{"id":56,"date":"2024-04-04T00:39:48","date_gmt":"2024-04-03T21:39:48","guid":{"rendered":"https:\/\/sisu.ut.ee\/lcms_method_validation\/93-estimating-lod\/"},"modified":"2024-06-18T07:23:09","modified_gmt":"2024-06-18T04:23:09","slug":"93-estimating-lod","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/lcms_method_validation\/93-estimating-lod\/","title":{"rendered":"9.3. Estimation of LoD"},"content":{"rendered":"<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><\/h5>\n<h5 style=\"text-align: center;\">Different approaches to estimate LoD<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23291\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23291<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=xk2Ou3jaovg\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=xk2Ou3jaovg<\/a><\/h5>\n<h5 style=\"text-align: center;\">\u00a0<\/h5>\n<p>There are a multitude of different approaches that can be used to estimate LoD, and no clear consensus exists on which approach is the best in different situations. The approach that we recommend in this course is discussed below in the video\u00a0\u201cImportant aspects of estimating LoD and CC\u03b1, CC\u03b2\u201d and in the tutorial review [ref 19 and ref 20]. A general overview of approaches from most prominent guidelines\u00a0to estimate LoD\u00a0from most prominent guidelines can be found in Table 1 (NB! For more specific overview of procedures, see the specific guideline!). These approaches can result in widely varying LoD estimates. Different guidelines often suggest different approaches and it is up to the analyst to choose which approach to use.\u00a0 If a specific approach is not demanded by the guideline, this choice must be made based on the necessities and properties of the analytical method.<\/p>\n<p>An Excel sheet with example calculations of LoD with approaches in Table 1 can be found at the end of this chapter.<\/p>\n<h4>Table 1. Different approaches for determining LoD, CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub>.\u00a0<\/h4>\n<table class=\"table table-hover\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td valign=\"top\">\n<p><strong>Group<\/strong><\/p>\n<\/td>\n<td style=\"width: 50px;\" valign=\"top\">\n<p><strong>Reference<\/strong><\/p>\n<\/td>\n<td valign=\"top\">\n<p><strong>What is obtained?<\/strong><\/p>\n<\/td>\n<td valign=\"top\">\n<p><strong>Equation<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>1<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 3,\u00a0 ref 9, ref 12, ref 15]<\/p>\n<\/td>\n<td valign=\"top\">\n<p style=\"text-align: left;\">LoD (considers false positive and negative results \u2013 the probability of false positive and negative values depends on the choice of <em>t<\/em>)<\/p>\n<\/td>\n<td valign=\"top\">\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"141\" height=\"25\" class=\"alignnone wp-image-438\" title=\"9.3_valem_1.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_1.png\" alt=\"9.3_valem_1.png\">(Eq 1)<\/h6>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"23\" height=\"17\" class=\"alignnone wp-image-439\" title=\"9.3_valem_1y.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_1y.png\" alt=\"9.3_valem_1y.png\">is mean value of blank samples or 0; <em>t<\/em> is Student\u2019s Coefficient; S(y) is standard deviation of blank or fortified samples.<\/p>\n<p>Equation gives LoD in intensity scale.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb25127-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb25127-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb25127-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb25127-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb25127-heading\">\n            <div class=\"accordion-body\">\n<p><strong>Description:<\/strong>\u00a0Concentration of fortified samples in LoD range (e.g. lowest level where S\/N &gt; 3) or at maximum residue limit (MRL);<br><em>t<\/em> is taken 3 or 4.65;<br>6 to 10 repeated measurements for blank and fortified samples;<br>all signal intensities and standard deviations have to be over 0;<\/p>\n<p><strong>Assumptions, simplifications:\u00a0<\/strong>Homoscedasticity;\u00a0<br>normal distribution of the replicates;<br>variability of the slope and intercept are not taken into account;\u00a0<br>linearity of the calibration data;<br><em>t<\/em> value is rounded and does not take into account the degrees of freedom;<br>only for single sample measurement results.<\/p>\n<p><strong>Notes:\u00a0<\/strong>Care must be taken when integrating blank samples;<br>Erroneous calibration function\u00a0can lead to negative LoD results;<br>Note that <img loading=\"lazy\" decoding=\"async\" width=\"23\" height=\"17\" class=\"alignnone wp-image-439\" title=\"9.3_valem_1y.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_1y.png\" alt=\"9.3_valem_1y.png\">\u00a0is not necessary (i.e.<img loading=\"lazy\" decoding=\"async\" width=\"23\" height=\"17\" class=\"alignnone wp-image-439\" title=\"9.3_valem_1y.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_1y.png\" alt=\"9.3_valem_1y.png\">is\u00a0equal as 0) if subtraction with intercept (or with<img loading=\"lazy\" decoding=\"async\" width=\"23\" height=\"17\" class=\"alignnone wp-image-439\" title=\"9.3_valem_1y.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_1y.png\" alt=\"9.3_valem_1y.png\">) is done to all measured results before calculations.<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>2<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 16]<\/p>\n<\/td>\n<td valign=\"top\">\n<p style=\"text-align: left;\">LoD essentially equivalent to CC<sub>\u03b1<\/sub> (considers only false positive results)<\/p>\n<\/td>\n<td valign=\"top\">\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"130\" height=\"21\" class=\"alignnone wp-image-433\" title=\"9.3_valem_2.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_2.png\" alt=\"9.3_valem_2.png\">(Eq 2)<\/h6>\n<p>S(x) is the standard deviation or pooled standard deviation of the analyte concentrations from the replicate measurements.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb2512f-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb2512f-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb2512f-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb2512f-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb2512f-heading\">\n            <div class=\"accordion-body\">\n<p><strong>Description:\u00a0<\/strong>A detailed procedure is given to choose fortified sample concentration (incl. estimating an approximate LoD first, measuring only 2 of the needed repeated samples before measuring the rest of the 7 samples);<br><em>t<\/em> is taken depending on the degrees of freedom;<br>Recommended analyte concentration range in fortified samples is 1-5 times LoD.<\/p>\n<p><strong>Assumptions, simplifications:\u00a0<\/strong>Normal distribution of replicates;\u00a0variability of the slope and intercept are not taken into account;<br>linearity of the calibration data;<br>heteroscedasticity is somewhat considered by careful choice of fortification concentration;<br>only for single sample measurement results.<\/p>\n<p><strong>Notes:<\/strong>\u00a0LoD as equivalent to CC<sub>\u03b1<\/sub>\u00a0(false negative results are not accounted for);<br>the background (mean of blank values or the intercept value) is subtracted from all other results.\u00a0<br>It is then suggested to iteratively check the LoD by estimating it again.<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>3<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 3]<\/p>\n<\/td>\n<td valign=\"top\">\n<p style=\"text-align: left;\">LoD (considers false positive and negative results \u2013 the probability of false positive and negative values depends on choice of <em>t<\/em>)<\/p>\n<\/td>\n<td valign=\"top\">\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"48\" class=\"alignnone wp-image-434\" title=\"9.3_valem_3.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_3.png\" alt=\"9.3_valem_3.png\">\u00a0(Eq 3)<\/h6>\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"58\" class=\"alignnone wp-image-435\" title=\"9.3_valem_4.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_4.png\" alt=\"9.3_valem_4.png\">\u00a0 \u00a0\u00a0(Eq 4)<\/h6>\n<p>where\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"44\" height=\"45\" class=\"alignnone wp-image-450\" style=\"background-color: transparent;\" title=\"a_katusega.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/a_katusega.png\" alt=\"a_katusega.png\">is the average intercept;<br><em style=\"background-color: transparent;\">n<\/em> is the number of repeated measurements of the sample;<br><em style=\"background-color: transparent;\">S<\/em>(y) is the standard deviation of the blank or fortified samples;\u00a0<br><em style=\"background-color: transparent;\">n<\/em><sub style=\"background-color: transparent;\">b<\/sub> is the number of repeated measurements of blank samples.<\/p>\n<p>Equations give LoD in intensity scale.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb25133-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb25133-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb25133-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb25133-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb25133-heading\">\n            <div class=\"accordion-body\">\n<p><strong>Description:\u00a0<\/strong>Second equation is used if LoD is estimated from single day measurement results and blank values are used for correction;<br><em>t<\/em> is taken as 3.<\/p>\n<p><strong>Assumptions, simplifications:<\/strong>\u00a0Homoscedasticity; normal distribution of the replicates;linearity of the calibration data; variability of the slope and intercept are not taken into account.<br><em>t<\/em> value is rounded and does not take into account the degrees of freedom.<br>Allows taking into account the averaging of sample measurement results.<\/p>\n<p><strong style=\"line-height: 21px; background-color: transparent;\">Notes:<\/strong>\u00a0Using intermediate\u00a0 precision (not repeatability standard deviation) to estimate LoD is suggested.<br>Monitoring of precision and regular recalculation of LoD values is suggested if LoD is used for making decisions.<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>4<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 17]<\/p>\n<\/td>\n<td valign=\"top\">\n<p style=\"text-align: left;\">LoD (considers false positive and negative results)<\/p>\n<\/td>\n<td valign=\"top\">\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"131\" height=\"44\" class=\"alignnone wp-image-436\" title=\"9.3_valem_5.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_5.png\" alt=\"9.3_valem_5.png\">\u00a0(Eq 5)<\/h6>\n<p><em>b<\/em> is the slope of the calibration function, <em>S<\/em><sub>d<\/sub> can be chosen as a standard deviation of the blank samples, residuals (<em>S<\/em><sub>y.x<\/sub>) or intercept. Instructions to calculate a standard deviation of the residuals and an intercept in Excel can be found in the video \u201cCalculating LoD\u201d below.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb2513c-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb2513c-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb2513c-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb2513c-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb2513c-heading\">\n            <div class=\"accordion-body\">\n<p><strong>Description:<\/strong>\u00a0Regression line must be in the range of LoD.<br>Calibration function\u00a0is used to estimate the slope and the standard deviation of the\u00a0residuals and the\u00a0intercept.<br>Number of repeated measurements is not specified.<\/p>\n<p><strong style=\"line-height: 21px; background-color: transparent;\">Assumptions, simplifications:<\/strong>\u00a0Homoscedasticity;<br>normal distribution of the replicates;<br>linearity of the calibration data; variability of the slope and intercept are not taken into account.<br>If repeated results at each calibration level are averaged and standard deviation of the residuals is used for estimate LoD then the number of repeated measurements must be the same as repeated measurements for each calibration level.<\/p>\n<p><strong>Notes:\u00a0<\/strong>The standard deviation of the intercept underestimates the variance of the\u00a0results at 0 concentration and should not be used.<br>Due to the\u00a0conservative LoD estimates, simple calculation procedure and reasonable workload (<em>S<\/em><sub>d<\/sub>\u00a0is taken from residual values), this is the suggested approach if a rigorous LoD estimate is not needed\u00a0[ref 19, ref 20].<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>5<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 3, ref 15]<\/p>\n<\/td>\n<td valign=\"top\">\n<p style=\"text-align: left;\">LoD (considers false positive and negative results)<\/p>\n<\/td>\n<td valign=\"top\">\n<p>Cut-off approach: number of repeated measurements (usually 10) are made at different concentrations near LoD. The lowest concentration at which all the samples are \u201edetected\u201c is used as the LoD. The detection threshold can be established for example based on the S\/N, visual evaluation or automatic integration for chromatographic methods.<\/p>\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb25140-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb25140-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb25140-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb25140-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb25140-heading\">\n            <div class=\"accordion-body\">\n<p><strong style=\"line-height: 21px; background-color: transparent;\">Assumptions, simplifications:\u00a0<\/strong>Uses robust statistics.<\/p>\n<p>This approach does not assume normal distribution.<br>Visual evaluation of the\u00a0presence of a peak depends on the analyst.<\/p>\n<p><strong style=\"line-height: 21px; background-color: transparent;\">Notes:<\/strong>\u00a0This approach is very work intensive;<br>If repeated estimations of the LoD need to be made,\u00a0this approach is not recommended for LC-MS\/MS methods;<br>It has also been suggested to plot the portion of the positive responses against concentration to find the lowest concentration at which necessary number of samples give the decision \u201edetected\u201c;<br>Each sample should be independent of the others.<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>6<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 5, ref 15]<\/p>\n<\/td>\n<td valign=\"top\">\n<p>CC\u03b1 and CC\u03b2<\/p>\n<\/td>\n<td valign=\"top\">\n<p><strong>CC<sub>\u03b1<\/sub>:\u00a0<\/strong><\/p>\n<p>1.\u00a0Calculated as\u00a0 \u00a0<\/p>\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"43\" class=\"alignnone wp-image-461\" style=\"width: 175px; height: 24px;\" title=\"cca_eq.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/cca_eq.png\" alt=\"cca\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/cca_eq.png 309w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/cca_eq-300x42.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\">\u00a0 (Eq 6)<\/h6>\n<p><span style=\"line-height: normal;\"><i><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">LCL<\/span><\/span><\/i><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\"> is the lowest concentration at which the measuring system has been calibrated (in case <i>MRL<\/i> has been set the concentration must be at <i>MRL<\/i>), <i>t<\/i> is Student\u2019s Coefficient and its value is based on the specific validation experiment, and <i>u<\/i> is combined standard measurement uncertainty at <i>LCL<\/i> (or <i>MRL<\/i>). NB! If Gaussian distribution (i.e. <i>n<\/i> = \u221e; one-sided) is taken as basis then <i>t<\/i> can be taken as 2.33 (or 1.64 if the substance has a set <i>MRL<\/i>).<\/span><\/span><\/span><\/p>\n<p style=\"margin-bottom: 7.5pt; text-align: justify;\"><span style=\"line-height: normal;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">2. Blank matrices are analyzed to estimate the noise in the analyte time window. The level at which S\/N &gt; 3 can be calculated and this level is stated as CC<\/span><\/span><sub><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">\u03b1<\/span><\/span><\/sub><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">. It is stated in 2021\/808 that this approach can only be used until 1 January 2026 \u2013 if a method is validated after this date, then using this approach is not acceptable.<\/span><\/span><\/span><\/p>\n<p>\u00a0<\/p>\n<p><strong>CC<sub>\u03b2<\/sub>:\u00a0<\/strong><\/p>\n<p>1. Calculated as<\/p>\n<h6>\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"46\" class=\"alignnone wp-image-462\" style=\"width: 175px; height: 26px;\" title=\"ccb_eq.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/ccb_eq.png\" alt=\"ccb\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/ccb_eq.png 309w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/ccb_eq-300x45.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\">\u00a0(Eq 7)<\/h6>\n<p style=\"margin-bottom: 7.5pt; text-align: justify;\"><span style=\"line-height: normal;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">In this equation <i>u<\/i> is combined standard measurement uncertainty at or above<i> CC<sub>\u03b1<\/sub><\/i>. NB! In this equation if Gaussian distribution (i.e. <i>n<\/i> = \u221e; one-sided) is taken as basis then <i>t<\/i> can be taken as 1.64 whether the substance has a set <i>MRL<\/i> or not.<\/span><\/span><\/span><\/p>\n<p style=\"margin-bottom: 7.5pt; text-align: justify;\"><span style=\"line-height: normal;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">2. Lowest concentration level is found where \u2264 5% of samples are compliant. This concentration is taken as CC<\/span><\/span><sub><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">\u03b2<\/span><\/span><\/sub><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">. For this, at least 20 samples at each concentration are necessary. If MRL has not been set for the analyte, the samples are considered compliant if the analysis result is below CC<sub>\u03b1<\/sub>. If MRL has been set, the sample is considered compliant if the result is below MRL.<\/span><\/span><\/span><\/p>\n<p style=\"margin-bottom: 7.5pt; text-align: justify;\"><span style=\"line-height: normal;\"><span lang=\"EN-GB\"><span style=\"color: #2f2f2f;\">Equations give LoD in intensity scale.<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb25144-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb25144-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb25144-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb25144-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb25144-heading\">\n            <div class=\"accordion-body\">\n<p><strong>Description:<\/strong>\u00a0Some simple approaches suggested to estimate CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>;<br>Similarly CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0estimation approaches are suggested in case a\u00a0MRL is set;<br>After estimating the intensity value corresponding to CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>,\u00a0the calibration function should be used to convert them to the concentration scale;<br>Approach 2 for estimating the CC<sub>\u03b1<\/sub>\u00a0and approach 3 for\u00a0estimating CC<sub>\u03b2<\/sub>\u00a0demand at least 20 replicates (at each level for CC<sub>\u03b2<\/sub>).<\/p>\n<p><strong style=\"line-height: 21px; background-color: transparent;\">Assumptions, simplifications:<\/strong>\u00a0<br>Linearity of the\u00a0calibration data; variability of the\u00a0slope and intercept are not taken into account.<br>Possible heteroscedasticity is considered to some extent: CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0are not found using the same variance.<br>In these approaches the \u03b1 value is 1 %\u00a0if MRL has not been set for the analyte and 5 % if MRL has been set for the analyte, and the \u03b2 value is 5 %.<br>The coefficients in equations do not take into account the degrees of freedom.<\/p>\n<p><strong>Notes:<\/strong>\u00a0CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0are found for minimum required performance level or MRL.<br>Identification requirements have to be followed (only after identification of the analyte can the sample be used for CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0evaluation).<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\">\n<p>7<\/p>\n<\/td>\n<td valign=\"top\">\n<p>[ref 18]<\/p>\n<\/td>\n<td valign=\"top\">\n<p>CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub><\/p>\n<\/td>\n<td valign=\"top\">\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"225\" height=\"49\" class=\"alignnone wp-image-448\" title=\"9.3_valem_9.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_9.png\" alt=\"9.3_valem_9.png\">\u00a0(Eq 8)<\/h6>\n<h6><img loading=\"lazy\" decoding=\"async\" width=\"211\" height=\"55\" class=\"alignnone wp-image-443\" title=\"9.3_valem_10.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_10.png\" alt=\"9.3_valem_10.png\">\u00a0(Eq 9)<\/h6>\n<h6>\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"146\" height=\"57\" class=\"alignnone wp-image-460\" title=\"9.3_eq11.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_eq11.png\" alt=\"9.3_eq11\">(Eq 10)<\/h6>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"20\" class=\"alignnone wp-image-445\" title=\"9.3_valem_10b.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_10b.png\" alt=\"9.3_valem_10b.png\">\u00a0is the estimated slope, <img loading=\"lazy\" decoding=\"async\" width=\"19\" height=\"20\" class=\"alignnone wp-image-446\" title=\"9.3_valem_10sigma.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_10sigma.png\" alt=\"9.3_valem_10sigma.png\">\u00a0is the estimated residual standard deviation, <em>t<\/em><sub>0.95<\/sub> is the 95% one-sided quantile of <em>t<\/em>-distribution (where <em>\u03bd<\/em> = <em>I<\/em>*<em>J<\/em> \u2013 2),<em> \u03b4<\/em> is non-centrality parameter of the non-central <em>t<\/em>-distribution (similar to <em>t<\/em><sub>0.95<\/sub>), <em>K<\/em> is the number of repeated preparations of the (unknown) sample, <em>I<\/em> is the number of calibration levels, <em>J<\/em> is the number of separate sample preparations at each concentration level, <img loading=\"lazy\" decoding=\"async\" width=\"19\" height=\"15\" class=\"alignnone wp-image-447\" title=\"9.3_valem_11x.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/9.3_valem_11x.png\" alt=\"9.3_valem_11x.png\">\u00a0is the mean value of the concentration levels, <em>x<\/em><sub>i<\/sub> is the concentration of ith calibration level.<\/p>\n<p>These equations are for homoscedastic data, for calculations in case of heteroscedastic data see [ref 18].<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"4\" valign=\"top\">\n<p><\/p><div class=\"accordion mb-3\">\n        <div class=\"accordion-item accordion-item--white\">\n        <h2 class=\"accordion-header\" id=\"accordion-69e1e2fb2514a-heading\">\n            <button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-69e1e2fb2514a-collapse\" aria-expanded=\"true\" aria-controls=\"accordion-69e1e2fb2514a-collapse\">Read more:<\/button>\n        <\/h2>\n        <div id=\"accordion-69e1e2fb2514a-collapse\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-69e1e2fb2514a-heading\">\n            <div class=\"accordion-body\">\n<p><strong>Description:<\/strong>\u00a0Given equations are for homoscedastic data;<br>iterative approach to estimate CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>, suggested for heteroscedastic data, is also given in the guideline;<br>Requirements of the approaches:<\/p>\n<ol>\n<li><em>K<\/em> should equal <em>J<\/em><\/li>\n<li><em>I<\/em> should be at least 3 (5 is recommended)<\/li>\n<li><em>J<\/em> should be at least 2<\/li>\n<li>Number of measurements per sample (<em>L<\/em>) should be at least 2 and identical for all samples.<\/li>\n<\/ol>\n<p>The blank measurements are required to also be included in the calibration points.<br>\u00a0<\/p>\n<p><strong>Assumptions, simplifications:<\/strong>\u00a0Normal distribution of the replicates;<br>linearity of the calibration data;<br>It is suggested to estimate whether the data are heteroscedastic based on prior knowledge and visual evaluation of the data;<br>In heteroscedastic approach standard deviation of results is assumed to increase linearly with concentration<\/p>\n<p><strong>Notes:<\/strong>\u00a0In this guideline the concentration scale is called the net state variable and the intensity scale is called the response variable.<br>Notice that 2 measurements are recommended for each preparation and the mean of these measurements is then used in the following calculations.<\/p><\/div>\n        <\/div>\n        <\/div>\n    <\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h5>\u00a0<\/h5>\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><\/h5>\n<h5 style=\"text-align: center;\">Calculating CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23348\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23348<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=BQ_dOEMDoDs\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=BQ_dOEMDoDs<\/a><\/h5>\n<h5 style=\"text-align: center;\">\u00a0<\/h5>\n<h2>Estimating CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub><\/h2>\n<p style=\"text-align: justify;\">The approaches that are usually suggested to estimate CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub>\u00a0are more complex than the approaches suggested for LoD. This is so because their definition is statistically more rigorous (demanding a known probability level of false positive and negative results) but the results are also more reliable. Some approaches to estimate CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0suggested in the guidelines and articles can be found in\u00a0Table 1.<\/p>\n<p style=\"text-align: justify;\">The CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0calculations [ref 18] take into account the standard deviation of the used linear regression line parameters (slope and intercept). This variance is propagated into the concentration values that are calculated by using these parameters. As CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0are used in the concentration scale (similarly to LoD) the variance of the slope and intercept must be taken into account when estimating them.<\/p>\n<p style=\"text-align: justify;\">Another property that must be considered is homo- and heteroscedasticity. Homoscedasticity means that the variance of signal is constant in case the concentration changes and heteroscedasticity therefore means that the variance changes with the concentration (see example in Figure 1). Analytical methods are often heteroscedastic \u2013 as the concentration\u00a0increases, the standard deviation of the measurements also increases. If it is shown that the collected calibration data collected is heteroscedastic then, weighted linear regression (WLS) should be used to take the variance of the slope\u00a0and intercept more accurately into account. A simplified approach that usually works sufficiently well is presented below.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" width=\"2386\" height=\"1090\" class=\"alignnone wp-image-452\" style=\"width: 800px; height: 365px;\" title=\"Figure1_section_9_3.jpg\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3.jpg\" alt=\"Figure1_section_9_3\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3.jpg 2386w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3-300x137.jpg 300w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3-1024x468.jpg 1024w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3-768x351.jpg 768w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3-1536x702.jpg 1536w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3-2048x936.jpg 2048w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/fig1_section_9_3-1920x877.jpg 1920w\" sizes=\"auto, (max-width: 2386px) 100vw, 2386px\"><\/p>\n<h4 style=\"text-align: center;\">Figure 1. Data in Plot A are homoscedastic and data in Plot B are heteroscedastic. In plot A as the concentration increases the variability of results in intensity scale does not increase. However, in Plot B the variability of intensity values increases as the concentration increases.<\/h4>\n<p style=\"text-align: justify;\">With WLS the propagated errors of the slope and intercept to the concentration value significantly decrease at lower concentration levels. Therefore, the CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0values are also significantly influenced. Using WLS can be complex and a possibility to avoid this is to select a narrow concentration range at lower concentrations from the calibration data that can be shown to be reasonably homoscedastic.\u00a0These data can then be used to estimate the slope and the intercept with ordinary linear regression (OLS) which assumes that the data are homoscedastic. As a result calculating the CC<sub>\u03b1<\/sub> and CC<sub>\u03b2<\/sub> estimates also becomes simpler.<\/p>\n<p>\u00a0<\/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><\/h5>\n<h5 style=\"text-align: center;\">Important aspects of estimating LoD and CC\u03b1, CC\u03b2<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"http:\/\/www.uttv.ee\/naita?id=23350\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=23350<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=9GFMa0AYkdA\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=9GFMa0AYkdA<\/a><\/h5>\n<h5 style=\"text-align: center;\">\u00a0<\/h5>\n<p style=\"text-align: justify;\">It should be considered how important the LoD value for a given analytical method is. Based on this knowledge it can be chosen whether a simple approach to estimate a LoD is enough or a more complex approach that makes less assumptions (e.g. about homoscedasticity) and therefore gives more accurate results should be used. The important assumptions made by different approaches are summarized in Table 1. Further details about how to evaluate whether these assumptions can be made is discussed in the following references [ref 19, ref 20]. If the analyte concentration will never come close to a LoD value then LoD does not have to be estimated at all. However, often LoD is still estimated in these cases just for proving that the samples are significantly above the LoD of the method. For example, when measuring calcium in milk by complexometric titration,\u00a0we do not have to worry that in some samples the concentration of calcium might be so low that it would be below a LoD for a reasonable titration procedure. However, if the LoD estimate is an important parameter used to interpret the results of an analysis, more complex and accurate approaches must be used to estimate LoD. For example, when analyzing blood samples of athletes for doping,\u00a0the method must\u00a0interpret the results correctly even if only very small amounts of the analyte is detected. Therefore, CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>\u00a0values estimated with complex approaches that make less assumptions (e.g. ISO [ref 18]) must be used.<\/p>\n<p style=\"text-align: justify;\">In some cases the analytical method can have properties that do not allow the use of some LoD estimation approaches. For example, it can be difficult to estimate the standard deviation of the blank for LC-MS\/MS methods as the noise can be zero due to the signal processing. As the blank values all give intensity of 0, the LoD value cannot be calculated from them but the standard deviation at 0 can be still estimated by other approaches: from the standard deviation of the\u00a0intercept value or from the standard deviation of the residuals. A more thorough discussion about the problems of processing chromatograms of samples at low concentrations can be found in the following references [ref 19, ref 20]. In conclusion, in general the analyst must understand which approaches cannot be used for a given analytical method.<\/p>\n<p style=\"text-align: justify;\">It should always be kept in mind that LoD is an estimated value and never represents the true LoD as it is calculated from the\u00a0parameters that deviate randomly from their true value between measurements. Moreover, the true value around which the results deviates can change randomly between days. For example,\u00a0the slope of the LC-MS\/MS changes significantly between days \u2013 this means that the true intensity value given by a concentration changes between days. For this reason, the within-day standard deviation is lower than the standard deviation of results collected on different days (see\u00a0<a href=\"https:\/\/sisu.ut.ee\/lcms_method_validation\/41-precision-trueness-accuracy\" target=\"_blank\" rel=\"noopener\">section 4.1<\/a>). Therefore, LoD also changes between days. To take this fact into account, the LoD should be estimated over a long period of time (e.g. a month) and the median LoD value can then be used [ref 18]. If it can be seen that the LoD estimate changes significantly between days (meaning the variation of LoD value within a day is significantly smaller than between days) and the estimate is important for the correct interpretation of the\u00a0results on that day, then the LoD should be estimated on that day and that value should be used for the interpretation. However, it can also be noted here that if the LoD is used only for simple characterization of the method and not used further (see above), then the LoD does not have to be estimated on multiple days. It must also be noted that the previous discussion also applies for CC<sub>\u03b1<\/sub>\u00a0and CC<sub>\u03b2<\/sub>.<\/p>\n<p style=\"text-align: justify;\">As the different approaches can give differently biased values, it should be always stated which approach is used to evaluate the LoD. If different approaches are used (to characterize the lab or the new method), then the comparison should be made with caution.<\/p>\n<p style=\"text-align: justify;\">A different concept for estimating LoD is by using the signal-to-noise ratio (S\/N). This approach is mostly used in chromatographic methods. Modern chromatography programs determine this value automatically. The signal value for this is found from the height of the peak and noise values are found from either the standard deviation of the noise or from so called peak-to-peak value (meaning the difference between the highest and lowest points in the noise). From this it can be seen that S\/N can be found for only one measurement of a sample. A single measurement however does not take into account the variability between measurements and therefore the LoD should not be evaluated from this result. A scheme has been suggested by Eurachem where 10 samples are measured on different concentration levels and the lowest concentration where all 10 are detected is taken as the LoD.\u00a0 Here the decision that an analyte has been detected can be made from the fact that the S\/N is equal to or over 3. However, this means that many measurements have to be made to estimate the LoD and due to the S\/N being conceptually different from other approaches, it will be difficult to compare the LoD estimates found with other approaches.<\/p>\n<h5 style=\"text-align: center;\">\u00a0<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><\/h5>\n<h5 style=\"text-align: center;\">Calculating LoD\u00a0<\/h5>\n<h5 style=\"text-align: center;\"><a href=\"\/\/www.uttv.ee\/naita?id=24440\" target=\"_blank\" rel=\"noopener\">http:\/\/www.uttv.ee\/naita?id=24440<\/a><\/h5>\n<h5 style=\"text-align: center;\"><a href=\"https:\/\/www.youtube.com\/watch?v=u7LCGkFuUFE\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=u7LCGkFuUFE<\/a><\/h5>\n<p>In case you have trouble with LINESt function in excel, we recommend you to review the following <a title=\"\" href=\"https:\/\/www.youtube.com\/watch?v=6wbcPbYbq6M&amp;ab_channel=JaredSpencer\" target=\"_blank\" rel=\"noopener\" data-url=\"https:\/\/www.youtube.com\/watch?v=6wbcPbYbq6M&amp;ab_channel=JaredSpencer\">video<\/a>.<\/p>\n<p>\u00a0<\/p>\n\n\n<div class=\"wp-block-group attached-files-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-0c0ffdf0-9bf5-43bd-a5c9-3e06469cf7ab\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_calculation_approaches_example.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_calculation_approaches_example.xlsx<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-15c432dc-3b4b-4482-a42a-9789e903807a\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_video_excel_solved.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_video_excel_solved.xlsx<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-b1f95f3c-aa8f-488d-a094-30c46736b45d\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_video_excel_unsolved.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_video_excel_unsolved.xlsx<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-e96ecfc5-b70a-47d2-99cb-a788bf7a208b\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_calculation_approaches_example.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_calculation_approaches_example.xlsx<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-7599cc95-8eea-4fa3-b213-a19082c9199a\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_video_excel_unsolved.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_video_excel_unsolved.xlsx<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-f1a91f74-9af1-4ff5-902a-bc8d7a699ffd\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_calculation_approaches_example.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_calculation_approaches_example.xlsx<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-f90ac933-e2db-49bd-bb55-4314cbdbc964\" href=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/130\/lod_video_excel_unsolved.xlsx\" target=\"_blank\" rel=\"noreferrer noopener\">lod_video_excel_unsolved.xlsx<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>To view third-party content, please accept cookies. Change consent Different approaches to estimate LoD http:\/\/www.uttv.ee\/naita?id=23291 https:\/\/www.youtube.com\/watch?v=xk2Ou3jaovg \u00a0 There are a multitude of different approaches that can be used to estimate LoD, and no clear consensus exists on which approach is &#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-56","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/56","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=56"}],"version-history":[{"count":3,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/56\/revisions"}],"predecessor-version":[{"id":1373,"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/pages\/56\/revisions\/1373"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/lcms_method_validation\/wp-json\/wp\/v2\/media?parent=56"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}