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Q: detailed statistical rationale with reference about counting bacteria ( Answered,   0 Comments )
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Subject: detailed statistical rationale with reference about counting bacteria
Category: Science > Biology
Asked by: svdh-ga
List Price: $75.00
Posted: 26 Nov 2003 15:29 PST
Expires: 26 Dec 2003 15:29 PST
Question ID: 280953
In microbiology, it is often necessary to determine the concentration
of bacteria in a sample (e.g., bacteria in blood, milk, or water
supply).  Bacteria are "plated out" on agar plates (petri dishes) and
counts are usually expressed in colony-forming units per milliliter
(CFU/ml).  A rule of thumb is that you should only count plates that
have between 30 - 300 colonies.  If there are over 300 colonies on a plate, you
may undercount the true number since some bacteria will not form
colonies because of overcrowding.

On the other hand, plates with fewer than 30 colonies may be affected
by random statistical errors or contamination.

My question: where is there a reference that substantiates "30
colonies" as the cutoff for counting?  I need to understand the actual
statistical reasoning behind this, and all I've been able to turn up
on the net is pretty much that this is what you're supposed to do. I
would like to know the mathematical/statistical foundation for this
claim, and a reference to a publication on it if possible.
Answer  
Subject: Re: detailed statistical rationale with reference about counting bacteria
Answered By: czh-ga on 27 Nov 2003 03:00 PST
 
Hello svdh-ga,

This was a very challenging research project. Just like you, at first
all my research revealed was the general guidance for using only
plates with 30 ?300 colonies. But I didn?t find this to be a firm rule
and some of the references were to 20 ?200 and other ranges as well.
The explanations for using these limits also varied with a fairly
clear statement of the necessity for the upper limit and only a
reference to ?statistical validity? for the lower limit.

Here are some of the explanations:


http://a-s.clayton.edu/furlong/BIOL3250/lab/data%20sheets/spread%20plate.pdf
Part D (Calculations) 
 -- Count the number of colonies on each plate. Plates that have over 300 colonies 
are ?too numerous to count? (TNTC). Don?t bother counting them. 

 -- Pick a set of plates to do your calculations (set B, C, D or E). You want to 
choose the set where each plate in the set has more than 30 colonies growing on 
them. If you do your calculations with a set that has fewer than 30 colonies your 
counts will be statistically invalid.

***** REASONS:     >300 ?too numerous to count?     <30  ?statistically invalid?

---------------------------------------

http://cwx.prenhall.com/bookbind/pubbooks/brock/chapter5/objectives/deluxe-content.html
Chapter 5: Microbial Growth
Introduction

Cell number can be determined by direct microscopic counts or by
viable counts. Direct microscopic counts are limited by the inability
to distinguish living from dead cells. Furthermore, cell densities
greater than 106 per ml are required to see enough cells to count. In
contrast, viable counts can detect very small numbers of cells; one is
limited only by how much material can be inoculated onto the surface
of the agar medium. This method detects only living cells; that is,
those capable of forming colonies on an appropriate nutrient medium.

Viable counts can take the form of spread plates and pour plates. The
difference is in the timing of cell entry on to the medium. The basis
for the technique is that individual cells are deposited at separate
locations on the plate so that each colony that arises was derived
from an individual cell. If this assumption is not true, the estimate
of cell number will be in error. The assumption is violated if cells
in the sample are in clumps, or if too many cells were inoculated onto
the plate. In the latter case, it becomes likely that more than one
cell is placed on a spot. Therefore, the resulting colony arose from
two, not one cell. On the other hand, if too few cells are plated, the
statistical precision of the result is poor. Therefore,
microbiologists try to plate 30 to 300 cells per plate for viable
counts.

***** Reasons:     >300 Cells may have clumped, some colonies arose
from more than one cell.      <30  Poor statistical precision.


---------------------------------------

http://www.homepage.montana.edu/~cbond/mb450/mb450ps1.pdf
Montana State University, Department of Microbiology
MB450 Research Methods in Microbiology, Problem Set 1

There are several views on the determination of the cell density from
the data obtained. Generally, duplicate or triplicate assays of each
dilution should be done. The data from the dilutions should be
consistent. Then the data is of a quality that a single dilution can
and should be used for the calculation. When calculating bacterial
colony counts or bacteriophage plaques, counts of 30 to 300 are
considered valid. More than 300 plaques or colonies are difficult to
count due to overlaps. On the other hand, less than 30 plaques or
colonies is generally considered to lack statistical significance.

***** REASONS:     >300 Cells may have clumped, some colonies arose
from more than one cell.      <30  Poor statistical precision.


-------------------------------------------------

http://www.cat.cc.md.us/courses/bio141/labmanua/lab4/lab4.html
LAB 4: ENUMERATION OF MICROORGANISMS

A. THE PLATE COUNT (VIABLE COUNT) 
The number of bacteria in a given sample is usually too great to be
counted directly. However, if the sample is serially diluted (see Fig.
7) and then plated out on an agar surface in such a manner that single
isolated bacteria form visible isolated colonies (see Fig. 1), the
number of colonies can be used as a measure of the number of viable
(living) cells in that known dilution. However, keep in mind that if
the organism normally forms multiple cell arrangements, such as
chains, the colony-forming unit may consist of a chain of bacteria
rather than a single bacterium. In addition, some of the bacteria may
be clumped together. Therefore, when doing the plate count technique,
we generally say we are determining the number of Colony-Forming Units
(CFUs) in that known dilution. By extrapolation, this number can in
turn be used to calculate the number of CFUs in the original sample.

Normally, the bacterial sample is diluted by factors of 10 and plated
on agar. After incubation, the number of colonies on a dilution plate
showing between 30 and 300 colonies (see Fig. 1) is determined. A
plate having 30-300 colonies is chosen because this range is
considered statistically significant. If there are less than 30
colonies on the plate, small errors in dilution technique or the
presence of a few contaminants will have a drastic effect on the final
count. Likewise, if there are more than 300 colonies on the plate,
there will be poor isolation and colonies will have grown together.

***** REASONS:     30 ?300 range is considered statistically
significant     >300 Poor isolation of colonies.      <30 Errors in
dilution technique or presence of contaminants can significantly
impact the count.


-------------------------------------------------

http://www.virtuallaboratory.net/firstSeries/GrowthLab/section_09.html
Bacterial Population Dynamics 

Counting living cells 
A simple way to count the number of living cells is to exploit their
ability to reproduce. On an agar-coated petri dish, each viable cell
will divide repeatedly, but its progeny will remain largely
immobilized -- it will form of colony. The cells of this colony are a
clone of the original cell that landed on the agar surface.  By
counting colonies, we get a direct estimate of the concentration of
viable bacteria or more accurately the number of colony forming units
- CFU per ml in the original culture.

If too many bacteria are plated on a dish, the colonies will grow
together to form a continuous lawn.

It is difficult, tedious, and increasingly inaccurate to count more
than ~500 colonies per plate, you can prove this to yourself if you
want.

At the same time, too few colonies results in increasing inaccuracies
due to sampling errors.

***** REASONS:     >300 It is difficult, tedious and error prone to
count large numbers of colonies.      <30  Inaccuracies because of
sampling errors.


-------------------------------------------------

http://www.devicelink.com/mddi/archive/99/04/009.html 
The survivor curve method is complicated by the number of serial
dilutions that must be prepared and the quality of the dilutions being
dependent on the skill of the person performing the test as well as
the precision of the equipment used. Only trained personnel who can
adequately practice aseptic technique should conduct this test.
Calibrated pipettes and dilution controls help ensure the test's
accuracy. The dilutions should also be chosen to yield counts between
30 and 300 CFUs. It is generally assumed that numbers ranging from 30
to 100 CFUs should be used because it is thought that higher numbers
of CFUs per plate could result in inaccurately low counts and that
numbers lower than 10 CFUs per plate could give unreliable counts. For
practical purposes, counts between 30 and 300 are generally
acceptable.

***** REASONS:     >300 Higher numbers can result in inaccurately low
counts.      <30  Unreliable counts.



================================================

As you can see from this sampling of instructions on how to measure
viable cells, the difficulty of counting 300+ colonies has to do with
the likelihood of crowding leading to inaccurate counts. The reason
for not using measurements under 30 colonies boils down to problems
with statistical validity. None of these college courses, textbooks or
papers explained how the statistical validity for the lower limit is
established.

I tried a variety of search phrases centered on ?statistical validity?
and ?plate count? to try to find the appropriate terminology to be
able to get a better explanation for why low colony numbers in
standard/viable plate counts produce statistically invalid results.

I eventually found some glossaries for microbiology terms that helped
with developing a better search strategy. Using ?limit of detection?
and ?limit of quantitation? from one of these glossaries led me to
some new avenues of searching.



http://www.dyerlabs.com/glossary/pharmaceutical.html

Pharmaceutical Terminology
Some Pharmaceutical Analysis/Testing Terminology (all in the
pharmaceutical laboratory context)

Limit of detection -- The lowest concentration of an analyte that can
be detected reliably (present or absent) in a particular sample. Exact
definitions vary.

Limit of quantitation -- The lowest concentration of an analyte that
can be determined quantitatively (at acceptable precision) in a
particular sample. Exact definitions vary.


======================================


My searching finally took me to the Association of Analytical
Communities (AOAC) and their Qualitative and Quantitative Microbiology
Guidelines for Methods of Validation. This document reflected that
there are various ranges for standard plate counts and referred to
?wide statistical bounds? for the testing methods. This reference led
me to keep looking for standards or methods that might have been
established by some regulatory bodies to help establish the
statistical bounds that led to the 30 ? 300 rule of thumb.


http://www.aoac.org/about/Overview.html
As the "Association of Analytical Communities," AOAC INTERNATIONAL is
committed to be a proactive, worldwide provider and facilitator in the
development, use, and harmonization of validated analytical methods
and laboratory quality assurance programs and services. AOAC also
serves as the primary resource for timely knowledge exchange,
networking, and high-quality laboratory information for its members.

http://www.aoac.org/testkits/app%20packet%203/Micguide.pdf
Microbiology Guidelines, Journal of AOAC International, Vol 82, No, 2, 1999
TECHNICAL COMMUNICATIONS
AOAC INTERNATIONAL Qualitative and Quantitative
Microbiology Guidelines for Methods Validation
These guidelines appear as Appendix E in the
Peer-Verified Methods Program Manual on Policies and Procedures.

Quantitative Microbiological Tests (pp. 409-410)
Performance Characteristics 
4. Linearity
In general, microbial enumeration methods yield results proportional
to the microbial analyte?s concentration as long as the samples are
quantitatively diluted to an appropriate concentration range. This
range is such as to give from 20?30 to 200?300 cfu per culture plate
in solid-culture-media methods. Subject to the wide statistical bounds
of the method, linearity applies in the MPN method.



==================================================

Using various combinations of the search terms listed below, I finally
found the guidelines for Accreditation in Microbiological Laboratories
which gave a short overview of the complexities involved in
quantitative biological test methods to achieve statistical validity.
?Specificity, sensitivity, relative trueness, positive deviation,
negative deviation, repeatability, reproducibility and the limit of
determination within a defined variability? are some of the elements
that go into developing the appropriate statistical methods that will
lead to the ?statistical validity? of the 30 ? 300 general rule.

Researching further I also discovered some helpful information on the
topic of measurement and uncertainty which helps to understand why
measurements above and below certain values are not statistically
valid.


http://www.eurachem.ul.pt/guides/EurachemEA_Micro.pdf
EA - 4/10 Accreditation in Microbiological Laboratories 

Validation of Test Methods (Page 9)
4.3 For quantitative microbiological test methods, the specificity,
sensitivity, relative trueness, positive deviation, negative
deviation, repeatability, reproducibility and  the limit of
determination within a defined variability should be considered and,
if  necessary, quantitatively determined in assays. The differences
due to the  matrices must be taken into account when testing different
types of samples. The results should be evaluated with appropriate
statistical methods.

Appendix A ? Glossary of Terms (Page 19)

Limit of determination: Applied to quantitative microbiological tests
- The lowest number of micro- organisms within a defined variability
that may be determined under the experimental conditions of the method
under evaluation.

Limit of detection  Applied to qualitative microbiological tests- The
lowest number of micro-organisms that can be detected, but in numbers
that cannot be estimated accurately.


---------------------------------------

http://www.ifcc.org/ejifcc/vol13no4/130401006n.htm
Uncertainty of measurement in clinical microbiology

An important part of the activity in a clinical microbiology
laboratory is the measurement of quantities related to concentrations
of microorganisms, antibodies nucleic acids, etc. When measuring a
microbiologic quantity random and systematic errors can act together
on the result producing an error of measurement and generating a doubt
 ?uncertainty? about the true value of the measured quantity.
International scientific organizations, keeping in mind these facts,
have developed the concept of uncertainty of measurement (1,2). The
importance of this concept is increasing in all fields of health
sciences (3-5). By this reason, it is important to clarify the concept
and show the practical way to bring estimate the uncertainty of
patients' results.


http://www.measurementuncertainty.org/mu/guide/index.html?content_frame=/mu/guide/appendix_f.html
Guide Quantifying Uncertainty in Analytical Measurement 
appendix f. measurement uncertainty at the limit of detection/determination

f.1 Introduction
f1.1. At low concentrations, an increasing variety of effects becomes
important, including, for example,
the presence of noise or unstable baseline, 
the contribution of interferences to the (gross) signal, 
the influence of any analytical blank used, and 
losses during extraction, isolation or clean-up. 
Because of such effects, as analyte concentrations drop, the relative
uncertainty associated with the result tends to increase, first to a
substantial fraction of the result and finally to the point where the
(symmetric) uncertainty interval includes zero. This region is
typically associated with the practical limit of detection for a given
method.


===============================================

These last two resources will give you an overview of some of the work
that is being done in the field of microbiology measurements. You can
delve as deeply as you feel necessary to explore further what are the
issues relating to ?statistical validity? that explain why standard
plate counts normally fall in the 30-300 colonies range.

I hope that you will find this research helpful. Please don?t hesitate
to ask for clarification if what I?ve provided is not a sufficient
answer to your question.

All the best.

~ czh ~



===============
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===============

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