Detection decision

Currie LA (1997) Detection International update, and some emerging dilemmas involving calibration, the blank, and multiple detection decisions. Chemometrics Intell Lab Syst 37 151... 

The basic detection concepts can be presented for the "zerodimensional case where detection decisions and detection limits are established simply from the characteristics of the chemical signal (instrument response), without giving detailed attention to other dimensions such as time, wavelength, analyte concentration, etc. Actually, higher dimensional situations (multiparameter separations or detector responses) reduce to this case either through sequential classification schemes or via algorithms which operate directly on the multidimensional data. 

Space remains for only a brief glance at detection in higher dimensions. The basic concept of hypothesis testing and the central significance of measurement errors and certain model assumptions, however, can be carried over directly from the lower dimensional discussions. In the following text we first examine the nature of dimensionality (and its reduction to a scalar for detection decisions), and then address the critical issue of detection limit validation in complex measurement situations. 

Chemometric quality assurance via laboratory and method intercomparisons of standardized test data sets, finally, is becoming recognized as essential for establishing the validity of detection decisions and estimated detection limits, especially when treating multidimensional data with sophisticated algorithms including several chemical components. 

The limit of detection is the analyte concentration that leads to a correct positive detection decision with sufficiently high probability (1 — jS). The detection decision amounts to comparing the prediction y with the critical level (Lc). This level is estimated in such a way that it allows for a positive detection decision with probability a when, in reality, the analyte is absent. The critical level is only determined by the distribution of the prediction under the null hypothesis (Hq not present). By contrast, the limit of detection is also determined by the distribution of y under the alternative hypothesis (Hp present at certain level). 

One of the most important performance characteristics in residue analysis is certainly the detection capability of a method. Unfortunately, many different definitions with regard to the detection and quantifying capability of an analytical method are found in the literature. Attempts have been made to harmonize the definitions with regard to the limit of detection (LoD) and the limit of quantification (LoQ). For the sake of consistency, here reference is made only to the harmonized definitions of IUPAC and ISO for the detection decision (Lc, critical value), LoD (minimum detectable value) and LoQ (minimum quantifiable value) (45 -47). ISO terminology is given between brackets. 

The assumption of heteroskedasticity is frequently rejected in analytical chemistry. Weighted regression can be used to correct for heteroskedasticity. The equations to calculate the detection decision and LoD in case of weighted linear regression models (WLRM) are given by ... 

The detection decision (xc) is calculated with the following equation ... 

If the alternate hypothesis is accepted at the detection phase, estimation of change by PCD method is initiated by reducing the forgetting factor to a small value at the detection instant. This will cause the filter to converge quickly to the new values of model parameters. Shewhart charts for each model parameter are used for observing the new identified values of the model parameters. At this point the out-of-control decision made at the detection phase can be reassessed. If the identified values of the parameters are inside the range defined by the null hypothesis, then the detection decision can be reversed and the alarm is declared false. 

In evaluating a chemical sensor, most studies determine whether an individual analyte can be detected by a sensor system at a given concentration. The sensor system itself can usually be tuned by changing one or more variables to increase sensitivity at the cost of selectivity. This trade-off is what the ROC curve quantifies. Since the detection is posed as a detect/no detect decision, a curve must be constructed for each specific concentration level of analyte where a detection decision is to be determined. 

The laboratory may often be required to make detection decisions about samples, but when the analyte activity is low enough, the relative uncertainty in the result may make it difficult to distinguish between a small positive activity and zero. The performance characteristic of the measurement process that describes its detection capability is called the minimum detectable value, minimum detectable activity, minimum detectable concentration (MDC), or lower limit of detection (LTD). These terms have been used to denote the theoretical concept of the smallest true value of the analyte in a sample that gives a specified high probability of detection. 

The common approach to detection decisions in radioanalytical chemistry is based on statistical hypothesis testing. In a hypothesis test, one formulates two mutually exclusive hypotheses, called the null hypothesis and the alternative hypothesis, and uses the data to choose between them. The null hypothesis is presumed to be true unless there is strong evidence to the contrary. When such evidence is present, the null hypothesis is rejected and the alternative hypothesis is accepted. 

If one performs the series of blank measurements described above, calculates Lc by Eq. (10.18), and subsequently calculates the blank-corrected activity A for an analyte-free sample, the probability of observing a value of A greater than Lc is approximately equal to a. If one makes the detection decision by comparing A to Lc, the false positive rate should be approximately a. 

In this case one makes the detection decision for a sample by comparing the observed net count rate Rn to the critical net count rate Sc-When Eq. (10.20) is used for the critical value and a = a commonly used approximation formula for the MDA is... 

A common problem in radioanalytical chemistry laboratories, especially those that analyze environmental samples, is the existence of an overwhelming number of samples without detectable radionuclide activity, which can lead analysts and data reviewers to expect such results as a matter of course. Reviewers who expect undetectable results for samples may tend to interpret small positive values as false positives even when they are not. The tendency to let one s preconceptions influence one s judgment in data interpretation must be resisted. Detection decisions and other evaluations of the data should always be based on objective criteria. If the laboratory s objective criteria indicate the presence of an unexpected radionuclide, an investigation may be needed to confirm that the measurement process is performing properly. 

Decision theory operates on the basis of an "objective function" which is in some way optimized through the setting of a decision threshold. A lucid presentation to alternative strategies for formulating detection decisions has been given by Liteanu and Rica (S, p. 192). The essence of the matter is that a threshold value kg for the Likelihood Ratio is derived from a) prior probabilities for the null and alternative hypotheses, b) a cost or... 

Hypothesis testing is applicable to all of the above factors. Detection decisions may be made, for example, using the critical level of Student s-t to test for bias, or the critical level of to test an assumed spectral shape or calibration model or error model. For a given measurement design and assumption test procedure, one can estimate the corresponding detection limit for the alternative hypothesis, e.g., the minimum detectable bias. As with analyte detection, the ability to detect erroneous assumptions rests heavily on the design of the experiment and the study of optimal designs is a field unto Itself. 

Analyte Detection. This is a primary focus for this volume, the specification of critical levels or thresholds for analyte detection decisions, and the design of CMP s to achieve requisite analyte detection limits. The following section includes an historical perspective on the topic. A tutorial is provided in the chapter by Kirchmer (14), where a crucial distinction is noted that is, the detection decision is made in reference to an observed, random experimental outcome (estimated concentration),... 

Table I has been prepared from this perspective. The authors selected are drawn primarily from those who have contributed basic statements on the issue of detection capabilities of chemical measurement processes ["detection limits"], as opposed to simply addressing detection decisions for observed results ["critical levels"]. In fairness to those not listed, it is important to note that a) a selection only, spanning the last several decades has been given, and that b) there also exist many excellent articles (15.16) and books (12.17.18 > which review the topic. It is immediately clear from Table I that the terminology has been wide ranging, even in those cases where the conceptual basis (hypothesis testing) has been Identical. Nomenclature, unlike scientific facts and concepts, can be approached, however, through consensus. The International Union of Pure and Applied Chemistry [lUPAC], which appears twice in Table I, is the international body of chemists charged with this responsibility. At this point it will be helpful to examine the position of lUPAC as well as the contributions of some of the other authors cited in Table I.

On the subject of nomenclature, a word concerning historically used terms for the detection decision point or level Is in order. As stated Immediately above, a number of analysts, following Kaiser, use "Limit of Detection" or "Detection Limit" as both the measure of (true concentration) detection capability and as a statistical critical level or threshold to make detection decisions. Following established practice in Statistics, the term "Critical Level" was recommended in (23 ). "Criterion of Detection" has been employed by Wilson (22) > Liteanu (8), who speaks of the "decision criterion" as a strategy, terms the numerical comparison level the "Decision (or Detection) Threshold."... 

In conclusion, it is urgent that the analytical community adopt a uniform and defensible approach to the concept of detection. Apart from ad hoc or unstated procedures, failure to recognize the error of the second kind [p] -- l.e., failure to distinguish between detection decisions and detection capabilities -- is the most serious conceptual fault, placing false negatives at the level of coin-flipping accuracy. Failure to take into account all major sources of error, especially the nature of the blank, is the most serious measurement fault. A review of some of the more critical assumptions and technical Issues related to valid detection limits follows. 

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