74.5 3.6 12.96
2 70.0 74.5 4.5 20.25
3 77.0 74.5 2.5 6.25
4 79.0 74.5 4.5 20.25
5 71.2 74.5 3.3 10.89
6 72.3 74.5 2.2 4.84
7 76.0 74.5 1.5 2.25
8 74.5 74.5 0.0 0.00
9 79.0 74.5 4.5 20.25
10 67.9 74.5 6.6 43.56
(mg/dL, X)
Mean
( X—)
Dierence
( X–X—)
Square of the
Dierence
Sum 745.0 141.50
Note
• Mean + 2 SD = 74.5 + 7.8 = 2.3; mean – 2 SD = 74.5 – 7.8 = 66.7
• The control specimen can be prepared in the laboratory by pooling normal serum or can be
purchased from commercial companies that provide the true value (manufacturer’s analysis). The laer helps to establish the accuracy of the procedure followed in the laboratory.
Establishing the tolerance range
The tolerance range accepts the normal variation expected in the analytical procedure. The
higher the SD, wider will be the tolerance range and lower will be the precision. For clinical
laboratories, that includes 95.4% of the data, ±2SD is calculated for the tolerance, which comes
to ±2 × 3.9 = ±7.8. Therefore, the tolerance range for the given data is 66.7 to 82.3, with the
mean of 74.5 (mg/100 mL) for the serum glucose value.
Drawing the quality control chart
After the mean and tolerance range are determined, a quality control (QC) chart is prepared
on a linear graph paper (Figure 7.2). The analytic values are on the Y-axis and dates on the
X-axis. The QC chart should show the mean (solid central line) and the tolerance range (doed
lines on two sides of the mean).
Good Laboratory Practices and Statistical Quality Control
225
Daily plotting (use of QC chart)
Run the rst analysis of the day with the control serum. The control serum used daily is
an aliquot of the same serum that was used for preparing the quality control chart. For
convenience the control serum is kept in small individual vials in frozen state and one vial is
thawed each day for running the ‘control’.
Take one of the frozen vials of control serum, bring to room temperature and analyse in
the same way as done in Step 1. Plot the result on the quality control (QC) chart (Table 7.6,
Figure 7.3). If the result of the control serum falls within the tolerance range, proceed with the
analysis of the specimens. An ideal QC chart should show plots uniformly distributed on two
sides of the mean. Deviation from this will be interpreted in the following way.
Table 7.6 Daily analysis of serum glucose with control serum (Data plotted on QC chart, Figure 7.3)
Date
1 75.0 11 74.5 21 73.0
2 73.5 12 76.0 22 74.5
3 75.0 13 69.0 23 75.0
4 69.5 14 73.0 24 73.5
5 75.0 15 77.0 25 70.0
6 72.0 16 73.0 26 64.5
7 75.0 17 74.5 27 68.5
8 77.0 18 73.0 28 72.0
9 85.0 19 75.0 29 72.0
Serum glucose
(mg/dL)
Date
Serum glucose
(mg/dL)
Date
30 74.5
Serum glucose
(mg/dL)
Interpretation of Quality Control Chart
The following are important principles in interpreting the quality control chart (Figure 7.4).
These are the set of considerations to be noted, as well as Westgard’s Rule that formalizes the
course of action to dene if a process is in control (Figure 7.4).
1. Inclination of the curve toward increase or decrease indicates a ‘trend’, which may
be caused by deterioration of reagent or a similar factor. The technician receives the
warning from the quality control chart and corrects the source of variation.
2. A drift of the curve toward one side indicates ‘shift’, which may be caused by
inappropriate operation of equipment or a similar factor. The technician should
investigate and continue specimen analysis only after the shift is corrected.
3. When the daily analysis of the control specimen crosses the tolerance range, an
immediate correction is necessary and no specimen should be analysed until the
variable factor is controlled.
Westgard’s rule
A set of guidelines, called Westgard’s Rule, gives laboratory sta insight as to whether a
quality control program is in control or not. It delineates acceptable variation in control
226
Medical Laboratory Technology: Volume 1
before patient test results should be rejected. Two dierent levels of control sera (normal and
abnormal) should be analysed, along with each set of patient samples. A run (set of patient
samples) is considered out of control if any of the following scenarios happen:
• Both controls are outside the +-2SD limit
• The same control level is outside the ±2SD limit on two subsequent runs
• Controls in four consecutive runs have values greater than ±1s all in same direction
• Ten consecutive control values fall on one side of the mean
Patient test results cannot be reported until the method is considered in control.
Summary
The overall goal of good laboratory practices is to provide reliable results with utmost
precision. Programs that assess quality should be part of every good laboratory’s daily
operations. Providing highest standards with well trained personnel and adherence to good
statistical principles ensure reliable test results and lead to optimum patient care.
review QueStionS
1. What is the signicance of quality control? Explain use of standards and controls in a
laboratory’s daily operations.
2. What is the signicance of coecient of variance? How can it be used to compare
methods of analysis?
3. Prepare a QC chart from the following data of total protein (g/dL) in 10 samples:
6.59, 7.14, 8.00, 6.82, 7.55, 7.00, 7.43, 7.60, 6.91 and 7.44
Answer SD = +0.429
4. Plot the following daily results on the above chart.
Date (Feb) 1 2 3 4 5 6 7
Total protein (g/dL) 7.21 6.73 7.69 7.95 8.26 7.01 5.91 6.56 7.24
OO
9
5. Interpret the curve of Question 4.
6. What precautionary measures are to be taken in a laboratory in order to maintain the
reliability of results?
7. What are the dierences between accuracy, precision, and reproducibility?
8. What are the guidelines for Westgard’s Rule?
2
Haematology and
Coagulation
Chapter 8: Introduction to Haematology
Chapter 9: Basic Laboratory Procedures in Haematology
Chapter 10: Routine Haematological Tests
Chapter 11: Special Haematological Tests
Chapter 12: Interpretation of Laboratory Findings in Haematology
Chapter 13: Introduction to Haemostasis and Haemostatic Disorders
Chapter 14: Laboratory Investigation of Bleeding Disorders