Total Anaytical Error
This is a very important figure of merit that is also quite simple to estimate. In order to calculate the total analytical error, the test results obtained with the device, are compared with the reference values. The errors are estimated for all pairs of results according to:
The total analytical error is defined as the range that contains a certain proportion (e.g., 95%) of the errors. A quick and non-parametric way to estimate the total analytical error is to sort the errors calculated in equation (1), assign ranks and calculate percentiles. If the distribution of the errors is shown to be normal, the total analytical error can be estimated using the mean error, the standard deviation of the errors and the appropriate t value from the t-distributions associated with the number of differences and the specified proportion of the distribution of errors.
If the total analytical error appears to be larger than anticipated, it is recommended that you examine a histogram of the errors for potential discrepancies and/or plot the errors (on the y-axis) versus the reference values (x-axis) and inspect the plot for trends. The errors computed in equation (1) above may increase as the analyte level (the reference value) increases. In this case, it may be more appropriate to use relative errors instead of absolute errors at high analyte levels. The total analytical error may also be estimated at different ranges of reference values. Three clinically relevant ranges (low, medium and high) are typically used.
It is important to note that if the total analytical error is specified for 95% of the errors, the remaining 5% of the errors must not be so large as to cause harmful treatment to patients. The proportion of the errors that are large enough to cause a harmful outcome must be evaluated with respect to the size of patient sample used in estimating the total analytical error.
Total analytical error can be very useful in deciding which device is suitable for a certain application. Consider, for example, a case of tight glycemic control where a patient's blood glucose is to be kept in the range 80 mg/dL to 110 mg/dL. If the patient is treated such that the blood glucose level is maintained at 95 mg/dL and is measured by a particular device to be 95 mg/dL, then the device's total analytical error at this concentration must be in the range -15 mg/dL to +15 mg/dL 100% of the time (i.e., 100% of the errors at 95 mg/dL are in the range -15 mg/dL to +15 mg/dL.) If only 80% of the device's errors are in the range -15 mg/dL to +15 mg/dL at 95 mg/dL, then the treating physician can not be certain that the patient is kept in the target range of 80 mg/dL to 110 mg/dL.