Applications of Microbiolgical
DataTim Sandle
Microbiology 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 And microbial counts tend to be skewed (or positive or negative exponential distribution)
For example, a Water-for-Injection system…
Distribution
Typical distribution of m icro-organism s in W FI
050100150200250300350
1 2 3 4 5 6 7Count (cfu / 100 m l)
Number o
f sam
ples
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 When the data is examined for its distribution, using a simple ’blob’ chart:
CI for Mean
0 2 4 6 8Count
Distribution Whereas if the square root is taken:W eek Num ber M ean count Square root
per w eek (cfu / 100 m l) of m ean1 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 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 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 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 W FI System over 62 w eeks w ith trend line
-1-0.50
0.51
1.52
2.53
3.5
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61
Num ber of w eeks
Sq ro
ot of m
ean coun
t /
week
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.