Bias-corrected standard error

We can summarise some other ideas for evaluating the predictive ability of the PLS model. First, you can compare the average error (RMSEP) with the concentration levels of the standards (in calibration) and evaluate whether you (or your client) can accept the magnitude of this error (fit-for-purpose). Then, it is interesting to calculate the so-called "ratio of prediction to deviation", which is just RPD=SD/SEP, where, SD is the standard deviation of the concentrations of the validation samples and SEP is the bias-corrected standard error of prediction (for SEP, see Section 4.6 for more details). As a rule of thumb, an RPD ratio lower than 3 suggests the model has poor predictive capabilities [54]. 

Statistics The Bias-Corrected Standard Error Abbreviation(s) SEC(C), SEP(C)... 

Comments Bias-corrected standard error measurements allow the characterization of the variance attributable to random unexplained error. The bias value is calculated as the mean difference between two columns of data, most commonly actual minus NIR predicted values. 

SD is the standard deviation of the concentrations of the validation samples and SEP is the bias-corrected standard error of prediction [SEP, see eqn (5.16) in Section 5.8 for more details]. As a rule of thumb, an RPD ratio lower than 3 suggests the model has poor predictive capabilities. ... 

Finally, the precision of the multivariate calibration method can be estimated from the standard error of prediction (SEP) (also called standard error of performance), corrected for bias ... 

M. H. Quenouille introduced the jackknife (JKK) in 1949 (12) and it was later popularized by Tukey in 1958, who first used the term (13). Quenouille s motivation was to construct an estimator of bias that would have broad applicability. The JKK has been applied to bias correction, the estimation of variance, and standard error of variables (4,12-16). Thus, for pharmacometrics it has the potential for improving models and has been applied in the assessment of PMM reliability (17). The JKK may not be employed as a method for model validation. 

Bias correction can be dangerous in practice because of the high variabihty in its estimate. In spite of this, its estimation is usually worthwhile. If bias is small relative to the standard error of the parameter, then it is best to use 0 rather than 6. If the bias is large compared to the SE of the parameter, then it is an indication that 0 is not an appropriate estimate of the parameter 0. 

It can be assumed that with the development and study of new methods, the ability to determine M (S), the method bias component of uncertainty, cannot be done given that it can be evaluated only relative to a true measure of analyte concentration. This can be achieved by analysis of a certified reference material, which is usually uncommon, or by comparison to a well-characterized/accepted method, which is unlikely to exist for veterinary drug residues of recent interest. Given that method bias is typically corrected using matrix-matched calibration standards, internal standard or recovery spikes, it is considered that the use of these approaches provides correction for the systematic component of method bias. The random error would be considered part of the interlaboratory derived components of uncertainty. 

In the best of instruments, isotope ratio errors may occur as a result of inefficient counting, from mass bias, and other causes. Correction standards at approximately the same concentrations as quality control (QC) samples and unknown samples are used to correct for these sources of error. A natural uranium spike is used because low-concentration endogenous uranium in the base urine and any small amounts of contamination from environmental sources are presumed to be natural, thus will not affect the true ratio in the event of environmental contamination. Correction with an unadulterated isotope ratio is assured. Considering the nature of the urine sample and the problems that must be overcome for uranium accurate isotope ratio analysis with acceptable sample throughput, two sample preparation... 

Accuracy (systematic error or bias) expresses the closeness of the measured value to the true or actual value. Accuracy is usually expressed as the percentage recovery of added analyte. Acceptable average analyte recovery for determinative procedures is 80-110% for a tolerance of > 100 p-g kg and 60-110% is acceptable for a tolerance of < 100 p-g kg Correction factors are not allowed. Methods utilizing internal standards may have lower analyte absolute recovery values. Internal standard suitability needs to be verified by showing that the extraction efficiencies and response factors of the internal standard are similar to those of the analyte over the entire concentration range. The analyst should be aware that in residue analysis the recovery of the fortified marker residue from the control matrix might not be similar to the recovery from an incurred marker residue. 

Today, clinical trials must adhere to nationally and internationally agreed codes of good clinical practice, which define ethical and scientific standards. Good clinical trial design and conduct should apply scientific methods. Skilful analysis can never correct for poor design. The purpose of the trial should be defined and specific hypotheses stated in the written study protocol, which will also include details of how the trial will be conducted. Errors in the data have two components, purely random errors and systemic errors or bias, which are not a consequence of chance alone. Randomisation of subjects is important both to avoid observer bias and to prevent or minimise the influence of unknown factors that might influence the results. 

As mentioned earlier, the matrix-related random interferences may not be independent. In this case, simple addition of the components is not correct, because a covariance term should be included. However, we can estimate the combined effect corresponding to the bracket term, which then strictly refers to the CV of the differences (CV b2-rb])- As in the case with constant standard deviations, information on the analytical components is usually available, either from duplicate sets of measurements or from quality control data, and the combined random bias term in the second bracket can then be derived by subtracting the analytical component from CV21. Systematic and random errors can then be determined, and it can be decided whether a new field method can replace an existing one. Figure 14-31 shows an example with proportional random errors around the regression line. 

Systematic errors (bias) represent a constant or multiplicative part of the experimental error. This error cannot be decreased by repetitive measurements. In analytics, the trueness of values, that is, the deviation of the mean from the true value, is related to a systematic error. Appropriate measurements with standards are used to enable recognition of systematic errors in order to correct them at later measurements. 

Precision, by definition, does not include any systematic error or bias, but accuracy, by definition, does. Precision is a measure of the degree to which replicate data and/or measurements conform to each other the degree of agreement among individual test results obtained under prescribed similar conditions. Hence, it is possible that data can be very precise without necessarily being correct or accurate. Precision is commonly expressed inversely by the imprecision of results in terms of their standard deviation or their variance. Precision, by definition, does not include systematic error or bias. 

Affect precision - repeatability or reproducibility Cause replicate results to fall on either side of a mean value Can be estimated using replicate measurements Can be minimized by good technique but not eliminated Caused by both humans and equipment Produce bias - an overall deviation of a result from the true value even when random errors are very small Cause all results to be affected in one sense only - all too high or all too low Cannot be detected simply by using replicate measurements Can be corrected, e.g. by using standard methods and materials Caused by both humans and equipment... 

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