{"id":55,"date":"2024-04-04T00:39:48","date_gmt":"2024-04-03T21:39:48","guid":{"rendered":"https:\/\/sisu.ut.ee\/lcms_method_validation\/92-decision-limit-and-detection-capability\/"},"modified":"2025-01-31T11:11:21","modified_gmt":"2025-01-31T09:11:21","slug":"92-decision-limit-and-detection-capability","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/lcms_method_validation\/92-decision-limit-and-detection-capability\/","title":{"rendered":"9.2. Decision limit and Detection capability"},"content":{"rendered":"<h5 style=\"text-align: center;\"><strong><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div><\/strong>Decision limit (CC<sub>\u03b1<\/sub>) and detection capability (CC<sub>\u03b2<\/sub>)<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23306\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23306<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=posQ05DUCIc&amp;t=1s\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=posQ05DUCIc&amp;t=1s<\/a><\/h5>\n<h5 style=\"text-align: center;\"><\/h5>\n<p>As mentioned in the previous section, LoD by definition may or may\u00a0not take into account both false positive (results where the analyte is declared to be present although actually it is below LoD) and false negative (results where analyte is declared to be below LoD although it is not) errors at the same time.<\/p>\n<p><span style=\"line-height: normal;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">An example is given in Table 1 to better explain the concept of false positive and false negative results on the basis of a widely banned pesticide DDT (dichlorodiphenyltrichloroethane). The concentration of DDT is compared to the capability of the analytical method.<\/span><\/span><\/span><\/p>\n<h4><span style=\"line-height: normal;\"><span lang=\"EN-GB\">Table 1. Explanation of false positive and false negative results.<\/span><\/span><\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1968\" height=\"930\" class=\"alignnone wp-image-432\" style=\"width: 650px; height: 307px;\" title=\"Table1_section_9_2.jpg\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2.jpg\" alt=\"Table1_section_9_2\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2.jpg 1968w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2-300x142.jpg 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2-1024x484.jpg 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2-768x363.jpg 768w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2-1536x726.jpg 1536w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/table1_section_9_2-1920x907.jpg 1920w\" sizes=\"auto, (max-width: 1968px) 100vw, 1968px\"><\/p>\n<p>To account for both of these errors, Currie [ref 14] <span style=\"font-family: Arial,Helvetica,sans-serif;\">suggested t<\/span>o use two different quantities: decision limit (CC<sub>\u03b1<\/sub>) and detection capability (CC<sub>\u03b2<\/sub>). For example, when validating the analysis method for measuring DDT, it was found that CC<sub>\u03b1<\/sub> was at 0.005 \u03bcg\/L. Therefore, if a higher result than 0.005 \u03bcg\/L is received from the analysis there is\u00a0\u2264 5% probability that the result is just noise (noise can be defined as signal received when no analyte is present or the analyte concenrtation is so low that the analysis method cannot detect it). If we are relatively certain that the results are not simply noise, then we can say that we have detected DDT. In other words, CC<sub>\u03b1<\/sub> can be considered as the concentration at which we can decide that we are not measuring noise but we are receiving a signal from the analyte.<\/p>\n<p>CC<sub>\u03b1<\/sub> is defined as the concentration level, as determined by the method, at which there is probability \u03b1 (usually defined as 0.05 or 5%) that a blank sample will give a signal at this level or higher. CC<sub>\u03b2<\/sub> is defined as the concentration level of the analyte in sample at which there is a probability \u03b2 (again usually defined as 0.05 or 5%) that the method will give a result lower than CC<sub>\u03b1<\/sub>, meaning that the analyte will be declared as undetected (although the analyte content in the sample is in fact higher than CC<sub>\u03b1,\u00a0<\/sub>see Figure 1 for illustration of CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub> definitions).<\/p>\n<p>For example, in the example of DDT analysis method, CC<sub>\u03b1<\/sub> was found to be Y. This means that if a single measurement of a sample is above Y then the probability that the measurement is just noise, is \u2264 5%. Because of random variability of results, even if DDT is present in the sample at a concentration above CC<sub>\u03b1<\/sub>, there is the possibility that we receive a result that is below CC<sub>\u03b1<\/sub> and therefore interpret the result as negative (see the red curve in Figure 1). Therefore, we need to find CC<sub>\u03b2<\/sub> where the probability for this kind of false negative probability is small, in our example \u2264 5%.<\/p>\n<p>By these definitions, if the analyte is present at concentration of CC<sub>\u03b2<\/sub> (or above) it can be said with good certainty that the measurements are not simply noise (which otherwise would lead to false positive results) and that the analysis method can measure this concentration with only small probability of giving results below CC<sub>\u03b1<\/sub> (i.e. false negative results).<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"478\" height=\"429\" class=\"alignnone wp-image-431\" title=\"cca_ccb_joonis.jpg\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/cca_ccb_joonis.jpg\" alt=\"cca_ccb_joonis.jpg\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/cca_ccb_joonis.jpg 478w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/cca_ccb_joonis-300x269.jpg 300w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\"><\/p>\n<h4 style=\"text-align: center;\">Figure 1.\u00a0Relation between permitted limit, CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub><\/h4>\n<p>It must be noted that in some cases the name \u201climit of detection\u201d is used in place of CC<sub>\u03b2<\/sub>. When dealing with LoD, the precise definition under question must be clarified.\u00a0Although in most cases LoD can be considered equal to CC<sub>\u03b2<\/sub>\u00a0this is not always the case. The approaches to calculate LoD make many assumptions about the properties of the system \u2013 e.g. linearity and scedasticity. The approaches given by standards to estimate CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0are usually provide more complex and\u00a0do not make the same assumptions. Therefore,\u00a0in principle LoD and CC<sub>\u03b2<\/sub>\u00a0could be considered equal, but their values cannot always be compared in a meaningful way.<\/p>\n<p>If the\u00a0MRL value has been set for the analyte in the particular sample, then the following should be considered: (a) the MRL value should be above the CC<sub>\u03b2<\/sub>\u00a0or LoD value (see <a href=\"https:\/\/sisu.ut.ee\/lcms_method_validation\/91-definitions-and-important-aspects\" target=\"_blank\" rel=\"noopener\">Section 9.1<\/a>), and (b) the analyte\u00a0concentration should be estimated where\u00a0it can be said with known confidence (taking into account both false positive and false negative probabilities) that the concentration of the analyte is above the\u00a0MRL. For the second part, CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub> must be evaluated not for 0 concentration but at the MRL level (see Figure 1 where C = 0 or <strong>at MRL<\/strong>). It should be noted that for example Council Directive\u00a096\/23\/EC has defined CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0so that if a MRL is set, these values are not used to estimate the minimum amount that the method can detect, but for estimating when the result is over or under the MRL value. The same approaches to estimate CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0can\u00a0be used.<\/p>\n<p>In Figure 1, a normal distribution is used only to clearly and simply explain the concept of CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub>. It has been shown that often results from blank and very low concentration samples do not have a normal distribution. Moreover, it is more correct to use a t-distribution rather than a normal distribution in case if only a small number of replicate measurements are made. In addition, it should be noted that the data is heteroscedastic (width of the distribution is wider at higher concentration) in Figure 1 and homoscedastic (width of the distribution is same at both concentrations) in the video \u201cDecision limit (CC<sub>\u03b1<\/sub>) and Detection capability (CC<sub>\u03b2<\/sub>)\u201d.<\/p>\n<h5 style=\"text-align: center;\"><div class=\"ratio ratio-16x9 mb-3\"><div class=\"video-placeholder-wrapper video-placeholder-wrapper--16x9\">\n\t\t\t    <div class=\"video-placeholder d-flex justify-content-center align-items-center\">\n\t\t\t        <div class=\"overlay text-white p-2 w-100 text-center d-block justify-content-center align-items-center\">\n\t\t\t            <div>To view third-party content, please accept cookies.<\/div>\n\t\t\t            <button class=\"btn btn-secondary btn-sm mt-1 consent-change\">Change consent<\/button>\n\t\t\t        <\/div>\n\t\t\t    <\/div>\n\t\t\t<\/div>\n<\/div>Interpreting results with CC\u03b1\u00a0and CC\u03b2<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23349\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23349<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DP1wAdmXkIg\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=DP1wAdmXkIg<\/a><\/h5>\n<p>With CC<sub>\u03b1<\/sub> and CC<sub>\u03b2,\u00a0<\/sub>the results must be interpreted in the following way: (a) in case the result is below CC<sub>\u03b1<\/sub>, it must be reported that the analyte concentration in the sample is below CC<sub>\u03b2<\/sub> (this is so because it is not known whether our result is falsely negative or truly under CC<sub>\u03b1<\/sub>), (b) in case the result is over CC<sub>\u03b1<\/sub>, but below CC<sub>\u03b2<\/sub>, the sample can be said to contain the analyte with good probability, and (c) in case the value is over CC<sub>\u03b2<\/sub>, then the same statement can be made as in the point (b).<\/p>\n<p>However, only the CC<sub>\u03b2<\/sub> value can be used for the characterization of the method as at CC<sub>\u03b2<\/sub> we take into account the possibility of both false positive and false negative error.<\/p>\n<h5 style=\"text-align: center;\"><\/h5>\n","protected":false},"excerpt":{"rendered":"<p>To view third-party content, please accept cookies. Change consent Decision limit (CC\u03b1) and detection capability (CC\u03b2) http:\/\/www.uttv.ee\/naita?id=23306 https:\/\/www.youtube.com\/watch?v=posQ05DUCIc&amp;t=1s As mentioned in the previous section, LoD by definition may or may\u00a0not take into account both false positive (results where the analyte &#8230;<\/p>\n","protected":false},"author":60,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-55","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/55","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/users\/60"}],"replies":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/comments?post=55"}],"version-history":[{"count":3,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/55\/revisions"}],"predecessor-version":[{"id":1513,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/55\/revisions\/1513"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/media?parent=55"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}