Applications of Microbiolgical Data

Tim SandleMicrobiology information

resource: http://www.pharmamicroresources.com/

Introduction

Distribution of microbiological data Use of trend charts Calculation of warning and action

levels

Introduction

Examples from environmental monitoring and water testing

Broad and illustrative overview Written paper with more detail

Distribution of microbiological data

Why study distribution?• Impact on sampling• Impact on trending• Impact upon calculation of warning and

action levels

Distribution

Most statistical methods are based on normal distribution, and yet….

Most microbiological data does NOT follow normal distribution

Distribution

Micro-organisms, such as those in a typical, free-flowing water system, follow Poisson distribution

For example…

Distribution

S1 S2 S3S4 S5

Where S = sample= micro-organism

Distribution

And microbial counts tend to be skewed (or positive or negative exponential distribution)

For example, a Water-for-Injection system…

Distribution

Typical distribution of micro-organisms in WFI

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7

Count (cfu / 100 ml)

Nu

mb

er

of

sa

mp

les

Distribution

So, what can we do about it?

Skewed question mark

Distribution

Well:a) Use complex calculations and Poisson distribution tables, orb) Attempt to transform then data

We’ll go for the second option

Distribution

A general rule is:• For low count data e.g. Grade A

monitoring and WFI systems, take the square root

• For higher count data, e.g. Grade C and D environmental monitoring or a purified water system, convert the data into logarithms

Distribution

For example, some counts from a WFI system:

Distribution

When the data is examined for its distribution, using a simple ’blob’ chart:

CI for Mean

0 2 4 6 8

Count

Distribution

Whereas if the square root is taken:Week Number Mean count Square root

per week (cfu / 100 ml) of mean1 0 0.002 5.15 2.273 0.29 0.544 6.93 2.635 1.86 1.366 1.47 1.217 0.1 0.328 0 0.009 2.22 1.4910 3.95 1.9911 0.11 0.3312 1.25 1.1213 0 0.0014 6.34 2.5215 0.31 0.5616 0.45 0.6717 2.7 1.6418 0.89 0.9419 0.65 0.8120 3.45 1.86

Distribution

We move closer to normal distribution:

CI for Mean

0 0.5 1 1.5 2 2.5 3

Count

Distribution

Logarithms work in a similar way for higher counts

Remember to add ‘+1’ to zero counts (and therefore, +1 to all counts)

Trend Analysis

There is no right or wrong approach There are competing systems This presentation focuses on two

approaches, both described as ‘control charts’:• The cumulative sum chart• The Shewhart chart

Trend Analysis

Control charts form part of the quality system

They can be used to show:• Excessive variations in the data• How variations change with time• Variations that are ‘normally’ expected• Variations that are unexpected, i.e.

something unusual has happened

Trend Analysis

Control charts need:• A target value, e.g. last year’s average• Monitoring limits:

Upper limit Lower limit Control line / mean So the data can be monitored over time and

in relation to these limits

Trend Analysis

Of these,• The warning limit is calculated to represent a

2.5% chance• The action level is calculated to represent a

0.1% chance• So, if set properly, most data should remain

below these limits• These assumptions are based on NORMAL

DISTRIBUTION• Various formula can be used to set these or

validated software

Trend Analysis

Cumulative sum chart (cusum)• Suitable for large quantities of low count

data. It is very sensitive to small shifts• Shows shifts in the process mean

Shewhart chart• Suitable for higher count data. It shows

large changes more quickly.

Trend Analysis

Cusums• Harder to interpret• Displays the cumulative sum of a rolling

average of three values and plots these in comparison with the target value

• The direction and steepness of the slope are important

• Significant changes are called ‘steps’• V-masks can be used as a prediction to

the future direction

Trend Analysis

For example, a Grade B cleanroom Contact (RODAC) plates are

examined A target of 0.2 cfu has been used,

based on data from the previous year

Trend Analysis

Trend Analysis

Shewhart charts• Powerful for distinguishing between

special causes and common causes• Common causes are inherent to the

process and are long-term• Special causes are where something has

changed and maybe of a long or short term

Trend Analysis

Examples of special causes:• a) A certain process • b) A certain outlet • c) A certain method of sanitisation, etc. • d) Sampling technique• e) Equipment malfunction e.g. pumps, UV

lamps• f) Cross contamination in laboratory• g) Engineering work• h) Sanitisation frequencies

Trend Analysis

For example, a Grade C cleanroom• Active air-samples are examined• A target of 1.5, based on historical data

Trend Analysis

Trend Analysis

The previous charts were prepared using a statistical software package

However, MS Excel can also be used The next example is of a WFI system Notice the data has been converted

by taking the square root of each value

Trend Analysis

Trend of WFI System over 62 weeks with trend line

-1-0.5

00.5

11.5

22.5

33.5

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61

Number of weeks

Sq

ro

ot

of

mea

n c

ou

nt

/ w

eek

Trend Analysis

Alternatives:• Individual Value / Moving Range charts• Exponentially Weighted Moving Average

charts (EWMA)• These are useful where counts are NOT

expected, e.g. Grade A environments• They look at the frequency of intervals

between counts

Trend Analysis

Summary

Chart Type

Advantage

Disadvantage

Cumulative sum

Cusum charts are more

sensitive to small process

shifts.

Large,

abrupt shifts are not

detected as fast as in a

Shewhart chart.

Shewhart chart

Systematic shifts are

easily detected.

The probability of

detecting small shifts fast

is rather small

Limits Alert and action levels Based on PDA Tech. Report 13 (2001):

• Alert level: a level, when exceeded, indicates that the process may have drifted from its normal operating condition. This does not necessarily warrant corrective action but should be noted by the user.

• Action level: a level, when exceeded, indicates that the process has drifted from its normal operating range. This requires a documented investigation and corrective action.

Limits

Why use them?

• Assess any risk (which can be defined as low, medium or high)

• To propose any corrective action• To propose any preventative action

Limits

“Level” is preferable to “Limit” Limits apply to specifications e.g.

sterility test Levels are used for environmental

monitoring

Limits

Regulators set ‘guidance’ values e.g. EU GMP; USP <1116>; FDA (2004)

These apply to new facilities User is expected to set their own

based on historical data• Not to exceed the published values• Many references stating this• Views of MHRA and FDA

Limits

Things to consider:• The length of time that the facility has been in

use for• How often the user intends to use the limits for

(i.e. when the user intends to re-assess or re-calculate the limits. Is this yearly? Two yearly? And so on).

• Custom and practice in the user’s organisation (e.g. is there a preferred statistical technique?)

• They be calculated from an historical analysis of data.

• Uses a statistical technique.

Limits

Historical data• Aim for a minimum of 100 results• Ideally one year, to account for seasonal

variations

Limits

Statistical methods:• Percentile cut-off• Normal distribution• Exponential distribution• Non-parametric tolerance limits• Weibull distribution

Recommended by PDA Technical Report, No. 13

Limits

Assumptions:

a) The previous period was ‘normal’ and that future excursions above the limits are deviations from the normb) Outliers have been accounted for

Limits

Percentile cut-off• Good for low count data• May need to use frequency tables• May need to round up or down to

nearest whole zero or five• Warning level = 90th or 95th

• Action level = 95th or 99th

Limits

Percentile cut-off• Data is collected, sorted and ranked

90th percentile means that any future result that exceeds this is 90% higher than all of the results obtained over the previous year.

• Refer to PharMIG News Number 3 (2000) for excellent examples.

Limits

Normal distribution• Can only be used on data that is

normally distributed!• Could transform data but inaccuracies

can creep in• Most data will be one-tailed, therefore

need to adjust 2nd and 3rd standard deviation

Warning level = 1.645 + the mean Action level = 2.326 + the mean

Limits

Negative exponential distribution• Suitable for higher count data• Warning level: 3.0 x mean• Action level: 4.6 x mean

Limits

For all, do a ‘sore thumb’ activity by comparing to a histogram of the data

Does it feel right?

Conclusion

We have looked at:• Distribution of microbiological data• Trending

Cusum charts Shewhart charts

• Setting warning and action levels Percentile cut-off Normal distribution approach Negative exponential approach

Conclusion

Key points:• Most micro-organisms and microbial

counts do not follow normal distribution• Data can be transformed• Inspectors expect some trending and

user defined monitoring levels• Don’t forget to be professional

microbiologists – it isn’t all numbers!

Just a thought…

This has been a broad over-view If there is merit in a more ‘hands on’

training course, please indicate on your post-conference questionnaires.

Thank you