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To simplify the selection of tests for bacteriological typing methods, such as bacteriophage, bacteriocin, and biotyping, a computerised method was assessed. This uses a numerical index of discrimination (D) to facilitate the selection of an efficient typing set. The computer programs take the most discriminatory test as the initial test in the partial typing set, and then select the next test by combining each of the remaining candidates with the partial set and choosing the test which maximises D. This cycle is repeated until the remaining candidates do not increase the discriminatory power of the typing set. Options are provided for the investigator to pre-select certain tests for inclusion or exclusion from the typing set. It is concluded that the numerical index D is a simple means of test selection, but it must be emphasised that it is important to combine its use with data on the incidence of reaction in each test, on reproducibility, and on the similarity among tests.
Content may be subject to copyright.
J
Clin
Pathol
1989;42:763-766
Efficient
selection
of
tests
for
bacteriological
typing
schemes
M
A
GASTON,
P
R
HUNTER
Central
Public
Health
Laboratory,
Colindale,
London
SUMMARY
To
simplify
the
selection
of
tests
for
bacteriological
typing
methods,
such
as
bacterio-
phage,
bacteriocin,
and
biotyping,
a
computerised
method
was
assessed.
This
uses
a
numerical
index
of
discrimination
(D)
to
facilitate
the
selection
of
an
efficient
typing
set.
The
computer
programs
take
the
most
discriminatory
test
as
the
initial
test
in
the
partial
typing
set,
and
then
select
the
next
test
by
combining
each
of
the
remaining
candidates
with
the
partial
set
and
choosing
the
test
which
maximises
D.
This
cycle
is
repeated
until
the
remaining
candidates
do
not
increase
the
discriminatory
power
of
the
typing
set.
Options
are
provided
for
the
investigator
to
pre-select
certain
tests
for
inclusion
or
exclusion
from
the
typing
set.
It
is
concluded
that
the
numerical
index
D
is
a
simple
means
of
test
selection,
but
it
must
be
emphasised
that
it
is
important
to
combine
its
use
with
data
on
the
incidence
of
reaction
in
each
test,
on
reproducibility,
and
on
the
similarity
among
tests.
One
of
the
difficulties
associated
with
the
development
of
epidemiological
identification
(typing)
schemes
for
bacteria
is
the
selection
of
the
most
efficient
set
of
tests.
This
problem
is
particularly
acute
for
non-specialist
clinical
and
medical
microbiologists
setting
up
methods
to
study novel
organisms
or
to
investigate
local
outbreaks.
The
efficiency
of
typing
methods
are
measured
primarily
on
the
basis
of
typability,
reproducibility,
and
discrimination.
The
first
two
factors
are
relatively
easy
to
quantify
and
there
are
definitive
examples
to
guide
investigators.'
2
Discrimination
is
the
most
difficult
factor
to
quantify
but
it
is
arguably
the
most
important
at
the
initial
stages
of
selecting
the
typing
set.
There
is
little
point
in
assessing
the
reproducibility
and
typability
of
a
method
that
fails
to
discriminate
between
strains
of
the
target
organism.
The
problem
of
test
selection
is
particularly
acute
in
the
areas
of
biochemical,
bacteriophage,
and
bacteriocin
typing,
where
investigators
may
have
a
large
number
of
candidate
tests
which
must
be
reduced
to
a
more
practical
number
for
day
to
day
use.
In
our
experience,
each
of
the
candidate
tests
will
have
been
evaluated
on
a
large
collection
of
representative
strains,
and
there
is
a
sizeable
matrix
of
N
strains
by
T
tests,
which
forms
the
core
data
for
the
selection
process.
Even
for
bacteriologists
with
a
background
in
epidemiological
studies,
it
is
difficult
to
interpret
these
data
without
recourse
to
numerical
analysis.
Accepted
for
publication
2
February
1989
Bergan
evaluated
the
use
of
similarity
coefficients
in
selecting
a
bacteriophage
typing
set
for
Pseudomonas
aeruginosa.3
Such
coefficients
are
valuable
aids
to
the
identification
of
identical
or
very
similar
tests
that
would
be
redundant
if
included
in
the
typ:
g
set.
These
techniques
are
therefore
most
useful
as
negative
selectors
for
rejecting
a
proportion
of
the
candidate
tests.4
Quantitative
methods
that
could
facilitate
the
positive
selection
of
typing
tests
would
be
useful
aids
to
the
selection
process
and
several
indices
have
been
proposed
to
quantify
the
ability
of
individual
tests
to
separate
strains
or
biological
groups."8
Tests
with
high
values
of
discrimination
are
not
necessarily
useful
when
combined
in
typing
sets
as
they
may
provide
redundant
information.
The
selection
of
combinations
of
tests
is
more
complex."'0
Ideally,
the
discriminatory
ability
of
every
possible
combination
of
tests
should
be
determined,
but
this
approach
is
not
practicable,
as
even
for
a
limited
set
of
19
candidate
tests
there
are
over
500
000
possible
combinations.
An
approxima-
tion
is
to
select
tests
sequentially,
such
that
discrimina-
tion
is
maximised
at
each
stage.
Recently,
we
described
a
numerical
index
which
quantifies
the
ability
of
typing
schemes
to
discriminate
between
strains.
"
This
permits
easy
comparison
of
different
schemes.
A
second
and
powerful
use
for
this
index
is
the
quantitation
of
the
discrimination
of
partial
sets
of
tests.
Thus
combinations
of
tests
can
be
evaluated
and
the
data
used
to
build
up
efficient
typing
schemes.
We
developed
several
computer
programs
using
this
approach
which
facilitate
the
selection
and
763
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764
analysis
of
sets
of
typing
reagents.
Although
the
central
algorithm
is
based
on
simple
probability
theory,
no
mathematical
skill
is
required
to
operate
the
programs
or
to
interpret
the
results.
Methods
Test
results
are
entered
as
positive
(1),
negative
(0),
or
variable
(V).
The
most
discriminatory
tests
are
selec-
ted
from
the
results
by
two
programs
SEL
and
CHOISEL.
The
primary
algorithm
in
these
similar
programs
uses
a
numerical
index
D
to
quantify
the
ability
of
combinations
of
tests
to
subdivide
the
strains
in
the
data
file.
D
is
derived
from
elementary
probability
theory
and
is
given
by
equation
I:
D=l
N(N-1)
n
_
(n
I
j=
where
N
is
the
total
number
of
strains
in
the
popula-
tion,
s
is
the
total
number
of
types
described,
and
nj
is
the
number
of
strains
belonging
to
the
jth
type.
Alternatively,
D
can
be
defined
by
equation
II:
1
N
N(N-l1)
E
J
j
=
1
where
aj
is
the
number
of
strains
that
are
indis-
tinguishable
from
the
jth
strain.
This
is
the
more
flexible
of
the
two
definitions
and
allows
the
selection
of
tests
where
more
than
one
reaction
difference
is
required
to
separate
strains
or
where
equivocal
re-
actions
are
present.
The
programs
start
by
selecting
the
most
discriminatory
individual
test
as
the
initial
test
in
the
partial
typing
set.
This
test
is
then
combined
with
each
of
the
remaining
tests
in
turn
and
the
value
for
D
calculated.
The
test
that
maximises
D
is
chosen
as
the
Gaston,
Hunter
next
test
and
added
to
the
partial
typing
set.
This
cycle
is
repeated
until
the
remaining
tests
provide
no
extra
discrimination.
Where
there
are
more
than
one
equally
good
tests,
the
first
in
numerical
order
is
chosen,
although
the
others
are
printed
for
further
analysis.
Of
the
two
programs,
SEL
has
the
fastest
execution
time
(about
10
times
faster)
and
selects
tests
with
the
assumption
that
a
single
reaction
difference
between
strains
is
significant.
CHOISEL,
based
on
equation
II,
allows
the
investigator
to
choose
the
number
of
test
differences
that
are
required
before
strains
are
con-
sidered
to
have been
separated.
This
second
program
is
much
slower
as
a
table
of
reaction
differences
must
be
calculated
for
each
combination
of
tests.
Both
programs
allow
the
operator
to
select
candidate
tests
to
be
included
or
excluded
from
the
final
set,
the
programs
then
select
the
remaining
tests.
The
option
of
allowing
one
or
two
differences
in
reaction
before
strains
are
separated
has
been
provided
so
that
safeguards
can
be
built
into
the
typing
set,
to
circumvent
the
poor
reproducibility
of
some
biological
test
systems.
As
CHOISEL
works
by
choosing
the
combination
of
tests
which
produce
the
maximum
value
for
D
it
cannot
select
the
initial
one
or
two
tests
if
two
or
three
tests
are
required
to
separate
strain
pairs-that
is,
in
the
initial
tests,
no
strains
are
considered
to
be
separate-and
therefore
D
=
0
for
all
combinations.
CHOISEL
therefore
"cheats"
during
the
selection
of
the
initials
tests
by
assuming
any
test
difference
to
be
significant.
As
an
example
of
test
selection
for
epidemiological
studies
table
1
gives
a
subset
of
data
showing
the
patterns
of
inhibition
produced
by
19
strains
of
Serratia
marcescens
examined
for
bacteriocinogenic
activity
on
17
strains.
Data
were
selected
from
a
larger
matrix,
generated
in
a
epidemiological
study
of
S
marcescens
serotype
014
strains
from
clinical
material.
Table
1
Inhibition
of
Serratia
marcescens
serotype
014
strains
by
bacteriocinogenic
strains
Inhibition
by
bacteriocin
producer
strains*:
Strains
1
2
34
S
6
7
8
9
10
11
12
13
14
15
16 17
18
19
1
-
-
+
3
+ + +
+
+_+
+
+
4
6
+
+
...........
+
+
8
+
+
-
+++
+ +
. . . . .
+
+
9
+
+
+
-
+
+
+
+
+
+
1
3
+
+
+
1
5
+
+
+
+
+++
+
+
+
18
+
-
-
__
_
_
_
21
+ + + +
+
+
+ +
+
_
26
.........
+
+
27
+
+
+
+ +
+
28
+
+
+
+
+ +
+
+
+
+
+
+ +
31
+
....
..
+
42
+
+
+
+
+ +
+
+
+ +
+
+ +
68
+
-
...
..
+
71
+
+
- -
++
-
+
*Data
modified
by
exclusion
of
weak
reactions.
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Efficient
selection
of
tests
for
bacteriological
typing
schemes
Table
2
Discriminatory
tests
selected
based
on
inhibition
data
given
in
table
I
Automatic
selection
Preselection
of
test
18
D
index
Equally
D
index
Equally
Rank
Test
(x
100)
good
tests
Test
(x
100)
good
tests
1
7
52-9 18
18
52-9
NA
2
8
74-3
9,14
12
779
-
3
5
86-0
-
14
88-2
-
4
14
92-6
-
8
93-4
9
5
12
96-3
-
5
96-3
-
6
6
97-8
13.
18,
19
7
97-8
10,
11
7
1
98-5
3,
13,
16
1
98-5
3,
13,
16
8
3
99
3
13
3
99-3
13
9
13
100-0
-
13
100-0
-
Automatic
selection
requiring
two
reaction
differences
Automatic
selection
requiring
three
reaction
differences
1
7
0
18
7
0
18
2
11
397
-
11
0
-
3
4
57-4
-
12
301
19
4
8
64-0
9
4
44-2
6,14,17,18,19
5
9
77-2
-
19
55-9
-
6
6
80-9
14,
17
8
61-0
9
7
18
86-0
19
9
67-6
17
8
14
87-5
-
14
75-0
1
7
9
10
919
5
801
-
10
6
83-8
-
11
10
86-7
-
12
3
88-2
13,
18
13
13
90
4
-
14
18
912
-
15
2
91-9
15,16,17
NA:
not
applicable
with
a
preselected
test.
Table
2
gives
the
tests
selected
by
the
programs.
The
first
set,
automatic
selection,
produced
by
either
SEL
or
CHOISEL,
is
a
completely
automatic
selection
of
tests
based
on
the
premise
that
any
test
difference
separates
pairs
of
strains.
The
second
set,
also
produced
by
SEL
or
CHOISEL,
pre-selected
test
18
(the
inhibition
produced
by
strain
18)
and
shows
an
increase
in
discrimination
given
by
the
partial
sets
of
two,
three,
and
four
tests.
The
third
and
fourth
sets,
produced
by
CHOISEL
alone,
represent
an
automatic
selection
of
tests
based
on
the
assumption
that
two
and
three
differences,
respectively,
are
required
to
separate
pairs
of
strains.
CHOISEL
has
some
similarities
to
the
approach
of
Rypka
et
al9
and
the
sequential
method
of
Willcox
and
Lapage,'2
but
the
algorithm
presented
here
is
both
simple
and
flexible
and
offers
an
advantage
over
several
other
methods
of
test
selection
in
that
a
quantified
index
D
is
produced
that
allows
the
inves-
tigator
to
gauge
the
efficacy
of
the
selected
tests.
For
example,
in
the
first
and
second
series
in
table
2,
nine
out
of
a
possible
19
tests
gave
100%
discrimination
but
over
95%
discrimination
was
achieved
with
only
five
tests.
So
for
purely
practical
reasons
the
investigator
may
choose
this
shortened
set
of
tests
and
still
expect
a
high
level
of
discrimination.
The
programs
were
written
in
BASIC
for
an
Acorn
Achimedes/BBC
Microcomputer
system
and
contain
relatively
few
machine
specific
instructions.
They
could
therefore
be
readily
implemented
on
other
microcomputer
systems.
The
only
potential
drawback
with
the
current
programming
is
the
amount
of
memory
required
by
CHOISEL
which
dimensions
integer
arrays
of
N
x
N.
Thus
when
a
large
number
of
strains
are
used
in
the
analysis
a
very
large
amount
of
computer
memory
(RAM)
is
necessary.
To
cir-
cumvent
this
problem
we
developed
an
alternative
but
slower
version
(SLOWSEL)
that
requires
much
less
memory.
Given
a
sufficiently
discriminating
set
of
initial
data
these
programs
will
produce
a
minimal
typing
set-
that
is,
a
set
of
tests
with
just
enough
tests
to
distinguish
each
strain.
Thus
any
variation
in
the
patterns
of
reactions
of
a
test
may
decrease
the
overall
discrimination
of
the
selected
tests.
The
set
produced
by
this
approach
does
not
necessarily
represent
the
set
with
the
fewest
possible
number
of
tests.
Identifying
the
theoretical
minimum
set
of
tests,
possibly
by
comparing
every
possible
combination
of
tests,
may
take
a
prohibitive
amount
of
computer
time,
although
steps
may
be
taken
to
limit
the
number
of
comparisons
required.'2
The
ability
to
select
positively
combinations
of
tests
greatly
simplifies
the
development
of
efficient
epidemiological
typing
methods.
We
believe
that
the
numerical
index
D
provides
a
simple
measure
for
test
selection
and
that
it
could
be
a
useful
tool
for
many
investigators.
It
is
important,
however,
that
the
results
765
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766
Gaston,
Hunter
of
this
sort
of
analysis
are
put
into
context.
These
programs
work
on
one
set
of
data
which
may
not
be
absolutely
reproducible.
Indeed,
individual
tests
may
be
highly
irreproducible,
therefore
positive
test
selec-
tion
should
be
used
in
combination
with
data
on
the
incidence
of
reaction
of
each
test,
on
reproducibility,
and
on
the
apparent
similarity
between
tests
(based
on
similarity
coefficients).
Copies
of
the
programs
described
above
and
a
FOR-
TRAN
version
of
CHOISEL
are
available
from
the
authors.
References
I
Williams
REO,
Rippon
JE.
Bacteriophage
typing
of
Staphylococ-
cus
aureus.
JHyg
(Camb)
1952;50:320-53.
2
Anderson
ES,
Williams
REO.
Bacteriophage
typing
of
enteric
pathogens
and
staphylococci
and
its
use
in
epidemiology.
J
Clin
Pathol
1956;9:94-127.
3
Bergan
T.
Comparison
of
numerical
procedures
for
grouping
Pseudomonas
bacteriophages
according
to
lytic
spectra.
Acta
Pathol
Microbiol
Scand
1972;SOB:55-70.
4
Gaston
MA.
Isolation
and
selection
of
a
bacteriophage-typing
set
for
Enterobacter
cloacae.
J
Med
Microbiol
1987;24:285-90.
5
Gaston
MA,
Ayling-Smith
BA,
Pitt
TL.
New
bacteriophage
typing
scheme
for
subdivision
of
the
frequent
capsular
serotypes
of
Klebsiella
spp.
J
Clin
Microbiol
1987;25:1228-32.
6
Gyllenberg
H.
A
general
method
for
deriving
determination
schemes
for
random
collections
of
microbial
isolates.
Ann
Acad
Sci
Fenn
1963;69:1-23.
7
Niemela
SI,
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doi: 10.1136/jcp.42.7.763
1989 42: 763-766J Clin Pathol
M A Gaston and P R Hunter
bacteriological typing schemes.
Efficient selection of tests for
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... The genetic diversity of O157 strains in subclade 8a and subclade 8b was evaluated by the Hunter Gaston discriminatory index (HGDI), determined from multilocus variable-number tandem repeat analysis (MLVA) [34,35]. HGDI indicates the discriminatory power of the typing method used for the bacterial strains. ...
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Enterohemorrhagic Escherichia coli O157 (O157) strains can be classified into clades (one of several phylogenetic groups) by single nucleotide polymorphisms (SNPs): these are clade 1, clade 2, clade 3, descendant and ancestral clades 4/5, clade 6, clade 7, clade 8, clade 9, and clade 12. Some recent studies showed that some O157 strains in clade 8 produced a larger amount of Shiga toxin (Stx) 2 than other strains. In this study, 1121 epidemiologically unlinked strains of O157 isolated in Chiba Prefecture, Japan were classified into clades during 1996–2014. Clade 8 strains were further classified into subclade 8a (67 strains) and subclade 8b (48 strains) using SNP analysis. In the absence of mitomycin C (MMC), subclade 8a strains in this study produced significantly greater amounts of Stx2 than subclade 8b strains. However, in the presence of MMC, the levels of Stx2 production in subclade 8b strains were significantly greater than subclade 8a strains. On the other hand, a recent study reported that the Stx2 production level in O157 strains was determined mainly by the subtypes of Stx2a phage (ϕStx2_α, β, γ, δ, ε, and ζ). Using O157 strains in this study, the Stx2a phages were classified into these subtypes. In this study, all strains of subclades 8a and 8b carried ϕStx2a_γ and ϕStx2a_δ, respectively. Some strains in clade 6 also carried ϕStx2a_δ. In the presence of MMC, subclade 8b strains produced significantly greater amounts of Stx2 than clade 6 strains carrying ϕStx2_δ. In this study, we propose that Stx2 production in subclade 8b strains in the presence of MMC might be enhanced due to genetic factors other than ϕStx2_δ.
... В настоящее время доминирующее место в решении различных проблем медицинской микробиологии и эпидемиологии начинают занимать молекулярно-генетические методы. Методы ДНКтипирования являются наиболее предпочтительными для изучения генетики и филогении бактериальных популяций ввиду высокой дискриминирующей способности этих методов, оцениваемой по индексу разнообразия Симпсона [84,85], высокой пропускной способности, воспроизводимости, быстроте выполнения, возможности сопоставления и передачи результатов, выявления ранее неизвестных генетических полиморфизмов [86]. ...
... The discriminatory power was determined according to a modification of the numerical index method described by Gaston and Hunter ( 1989). This modification considers that phages types might differ by only one reaction from non-typable strains. ...
... Only isolates of 100% similarity, that is, isolates having the same number of tandem repeats in each locus, were assigned to the same cluster. The HG index/diversity index was calculated as described [22,23], using the Discriminatory Power Calculator (http://insilico.ehu.es/mini tools/discriminatory power/index.php). ...
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... It is determined by the number of bacterial types defined by the typing technique and the relative frequencies of these bacterial types. Algorithms that can be used to calculate the discriminatory power of a bacterial typing method are for example Simpson' s index of diversity or Hunter & Gaston's modification of this algorithm (16,27,33,66,85). Ideally, a typing method should include loci with different polymorphic behavior. ...
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