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# Understanding statistics in laboratory quality control

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Introduction to laboratory statistics including calculation of Mean values, Standard Deviation and Co-efficient of Variation. An overview of how to interpret Levey-Jennings charts and apply QC multi-rules is also provided.

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### Understanding statistics in laboratory quality control

1. 1. “revolutionising healthcare through continuously improving diagnostic solutions”
2. 2. UNDERSTANDING STATISTICS – LABORATORY QUALITY CONTROL
3. 3. Learning Objectives: 1. Be able to calculate your own mean and standard deviation for a set of QC results 2. Be able to calculate your own decision limits 3. Be able to draw a Levey-Jennings chart 4. Accept or reject results based on QC multi-rules
4. 4. Quality control is underpinned by statistics These statistics are used to provide confidence in data
5. 5. Assayed Control Vs. Precision Controls Precision (Unassayed) Controls Precision controls are supplied without target values or ranges as such laboratories will need to determine their own mean for comparison. Precision controls can effectively be used to assess precision however cannot be used in isolation to assess accuracy. (When combined with a Peer Group Reporting programme they may be used to monitor accuracy) Assayed controls Assayed controls can be used to assess both precision and accuracy and are supplied with pre-assigned target values and ranges. When using an assayed control however you may still be required to establish your own mean and range as sometimes the ranges supplied will be too wide and will not serve as a good measure of accuracy.
6. 6. How to interpret your QC results…. Remember IQC….. ………..is used to monitor the accuracy and precision of the complete analytical process both daily and over time in order to detect errors ….. so that you can decide if patient results are reliable and can be released. So in order to interpret your IQC results meaningfully you need to decide what is sufficient accuracy and what is sufficient precision for each analytical test performed, in order to ensure you are producing reliable patient results.
7. 7. 1. Calculate the mean 2. Calculate SD 3. Establish Decision limits 4. Create a Levey-Jennings chart 5. Accepts or reject results based on a defined set of QC rules. Steps in Interpreting Your QC Results
8. 8. Step 1 – Establishing the Mean a) Analyse the QC sample a minimum of 20 times over several days b) Calculate the average or mean value c) Compare the observed value to that quoted by the manufacturer. d) Providing the observed value falls within the quoted range it will then become the ‘new mean’
9. 9. Step 1 – Establishing the Mean • The mean provides a good estimate of the true value or accuracy for a specific level of control. May also be used to indicate the presence of systematic error. • External Quality Assessment (EQA) and Peer Group Comparison programs will provide useful information on the means and SDs observed in other laboratories. • Peer group comparison programmes can also be used to automatically calculate the mean and cumulative means.
10. 10. Formula: Step 2: Calculate the Standard Deviation a) Calculate the difference of each control result from the mean b) Square the difference c) Divide by the number of results minus 1 (n-1) d) Finally calculate the square root
11. 11. Step 2: Calculate the Standard Deviation • The SD quantifies how close numerical values are in relation to each other providing a good measure of precision and an indication of random error. • A small SD indicates good precision while a larger SD indicates variation in the results and thus poor precision. A large SD may also indicate random error. • Peer group reporting programmes will automatically calculate the Standard Deviation however the SD can be easily calculated using a scientific calculator or an excel spreadsheet
12. 12. Both the mean and SD are used to establish decision limits. A 2SD range is adopted by most laboratories. a) Once the mean and SD have been established calculate 2SD by multiplying the SD by 2 b) To establish the lower decision limits subtract 2SD from the mean c) To establish the upper decision limits add 2SD to the mean Example Results: 101, 102, 103, 104, 105 Mean: 103 1SD: 1.6 2SD: 1.6 x 2 = 3.2 Calculation: 103 – 3.2 = 99.8 103+3.2 = 106.2 +/- 2SD range = 99.8 - 106.2 Step 3: Establish Decision Limits
13. 13. Why use a 2SD range? • In a normalised distribution it is estimated that 68% of data points will be within + 1SD and 95% of data points will be within + 2SD
14. 14. Step 3: Establish Decision Limits • Both the mean and SD should be periodically recalculated throughout the shelf life of each control lot • Peer Group Reporting programmes will do this each time a control is analytes and will automatically calculated a cumulative mean and SD.
15. 15. Step 4: Create a Levey-Jennings chart Using the mean and a +/-3 SD range create a Levey-Jennings chart. Daily control data for each test and level of control is plotted to monitor trends in performance over time.
16. 16. Step 4: Create a Levey-Jennings chart • Levey-Jennings charts can be used to identify any positive/negative bias as well as trends over time • Ideally there will be an even spread of results (within 1/2SD) above and below the mean • Again a good QC program or Peer Group Reporting package will conveniently generate Levey-Jennings charts based on either the SD or percentage deviation from the mean
17. 17. Step 5: Accepts or reject results based on a defined set of QC rules. • QC rules are often referred to a Westgard rules are used to help minimise false rejections and maintain a high degree of error detection
18. 18. Step 5: Accepts or reject results based on a defined set of QC rules. IQC Data 12 s 13 s 22 s R4 s 4IS In - Control Accept Run Out – of - Control Reject Run No No No No No NoYes Yes Yes Yes Yes Yes
19. 19. Step 5: Accepts or reject results based on a defined set of QC rules. • The 12S rule is normally used as a warning rule before applying other QC rules • Most QC packages or peer group programs will allow laboratories to set user defined QC multi- rules for each individual test • The program will then automatically reject/alert any QC results that violate any of the rules
20. 20. Other Useful Statistics • Coefficient of Variation (CV) • Standard Deviation Index
21. 21. Coefficient of Variation (CV) • The CV is essentially the SD expressed as a percentage of the mean CV = (SD/Mean) x 100 • The SD of a method is dependent on concentration i.e. the higher the concentration the larger the SD. • The CV can therefore be used to assess performance over a range of concentrations
22. 22. Standard Deviation Index (SDI) • If participating in an EQA or peer group reporting program you will have come across the term SDI • SDI is a measure of your performance relative to others in your peer group without having to consider magnitude of change SDI = (Mean – Peer Group Mean) / SD of Peer Group
23. 23. THE FUTURE OF INTERLABORATORY DATA MANAGEMENT
24. 24. What is Acusera 24.7? • An internal quality control and peer group reporting package – Calculate internal statistics e.g. mean, SD, CV – Minimise false rejections and the number of repeat tests with user defined QC multi-rules – Detect and identify trends/errors through the use of Levey-Jennings and Histogram charts thus minimising expensive repeat tests and unnecessary troubleshooting
25. 25. Acusera 24.7 Live Online Benefits • Online QC monitoring 24 hours a day, 7 days a week – Acusera 24.7 can be accessed anytime, anywhere – The online nature eliminates the need to backup/update software • Peer group data generated from up to 20,000 laboratory participants – Peer group statistics available for a wide range of instruments and methods – Large peer groups to compare to – Availability of statistically valid data • Peer group statistics updated daily – Unique to Acusera 24.7 – Aids troubleshooting and may even help to identify issues before they arise in your lab
26. 26. Acusera 24.7 Live Online • Unique dashboard interface – Automatically displayed when a user logs in – Highlights poor performance at a glance – Highlights rejected/alerted results from the last 7 days • Interactive charts capable of combining multiple analytes, lots and instruments – The program will automatically generate Histogram, Levey-Jennings and performance summary charts – Easily identify if the same bias or trends are seen with more than one level of QC or more than one parameter
27. 27. Acusera 24.7 Live Online • Comprehensive reports for advanced bench review – Laboratory comparison report – Exception report – Peer goup statistics – Data rejection report – Affiliate group reports • Audit trail reports helping to meet regulatory requirements – Records all actions relating to creation/modification of data – Cannot be edited or destroyed – Excellent tool for documenting the review process • Automatic QC entry via Acusera 24.7 Connect – Connects to Middleware or LIMs for automated QC result entry – Eliminates issues with manual data entry – Increases efficiency and productivity
28. 28. Acusera 24.7 Data Entry Options
29. 29. Watch the Video
30. 30. Learning Objectives: 1. Be able to calculate your own mean and standard deviation for a set of QC results 2. Be able to calculate your own decision limits 3. Be able to draw a Levey-Jennings chart 4. Accept or reject results based on QC multi-rules