Quality Control: Analysis Of Data Pawan Angra MS Division of Laboratory Systems Public Health Practice Program Office Centers for Disease Control and Prevention Pawan Angra MS Division of Laboratory Systems Public Health Practice Program Office Centers for Disease Control and Prevention

2 How to carry out analysis of data? Need tools for data management and analysis  Basic statistics skills  Manual methods Graph paper Calculator  Computer helpful Spreadsheet Important skills for laboratory personnel Need tools for data management and analysis  Basic statistics skills  Manual methods Graph paper Calculator  Computer helpful Spreadsheet Important skills for laboratory personnel

3 Analysis of Control Materials Need data set of at least 20 points, obtained over a 30 day period Calculate mean, standard deviation, coefficient of variation; determine target ranges Develop Levey-Jennings charts, plot results Need data set of at least 20 points, obtained over a 30 day period Calculate mean, standard deviation, coefficient of variation; determine target ranges Develop Levey-Jennings charts, plot results

4 Establishing Control Ranges Select appropriate controls Assay them repeatedly over time (at least 20 data points) Make sure any procedural variation is represented: different operators, different times of day Determine the degree of variability in the data to establish acceptable range Select appropriate controls Assay them repeatedly over time (at least 20 data points) Make sure any procedural variation is represented: different operators, different times of day Determine the degree of variability in the data to establish acceptable range

5 Measurement of Variability A certain amount of variability will naturally occur when a control is tested repeatedly. Variability is affected by operator technique, environmental conditions, and the performance characteristics of the assay method. The goal is to differentiate between variability due to chance from that due to error. A certain amount of variability will naturally occur when a control is tested repeatedly. Variability is affected by operator technique, environmental conditions, and the performance characteristics of the assay method. The goal is to differentiate between variability due to chance from that due to error.

6 Measures of Central Tendency Data distribution- central value or a central location Central Tendency- set of data Data distribution- central value or a central location Central Tendency- set of data

7 Measures of Central Tendency Median = the central value of a data set arranged in order Mode = the value which occurs with most frequency in a given data set Mean = the calculated average of all the values in a given data set Median = the central value of a data set arranged in order Mode = the value which occurs with most frequency in a given data set Mean = the calculated average of all the values in a given data set

8 Calculation of Median Data set ( 30.0, 32.0, 31.5,45.5, 33.5, 32.0, 33.0, 29.0, 29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5, 30.0, 34.0, 32.0, 32.0, 35.0, 32.5.) mg/dL Outlier: 45.5 Arrange them in order ( 29.0, 29.5, 30.0, 30.0, 30.5, 31.0, 31.5, 31.5, 32.0, 32.0, 32.0, 32.0, 32.5, 32.5, 33.0, 33.5, 33.5, 34.0, 34.5, 35.0) mg/dL Data set ( 30.0, 32.0, 31.5,45.5, 33.5, 32.0, 33.0, 29.0, 29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5, 30.0, 34.0, 32.0, 32.0, 35.0, 32.5.) mg/dL Outlier: 45.5 Arrange them in order ( 29.0, 29.5, 30.0, 30.0, 30.5, 31.0, 31.5, 31.5, 32.0, 32.0, 32.0, 32.0, 32.5, 32.5, 33.0, 33.5, 33.5, 34.0, 34.5, 35.0) mg/dL

9 Calculation of Mode Data set (30.0, 32.0, 31.5, 33.5, 32.0, 33.0, 29.0, 29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5, 30.0, 34.0, 32.0, 32.0, 35.0, 32.5.) mg/ dL

10 Calculation of Mean Data set (30.0, 32.0, 31.5, 33.5, 32.0, 33.0, 29.0,29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5, 30.0, 34.0,32.0, 32.0, 35.0, 32.5.) mg/ dL The sum of the values (X 1 + X 2 + X 3 … X 20 ) divided by the number (n) of observations The mean of these 20 observations is (639.5  20) = 32.0 mg/dL Data set (30.0, 32.0, 31.5, 33.5, 32.0, 33.0, 29.0,29.5, 31.0, 32.5, 34.5, 33.5, 31.5, 30.5, 30.0, 34.0,32.0, 32.0, 35.0, 32.5.) mg/ dL The sum of the values (X 1 + X 2 + X 3 … X 20 ) divided by the number (n) of observations The mean of these 20 observations is (639.5  20) = 32.0 mg/dL

11 Normal Distribution All values are symmetrically distributed around the mean Characteristic “bell-shaped” curve Assumed for all quality control statistics All values are symmetrically distributed around the mean Characteristic “bell-shaped” curve Assumed for all quality control statistics

12 Normal Distribution

13 Accuracy and Precision “Precision” is the closeness of repeated measurements to each other. Accuracy is the closeness of measurements to the true value. Quality Control monitors both precision and the accuracy of the assay in order to provide reliable results. “Precision” is the closeness of repeated measurements to each other. Accuracy is the closeness of measurements to the true value. Quality Control monitors both precision and the accuracy of the assay in order to provide reliable results.

14 Precise and inaccurate Precise and inaccurate

15 Imprecise and inaccurate Imprecise and inaccurate

16 Precise and accurate Precise and accurate

17 Measures of Dispersion or Variability There are several terms that describe the dispersion or variability of the data around the mean: Range Variance Standard Deviation Coefficient of Variation There are several terms that describe the dispersion or variability of the data around the mean: Range Variance Standard Deviation Coefficient of Variation

18 Range Range is the difference or spread between the highest and lowest observations. It is the simplest measure of dispersion. It makes no assumption about the central tendency of the data. Range is the difference or spread between the highest and lowest observations. It is the simplest measure of dispersion. It makes no assumption about the central tendency of the data.

19 Calculation of Variance Variance is the measure of variability about the mean. It is calculated as the average squared deviation from the mean.  the sum of the deviations from the mean, squared, divided by the number of observations (corrected for degrees of freedom) Variance is the measure of variability about the mean. It is calculated as the average squared deviation from the mean.  the sum of the deviations from the mean, squared, divided by the number of observations (corrected for degrees of freedom)

20 Calculation of Variance (S 2 )

21 Degrees of Freedom Represents the number of independent comparisons that can be made among a series of observations. The mean is calculated first, so the variance calculation has lost one degree of freedom (n-1) Represents the number of independent comparisons that can be made among a series of observations. The mean is calculated first, so the variance calculation has lost one degree of freedom (n-1)

22 Calculation of Variance (Urea level 1 control) mg/dl 52.25/19 mg/dl 1n )X(X )(S Variance      

23 Calculation of Standard Deviation The standard deviation (SD) is the square root of the variance -SD is the square root of the average squared deviation from the mean -SD is commonly used due to the same units as the mean and the original observations -SD is the principle calculation used to measure dispersion of results around a mean The standard deviation (SD) is the square root of the variance -SD is the square root of the average squared deviation from the mean -SD is commonly used due to the same units as the mean and the original observations -SD is the principle calculation used to measure dispersion of results around a mean

24 Calculation of Standard Deviations Urea level 1 control

25 Calculation of 1, 2 & 3 Standard Deviations 3s = 1.66 x 3 = 4.98 mg/dl mg/dl x s mg/dl s    

26 Standard Deviation and Probability 68.2% 95.5% 99.7% Frequency -3s-2s-1sMean+1s+2s+3s

27 Standard Deviation and Probability For a data set of normal distribution, a value will fall within a range of:  +/- 1 SD 68.2% of the time  +/- 2 SD 95.5% of the time  +/- 3 SD 99.7% of the time For a data set of normal distribution, a value will fall within a range of:  +/- 1 SD 68.2% of the time  +/- 2 SD 95.5% of the time  +/- 3 SD 99.7% of the time

28 Calculation of Range Urea level 1 control 68.2% confidence limit: (1SD) Mean + s = mg/dl Mean - s = mg/dl Range mg/dl 68.2% confidence limit: (1SD) Mean + s = mg/dl Mean - s = mg/dl Range mg/dl

% confidence limit: (2SD) Mean + 2s = mg/dl Mean - 2s = mg/dl Range – mg/dl 95. 5% confidence limit: (2SD) Mean + 2s = mg/dl Mean - 2s = mg/dl Range – mg/dl Calculation of Range Urea level 1 control

% confidence limit: (3SD) Mean + 3s = Mean - 3s = Range – mg/dl % confidence limit: (3SD) Mean + 3s = Mean - 3s = Range – mg/dl Calculation of Range Urea level 1 control

31 Standard Deviation and Probability In general, laboratories use the +/- 2 SD criteria for the limits of the acceptable range for a test When the QC measurement falls within that range, there is 95.5% confidence that the measurement is correct Only 4.5% of the time will a value fall outside of that range due to chance; more likely it will be due to error In general, laboratories use the +/- 2 SD criteria for the limits of the acceptable range for a test When the QC measurement falls within that range, there is 95.5% confidence that the measurement is correct Only 4.5% of the time will a value fall outside of that range due to chance; more likely it will be due to error

32 Coefficient of Variation The Coefficient of Variation (CV) is the standard Deviation (SD) expressed as a percentage of the mean -Also known as Relative Standard deviation (RSD) CV % = (SD ÷ mean) x 100 The Coefficient of Variation (CV) is the standard Deviation (SD) expressed as a percentage of the mean -Also known as Relative Standard deviation (RSD) CV % = (SD ÷ mean) x 100

33 Summary Data set of at least 20 points, obtained over a 30 day period Calculate mean, standard deviation, coefficient of variation Determine target range Data set of at least 20 points, obtained over a 30 day period Calculate mean, standard deviation, coefficient of variation Determine target range