Data analysis ( Bio-statistic )
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The document discusses key concepts for interpreting clinical biochemical data, including: 1. Calculating measures of central tendency like the mean and measures of variability like the standard deviation and range to establish normal reference values. 2. Factors that determine the validity and reliability of analytical tests, and the importance of quality assurance and quality control. 3. Methods for describing data distribution including the coefficient of variation and using critical differences to determine the clinical significance of changes in serial measurements. 4. Concepts related to screening tests like sensitivity, specificity, and the ability to correctly identify individuals with and without the disease.
Data analysis ( Bio-statistic )
- 1. 1 Interpretation of Clinical Biochemical Data ◘ Course Objectives : (1) To distinguish between people in the population who have the diseases and those who do not (2) To determine how good the test is in separating populations of people with and without the disease in question. ◘ The Objectives include: (1) Define the Key Terms (2) Discuss how statistics is used to determine normal values and establish Quality Control ranges (3) Given numerical observations, calculate the: a. Mean b. Range c. SD d. CV% e. CD ◘ INTRODUCTION (1) When evaluating laboratory results, how do we determine what is normal or acceptable? That is: What is “normal” or “OK”? (2) When does a laboratory test result become “weird” or “abnormal”? When do we become uncomfortable with a result? (3) At some point we have to draw a “line”… on this side of the line you are normal … on the other side of the line, you are abnormal
- 2. 2 ◘ Review of Statistical concepts • Measures of Central tendency: How numerical values can be expressed as a central value?. E.g., mean • Dispersal about the central value: How spread out are the numbers? E.g. range, or SD Using these 2 main ideas we can begin to: (1) Understand how basic statistics are used in clinical chemistry to define normal values, and (2) When our instruments are (or are not) generating expected numerical results • Analytical Tests include both • Screening Tests • Diagnostic Tests Both should have Validity and Reliability ◘ Validity and reliability of analytical tests • Validity (الصالحية لتحقيق الهدف ) The degree to which the tests accomplish the purpose for which they are being used. • Reliability (دقة اإلختبار ) The measure of how stable, dependable, trustworthy, and consistent a test is in measuring the same thing each time ◘ Quality Assurance & Quality Control • Quality Assurance (QA) Includes pre-analytic, analytic and post analytic factors • Accuracy versus Precision The laboratory must produce results that are both accurate and reproducible.
- 3. 3 ◘ Classification of errors The variables: Pre-analytical variables • Right specimen from right patient and in right condition Analytical variables • All parts of testing procedure performed properly, controls in range Post analytical variables • Correct report to correct person, interpreted correct • All the phases of the testing process are subject to errors and must be closely monitored, to maintain quality assurance. ♦ Accuracy: A measure of how close the observations are to the “true” or “correct” value • In the laboratory, we need to report tests with accuracy and precision. • But how accurate do we need to be? It is not possible to hit the bulls-eye every time. So how close is “close enough?”• ♦ Precision 3 possible testing outcomes - Hitting the targe
- 4. 4 ◘ DESCRIBING DATA ♦ Measures of the center of data Mean ♦ Measure of data variability Standard deviation (variance) Range ◘ Establishment of Reference Ranges Each lab must establish its own reference ranges (normal range) based on local population. You should not depend on the kit‟s reference range The following steps show how to calculate the reference range: Mean & Variance Step (1): Sample Mean: The Average or Arithmetic Mean Add up data, then divide by sample size (n) The sample size n is the number of observations (pieces of data) Mean: Example Five systolic blood pressures (mmHg) • (n = 5) • 120, 80, 90, 110, 95 • Can be represented with math type notation: • x1= 120 • x2 = 80 • x2 = 90 • x2 = 110 • x5 = 95 • The sample mean is easily computed by adding up the five values and dividing by five. • In statistical notation the sample mean is frequently represented by a letter with a line over it
- 5. 5 ♦ For example (pronounced “x bar”) Notes on Sample Mean • Generic formula representation • In the formula to find the mean, we use the “summation sign”: Σ • This is just mathematical shorthand for “add up all of the observations” Notes on Sample Mean Also called sample average or arithmetic mean Sensitive to extreme values One data point could make a great change in sample mean Step (2): Describing Variability Sample variance (s²): Is the average of the square of the deviations about the sample mean Sample standard deviation (s or SD): Is the square root of s² (to determine range)
- 6. 6 Standard Deviation (SD) Ʃ = the sum of all observations = the mean value x = the value of each individual observation n = number of observations • The greater the SD, the more spread out the observations are Example: Describing Variability Five systolic blood pressures (mmHg) (n = 5): 120, 80, 90, 110, 95 The sample mean x= 99 mmHg
- 7. 7 Example: Describing Variability Sample variance (s²) Sample standard deviation (SD) = √s² SD = 15.97 (mmHg) ∴ Blood pressure = 99 ± 16 mmHg ∴ Blood pressure = 99 ± 16 mmHg
- 8. 8 • A standard normal curve showing the normal range, which encloses 95% of the data and is bounded by the mean ± 2 standard deviations. • Five systolic blood pressures (mmHg) (n = 5) : 120, 80, 90, 110, 95 • A standard normal curve showing the normal range, which encloses 95% of the data and is bounded by the mean ± 2 standard deviations. (67 – 131)
- 9. 9 ♦ Notes on SD • The bigger SD is, the more variability there is • SD measures the spread about the mean • SD can equal 0 only if there is no spread • All n observations have the same value • The units of SD are the same as the units of the data (for example, mm Hg) ◘ Establishment of Reference Ranges ♦ Reference ranges: Normal ranges ( reference ranges ) are defined as being within +/- 2 Standard Deviations from the mean Each lab must establish its own reference ranges based on local population ♦ Factors affecting reference ranges Age Sex Diet Medications Physical activity Pregnancy Personal habits ( smoking, alcohol ) Geographic location ( altitude ) Body weight Laboratory instrumentation ( methodologies ) Laboratory reagents
- 10. 11 ♦ An example of the Standard Deviation to determine Reference Range • A minimum of 20 observations should be sampled in order to obtain valid results (but I will use just 6 to save time) • Let us determine the normal range for fasting plasma glucose using 6 people: Ahmed glucose = 98 mg/dl Aly glucose = 100 mg/dl Fahmy glucose = 105 mg/dl Magdy glucose = 150 mg/dl Mohamed glucose = 102 mg/dl Nabil glucose = 101 mg/dl - Mean = 109 mg/dl - SD = 20.0 mg/dl - 2 SD = 40.0 mg/dl • That means that the normal range for this group is 109 ± 40, or from 69 – 149 which is Mean ± 2 SD • Magdy is considered abnormal if we use these commonly accepted criteria to define normal and abnormal Example 2: Use of Standard Deviation to obtain the „range of acceptable results’ Mean of group of control values = 104 mg/dL Standard Deviation = ± 5 mg/dL 1. Determine the Range of ± 2 SD; (which will allow you to evaluate the reference range) 2. Is a control value of 100 mg/dL acceptable? 3. Using 95% confidence limits, how often will a control be out of range (statistically)?
- 11. 11 Answer: 5% of the time That is 1 out of every 20 times! What if the control specimen is “out of control?” “Out of control” means that there is too much dispersion in your result compared with the rest of the results – it‟s “weird” This suggests that something is wrong with the process that generated that observation Patient test results cannot be reported to physicians when there is something wrong with the testing process that is generating inaccurate reports Things that can go wrong, and their corrections I.e. Corrective methods 1. Instrumentation malfunction ( fix the machine) 2. Reagents deteriorated, contaminated, improperly prepared or simply used up (get new reagents) 3. Tech error (identify error and repeat the test) 4. Control specimen is deteriorated or improperly prepared (get new control) ◘ Coefficient of Variation (CV %) • A way of expressing standard deviation in terms of average value of the observations used in the calculation • The CV allows us to compare different sets of observations relative to their means.
- 12. 12 ♦ Example: • Compare two different procedures for glucose They use different reagents, have different means, produce different SDs, etc. Since they are different and cannot be compared directly, use CV formula. The CV allows us to compare different sets of observations relative to their means You cannot use the SD to compare different groups of data because they are measuring different observations - you cannot compare apples to oranges. The CV can turn all groups of observations into a percentage of their relative means - everything gets turned into “oranges.” The smaller the CV, the more reproducible the results: more values are closer to the mean. ◘ Critical Differences (CD) • The preceding discussion relates to the comparison of measured data with expected values based on observations on other people. • When a measurement has been repeated, it is more relevant to consider it in relation to the previous value (Follow-up). The relevant question is whether the two values differ significantly. This will depend on two factors: 1) The change in the parameter level being measured (biological variation), and 2) The analytical variation Both of these can be determined from the results of repeated measurements of the same samples, and a function known as the critical difference (CD) calculated from the equation: 3) Where SDA and SDB are the analytical and biological standard deviations, respectively (they should be available for each Lab)
- 13. 13 - Values for some CDs should be available from the local laboratory ♦ Critical differences are independent of normal ranges. - Indeed, two results may be critically different yet both are within the normal range. ♦ Example: • The typical human reference ranges for serum creatinine are - 0.5 to 1.0 mg/dL for women - and 0.7 to 1.2 mg/dL for men. • Consider, for example, an increase in serum creatinine concentration from 0.9 to 1.13 mg/dL = 0.23 mg/dL • The CD for creatinine in this range of concentrations is about 0.19 mg/dL (Calculated from different laboratories) (See References). • Thus, an increase of 0.23 mg/dL is of potential clinical significance (implying a decrease in renal function), even though both values are within the normal range. • This discussion emphasizes the fact that serial measurements in individuals can (and in practice frequently are) more informative than „one-off‟ measurements. NB: Creatinine 1 mg/dL = 88.4 μmol/L
- 14. 14 ◘ Screening Tests ♦ Terms Related to Screening Tests Sensitivity - ability of a test to identify those who have disease Specificity - ability of a test to exclude those who do not have disease Tests with dichotomous results – tests that give either positive or negative results Tests of continuous variables – tests that do not yield obvious “positive” or “negative” results, but require a cutoff level to be established as criteria for distinguishing between “positive” and “negative” groups An important public health consideration, is: How good is the test at identifying people with the disease and without the disease? ♦ In other words: If we screen a population, what proportion of people who have the disease will be correctly identified?
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- 16. 16 Sample variance (s²)◘Sample Mean◘ ◘ The normal range = the mean ± 2 standard deviations. ◘Sample standard deviation (s or SD) Critical Differences (CD)◘ • SDA and SDB are the analytical and biological standard deviations, respectively ◘ Coefficient of Variation (CV %) ◘ The median ◘ The Mode ◘ Screening Test