Statistical Aspects of the Microbiological Examination of Foods

325 Pages·2016·13.007 MB·English

by  Basil Jarvis

Statistical Aspects
of the Microbiological
Examination of Foods
Third Edition
Basil Jarvis
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Preface to the Third Edition
In my first post as a graduate bacteriologist, my manager impressed upon me the
need for proper use of statistical analysis in any work in applied microbiology. So
insistent was he that I attended a part-time course in statistics for use in medical
research at University College, London – unfortunately the course was presented by
a mathematician who failed to recognise that detailed mathematical concepts often
cause non-mathematicians to ‘switch off’! In those days before the ready availability
of personal computers and electronic calculators, statistical calculations were done
manually, sometimes aided by mechanical calculators. Even simple calculations that
nowadays take only a few minutes would often take days and nights to complete.
Nonetheless, my interest in the use of statistics has stayed with me throughout my
subsequent career.
In the early 1970s, I was fortunate to work with the late Dr Eric Steiner, a chemist
with considerable knowledge and experience of the use of statistics who opened
my eyes to a wider appreciation of statistical methods. I was also privileged for a
time to have guidance from Ms Stella Cunliffe, the first woman President of the
Royal Statistical Society. Over several years I lectured on statistical aspects of ap-
plied microbiology at various courses, including the WHO-sponsored course in Food
Microbiology that I set up at the University of Surrey, UK. During that time I became
aware of a lack of understanding of basic statistical concepts by many microbiolo-
gists and the total lack of any suitable publication to provide assistance. In the early
1990s I prepared a report on statistical aspects of microbiology for the then UK
Ministry of Agriculture, Food and Fisheries (MAFF). It is from that background that
the first edition of this book arose.
This book is intended as an aid to practicing microbiologists and others in the
food, beverage and associated industries, although it is relevant also to other aspects
of applied microbiology. It is also addressed to students reading food microbiology at
undergraduate and postgraduate levels. With greater emphasis now being placed on
quantitative microbiology, the need to understand relevant statistical matters assumes
even greater importance in food microbiology.
This book is written not by a professional statistician but by a microbiologist, in
the sincere hope that it will help future applied microbiologists. Over the past 2 or
3 years, discussions with colleagues from various organisations identified a number
of developments in microbiological methods and in statistical analyses of micro-
biological data. Some are related to the growing importance of risk analysis and
particularly the need to understand the statistical implications of the distribution of
over-dispersed populations of pathogenic microbes in foods, others to changes in
Europe and the USA in the procedures for validation of microbiological methods;
others were concerned with methods for estimation of microbiological measurement
uncertainty.
xxiii
xxiv Preface to the third edition
I was considering whether there was a need to revise the book when the pub-
lisher asked me if such revision would be timely. In editing and revising the book,
I have received helpful comment and advice from colleagues in many countries.
I would particularly acknowledge numerous helpful discussions on diverse topics
with members of the AOAC Presidential Taskforce on ‘Best Practices in Microbio-
logical Methodology’ and members of the ISO Statistics Working Group (TC34/
SC9/WG2), especially Professor Peter Wilrich (Free University of Berlin) and
Dr Bertrand Lombard (ANSES, Paris, France). I am especially indebted to Dr Alan
Hedges (University of Bristol Medical School) and Dr Janet E.L. Corry (University
of Bristol Veterinary School) for their critiques of the second edition and on drafts of
this manuscript; to Dr Andreas Kiermeier (Australia) who kindly provided a copy of
the FAO/WHO spreadsheet system for setting up sampling plans; and to Dr Sharon
Brunelle of AOAC for again providing the chapter on method validation. But all
errors of omission or commission are mine alone. I acknowledge the help received
from the editors at Academic Press, especially Halima Williams. I would also wish
to thank the many authors and publishers who have kindly granted me the rights to
re-publish tables and figures previously published elsewhere. Details of these per-
missions are quoted in the text.
Finally, I thank my wife, my family and our friends, for their continuing support
and for putting up with me over this period of rewriting.
Basil Jarvis
Upton Bishop, Ross-on-Wye
Herefordshire, UK
December 2015
CHAPTER
1
Introduction
One morning a professor of statistics sat alone in a bar at a conference. When his col-
leagues joined him at the lunch break, they asked why he had not attended the lecture
sessions. He replied, saying, ‘If I attend one session I miss nine others; and if I stay
in the bar I miss all ten sessions. The probability is that there will be no statistically
significant difference in the benefit that I obtain!’ Possibly a trite example, but statis-
tics are relevant in most areas of life.
The word ‘statistics’ means different things to different people. According to
Mark Twain, Benjamin Disraeli was the originator of the statement ‘There are lies,
damned lies and statistics!’ from which one is supposed to conclude that the ob-
jective of much statistical work is to put a positive ‘spin’ onto ‘bad news’. Whilst
there may be some political truth in the statement, it is generally not true in science
provided that correct statistical procedures have been used. Herein lies the rub! To
many people, the term ‘statistics’ implies the manipulation of data to draw conclu-
sions that may not be immediately obvious. To others, especially many biologists,
the need to use statistics implies a need to apply numerical concepts that they hoped
they had left behind at school. But to a few, use of statistics offers a real opportunity
to extend their understanding of bioscience data in order to make better use of the
information available.
Much statistical analysis is used to decide whether one set of data differs from
another and it is essential to recognise that sometimes a difference that is statistically
significant may not be of practical significance, and vice versa. Always bear in mind
that statistical methods serve merely as a tool to aid interpretation of data and to en-
able inferences to be drawn. It is essential to understand that data should be tested for
goodness of fit by seeking to fit an appropriate statistical model to the experimental
data.
Microbiological testing is used in industrial process verification and sometimes
to provide an index of quality for ‘payment by quality’ schemes. Examination of
food, water, process plant swabs, etc., for microorganisms is used frequently in the
retrospective verification of the microbiological ‘safety’ of foods and food process
operations. Such examinations include assessments for levels and types of microor-
ganisms, including tests for the presence of specific bacteria of public health signifi-
cance, including pathogens, index and indicator organisms.
During recent years, increased attention has focused, both nationally and interna-
tionally, on the establishment of numerical microbiological criteria for foods. All too
often such criteria have been devised on the misguided belief that testing of foods
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Statistical Aspects of the Microbiological Examination of Foods. http://dx.doi.org/10.1016/B978-0-12-803973-1.00001-2
Copyright © 2016 Elsevier B.V. All rights reserved.
2 CHAPTER 1 Introduction
for compliance with numerical, or other, microbiological criteria will enhance con-
sumer protection by improving food quality and safety. I say ‘misguided’ because no
amount of testing of finished products will improve the quality or safety of a prod-
uct once it has been manufactured. Different forms of microbiological criteria have
been devised for particular purposes; it is not the purpose of this book to review the
advantages and disadvantages of microbiological criteria – although some statistical
matters relevant to criteria will be discussed in Chapter 14.
Rather, the objective is to provide an introduction to statistical matters that are im-
portant in assessing and understanding the quality of microbiological data generated
in practical situations. Examples, chosen from appropriate areas of food microbiol-
ogy, are used to illustrate factors that affect the overall variability of microbiological
data and to offer guidance on the selection of statistical procedures for specific pur-
poses. In the area of microbiological methodology it is essential to recognise the di-
verse factors that affect the results obtained by both traditional methods and modern
developments in rapid and automated methods.
The book considers the distribution of microbes in foods and other matrices; sta-
tistical aspects of sampling; factors that affect results obtained by both quantitative
(eg, colony count) and quantal methods [eg, presence/absence and most probable
number (MPN) methods]; the meaning of, and ways to estimate, microbiological un-
certainty; the validation of microbiological methods; and the implications of statisti-
cal variation in relation to food safety and use of microbiological criteria for foods.
Consideration is given also to quality monitoring of microbiological practices and
the use of statistical process control for trend analysis of data both in the laboratory
and in manufacturing industry.
The book is intended as an aid for practising food microbiologists. It assumes a
minimal knowledge of statistics and references to standard works on statistics are
cited whenever appropriate.
CHAPTER
2
Some basic statistical
concepts
POPULATIONS
The true population of a particular ecosystem can be determined only by carrying out
a census of all living organisms within that ecosystem. This applies equally whether
one is concerned with numbers of people in a town, state or country or with numbers of
microbes in a batch of a food commodity or a product. Whilst it is possible, at least the-
oretically, to determine the human population in a non-destructive manner by undertak-
ing a population census, the same does not apply to estimates of microbial populations.
When a survey is carried out on people living, for instance, in a single town or
village, it would not be unexpected that the number of residents differs between dif-
ferent houses, nor that there are differences in ethnicity, age, gender, health and well-
being, personal likes and dislikes, etc. Similarly, there will be both quantitative and
qualitative differences in population statistics between different towns and villages,
different parts of a country and different countries.
A similar situation pertains when one looks at the microbial populations of a food.
The microbial association of foodstuffs differs according to diverse intrinsic and ex-
trinsic factors, especially the acidity and water activity, and the extent of any pro-
cessing effects. Thus the primary microbial population of acid foods will generally
consist of yeasts, moulds and acidophilic bacteria, whereas the primary population of
raw meat and other protein-rich foodstuffs will consist largely of Gram-negative non-
fermentative bacteria, with smaller populations of other organisms (Mossel, 1982).
In enumerating microbes, it is essential first to define the population to be counted.
For instance, does one need to obtain an estimate of the total population, that is, liv-
ing and dead organisms, or only the viable population; if the latter, is one concerned
only with specific groups of organisms, for example, aerobes, anaerobes, psychro-
trophs and psychrophiles, mesophiles or thermophiles? Even when such questions
have been answered, it would still be impossible to determine the true ecological
population of a particular ‘lot’ or ‘batch’ of food, since to do so would require testing
of all the food. Such a task would be technically and economically impossible.
LOTS AND SAMPLES
An individual ‘lot’ or ‘batch’ of product consists of a quantity of food that has been
processed under essentially identical conditions on a single occasion. The food may
be stored and distributed in bulk or as pre-packaged units each containing one or
3
Statistical Aspects of the Microbiological Examination of Foods. http://dx.doi.org/10.1016/B978-0-12-803973-1.00002-4
Copyright © 2016 Elsevier B.V. All rights reserved.
4 CHAPTER 2 Some basic statistical concepts
more individual units of product, for example, a single meat pie or a pack of frozen
peas. Assuming that the processing has been carried out under uniform conditions,
theoretically, the microbial population of each unit should be typical of the popula-
tion of the whole lot. In practice, this will not always be the case. For instance, high
levels of microbial contamination may be associated only with specific parts of a lot
due to some processing defect or the incomplete mixing of ingredients. In addition,
estimates of microbial populations will be affected by the choice of test protocol that
is used.
It is not feasible to determine the levels and types of aerobic and anaerobic organ-
isms, or of acidophilic and non-acidophilic organisms, or other distinct classes of mi-
croorganism using a single test. Thus when a microbiological examination is carried
out, the types of microorganisms that are detected will be defined in part by the test
protocol. All such constraints therefore provide a biased estimate of the microbial
population of the ‘lot’. Hence, sampling of either bulk or pre-packaged units of a
‘lot’ merely provides an indication of the types and numbers of microorganisms that
make up the population of the ‘lot’ and such population samples will themselves be
further sampled by the choice of examination protocol. In order to ensure that a series
of samples drawn from a ‘lot’ properly reflect the diversity of types and numbers of
organisms associated with the product it is essential that the primary samples should
be drawn in a random manner, either from a bulk or as individual packaged units of
the foodstuff.
Analytical chemists frequently draw large primary samples that are blended and re-
sampled before taking one or more analytical samples – the purpose is to minimise the
between-sample variation in order to determine an ‘average’ analytical estimate for a
particular analyte. It is not uncommon for several kilograms of material to be taken as a
number of discrete samples that are then combined, blended and resampled to provide
the series of analytical samples. The sampling of foods for microbiological examina-
tion cannot generally be done in this way because of the risks of cross-contamination
during the mixing procedure, although examples of techniques for producing compos-
ite samples have been published (see, eg, Corry et al., 2010).
A ‘population sample’ (eg, a unit of product) may itself be sub-divided for ana-
lytical purposes and it is important, therefore, to consider the implications of deter-
mining microbial populations in terms of the number, size and nature of the samples
taken. In only a few instances is it possible for the analytical sample to be truly rep-
resentative of the ‘lot’ sampled. Liquids, such as milk, can be sufficiently well mixed
that the number of organisms in the analytical sample is representative of the milk
in a bulk storage tank. However, because of problems of mixing, samples withdrawn
from a grain silo, or even from individual sacks of grain, may not necessarily be
truly representative. In such circumstances, deliberate stratification (qv) may be the
only practical way of taking samples. Similar situations obtain when one considers
complex raw material such as animal carcases, or composite food products such as
ready-to-cook frozen meals containing slices of cooked meat, Yorkshire pudding,
peas, potato and gravy. It is necessary to consider also the actual sampling protocol
to be used: for instance, in sampling from a meat or poultry carcase, is the sample to
Average sample populations 5
be taken by swabbing, rinsing or excision of skin? Where on the carcase should the
sample be taken? For instance, one area (eg, chicken neck skin) may be more likely
to carry higher numbers and types of organism than other areas. Hence, standardisa-
tion of sampling protocols is essential. In situations where a composite food consists
of discrete components, a sampling protocol needs to be used that reflects the pur-
pose of the test–is a composite analytical sample required (ie, one made up from the
various ingredients in appropriate proportions) or should each ingredient be tested
separately? These matters are considered in more detail in Chapter 5.
AVERAGE SAMPLE POPULATIONS
If a single sample is analysed, the result provides a method-dependent single-point
estimate of the population numbers in that sample. Replicate tests on a single sample
provide an improved estimate of population numbers within that sample based on
the average of the results, together with a measure of variability of the estimate for
that sample. Similarly, if replicate samples are tested, the average result provides a
better estimate of the number of organisms in the population based on the between-
sample average and an estimate of the variability between samples. Thus, we can
have greater confidence that the ‘average sample population’ will reflect more close-
ly the population in the ‘lot’. The standard error of the mean (SE ; qv) provides an
M
estimate of the extent to which the average value is reliable. If a sufficient number of
replicate samples is tested, then we can derive a frequency distribution for the counts,
such as that shown in Fig. 2.1 (data from Blood, 1974). Note that this distribution
curve has a long left-hand tail and that the curve is not symmetrical, possibly because
the data were compiled from results obtained in two different production plants. The
statistical aspects of common frequency distributions are discussed in Chapter 3.
FIGURE 2.1 Frequency Distribution of Colony Count Data Determined at 30°C on Beef
Sausages Manufactured in Two Factories
Modified from Blood (1974). Reproduced by permission of Leatherhead Food International
6 CHAPTER 2 Some basic statistical concepts
Adding the individual values and dividing by the number of replicate tests pro-
[x¯=(x +x +x +⋯+xn)/n vides a simple arithmetic mean of the values [x=(x +x +x +(cid:31)+x )/n=∑n x /n],
1 2 3 1 2 3 n i=1 i
=∑i=1nxi/n] where x is the value of the ith test and n is the number of tests done. However, it is
i
possible to derive other forms of average value. For instance, multiplying the indi-
vidual counts on n samples and then taking the nth root of the product provides the
(x¯9) geometric mean value (x′):
x¯9=x⋅x⋅x⋯xnn x′=n x1⋅x2⋅x3(cid:31)xn
1 2 3
It is simpler to determine the approximate geometric mean by taking logarithms
(y=log10⁡x) of the original values (y=log x), adding the log-transformed values and dividing
10
log⁡x¯9 (y¯) the sum by n to obtain the mean log value (y), which equals logx′. This value can
be back-transformed by taking the antilog to obtain an estimate of the geometric
mean value:
∑n y ∑n log x
y= i=1 i = i=1 10 i =log x′
y¯=∑i=1nyin=∑i=1n n n 10
log10⁡xin=log10⁡x¯9
The geometric mean is appropriate for data that conform to a lognormal distribu-
tion and for titres obtained from n-fold dilution series. It is important to understand
the difference between the geometric and the arithmetic mean values since both are
used in handling microbiological data. In terms of microbial colony counts, the log
mean count is the log of the arithmetic mean; by contrast, the mean log count is
10
the arithmetic average of the log -transformed counts that, on back-transformation,
10
gives the geometric mean count. The methods are illustrated in Example 2.1.
EXAMPLE 2.1 DERIVATION OF SOME BASIC STATISTICS THAT DESCRIBE
A DATA SET
Assume that we wish to determine the statistics that describes a series of replicate colony counts on
a number (n) of samples, represented by x, x, x, …, x, for which the actual values are 1540, 1360,
1 2 3 n
1620, 1970 and 1420 as colony-forming units (cfu) per gram.
Range
The range of colony counts provides a measure of the extent of overall deviation between the largest
and smallest data values and is determined by subtracting the lowest value from the highest value;
for the example data, the range is 1970 − 1360 = 610.
Median
The median colony count is the middle value in an odd-numbered set of values or the average of the
two middle values in an even-numbered set of values; for this sequence of counts the median value
of 1360, 1420, 1540, 1620, 1970 = 1540.
The interquartile range
This is the range covered by the middle 50% of data values, which is often more useful than the
absolute range of values. We have determined the median value as 1540 – this is the second quartile
or Q2 value. We now determine the first quartile value (Q1) as the median of the values below and
including Q2, and the third quartile value (Q3) as the median of the values including and greater
than Q2. In this case because we have only 5 values we can say that Q1 = 1420 and Q3 = 1620, so
the inter-quartile range (IQR) is given by 1620 − 1420 = 200.