lecture 3

Important terms Mean Normal distribution Standard deviation Specificity Sensitivity Accuracy Precision = reproducibility

Mean Mean= the average of the numbers: a calculated "central" value of a set of numbers. To calculate: Just add up all the numbers, then divide by how many numbers there are.

Normal distribution: If many measurements are taken, and the results are plotted on a graph, the values form a bell-shaped curve as the results vary around the mean. This is called a normal distribution. The distribution can be seen if data points are plotted on the x- axis and the frequency with which they occur on the y-axis.

Standard deviation Standard deviation = quantity expressing by how much the members of a group differ from the mean value for the group “ is a measure of how spread out numbers are.” 1 SD 2 SD 3 SD

This is important because a characteristic of the normal distribution is that, when measurements are normally distributed: 68 % of the values will fall within –1 SD and +1 SD of the mean. 95 % fall within –2 SD and +2 SD. 99 % fall between –3 SD and +3 SD of the mean.

True positive True negative False positive False negative

Accuracy & Precision Accuracy Precision - the closeness of the estimated value to the true mean can be checked by the use of reference materials which have been assayed by independent methods of known precision Precision - reproducibility of a results, whether accurate or inaccurate within a define frame time ( eg: within the same day, from week to week etc ) - can be controlled by replicate tests, check tests on previously measured specimens and statistical evaluation of results

Good Accuracy Good Precision Good Precision Only Neither Good precision Nor Accuracy

Sensitivity (Ability to exclude false negatives) Sensitivity is a measure of the incidence of positive results in patients known to have a condition, that is 'true positive' (TP). A sensitivity of 90% implies that only 90% of people known to have the disease would be diagnosed as having it on the basis of that test alone: 10% would be 'false negatives' (FN).

Specificity (Ability to exclude false positives) The specificity of a test is a measure of the incidence of negative results in persons known to be free of a disease, that is 'true negative' (TN). A specificity of 90% implies that 10% of disease-free people would be classified as having the disease on the basis of the test result: they would have a 'false positive' (FP) result.

Calculations Specificity and sensitivity are calculated as follows:

Sensitivity Ability to correctly identify individuals with disease 1000 people tested 875 positive tests (275 false positive) 125 negative tests (25 false negative) TP/(TP + FN) – may be expressed as a percent Sensitivity = 600/600 +25 = 0.96 (96%)

Specificity Ability to correctly identify individuals without disease 1000 people tested 875 positive tests (275 false positive) 125 negative tests (25 false negative) TN /(TN + FP) Specificity = 100/(100+275) = 0.27 or 27% True pos= 600, True Neg= 100

High Sensitivity desired when Disease is serious and should not be missed Disease is treatable False positives do not lead to serious psychological or emotional trauma

High Specificity desired when Disease is serious but is not treatable or curable Knowledge that disease is absent has physiological or public health value False-positive results can lead to serious psychological or economic trauma

Ideal Test An ideal diagnostic test would be: 100% sensitive, giving positive results in all diseased subjects, and also 100% specific, giving negative results in all subjects free of disease. Individual tests do not achieve such high standards. Factors that increase the specificity of a test tend to decrease the sensitivity and vice versa. 19

The closer the hits are, the more precise they are The closer the hits are, the more precise they are. If most of the hits are in the bull’s eye, they are both precise and accurate. The values in the middle are precise but not accurate because they are clustered together but not at the bull’s eye. The figure on the right shows a set of hits that are imprecise.

E.g. The fecal occult blood(FOB) screen test was used in 2030 people to look for bowel cancer:

Summary Mean Standard deviation Normal distribution Specificity Sensitivity Accuracy Precision = reproducibility

Reference Some slides were taken from M. Zaharna Clin Chem. Presentation 2009