{"id":39,"date":"2024-04-04T00:39:47","date_gmt":"2024-04-03T21:39:47","guid":{"rendered":"https:\/\/sisu.ut.ee\/lcms_method_validation\/51-bias-and-its-constituents\/"},"modified":"2024-04-04T00:41:46","modified_gmt":"2024-04-03T21:41:46","slug":"51-bias-and-its-constituents","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/lcms_method_validation\/51-bias-and-its-constituents\/","title":{"rendered":"5.1 Bias and its constituents"},"content":{"rendered":"

\r\n\tDifferent guidance materials use different terms for expressing trueness (Table 1). In this course we use the term trueness with the meaning given in the International Vocabulary of Metrology (VIM) [ref 6] \u2013 closeness of agreement between the average of an infinite number of replicate measured quantity values and a reference quantity value. The term accuracy has a different meaning and will be discussed more thoroughly in section 7<\/a>.\r\n<\/p>\r\n\r\n

\r\n\tTable 1. Terms used for trueness in different guidance materials.\r\n<\/h4>\r\n\r\n\r\n\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t
\r\n\t\t\t\t

\r\n\t\t\t\t\tOrganization<\/strong>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tTerm<\/strong>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tMeaning according to VIM<\/strong>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tEurachem, AOAC, ISO\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tAccuracy\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tTrueness\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tAccuracy\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tTrueness\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tICH, FDA, EMA\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tAccuracy\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tTrueness\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tIUPAC, NordVal\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tTrueness\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tTrueness\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n

\r\n\t\u00a0\r\n<\/p>\r\n\r\n

\r\n\tAs a rule, trueness of a method is quantitatively expressed as bias or relative bias. Bias is defined as the estimate of the systematic error. In practice bias is usually determined as the difference between the mean obtained from a large number of replicate measurements with a sample having a reference value. It can be expressed as an absolute bias (Eq. 1 below), i.e. simply the difference, or as a\u00a0relative bias (Eq 2 below), i.e. as a difference divided by the reference value.\u00a0The main causes of bias in LC-MS results can be termed as bias constituents and are the following:
1. Bias caused by the analyte loss during sample preparation, expressed quantitatively by recovery (R<\/em>);
2. Bias due to the limited stability of the analyte\u00a0(see in Stability section<\/a>)\u00a0in the sample solution (B<\/em>stab<\/sub>);
3. Bias due to the ionization suppression\/enhancement, i.e. matrix effect\u00a0(ME<\/em>ionization<\/sub>);
4. Bias due to other possible effects (B<\/em>other<\/sub>), e.g. purity of the standard substance, calibration bias of volumetric ware.\r\n<\/p>\r\n\r\n

\r\n\tTable 2 presents the relations between these terms.\r\n<\/p>\r\n\r\n

\r\n\tTable 2.\u00a0Bias and related terms together with the equations for calculating them.\r\n<\/h4>\r\n\r\n\r\n\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t
\r\n\t\t\t\t

\r\n\t\t\t\t\tExpression<\/strong>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tCalculation\u00a0(1)<\/a><\/strong>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tComments<\/strong>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tBias\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tAbsolute bias:<\/em>\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\"eq1\"(Eq 1)\r\n\t\t\t\t<\/h6>\r\n\r\n\t\t\t\t
\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/h6>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0<\/em>\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0<\/em>\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0<\/em>\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tRelative bias<\/em> (2)<\/a>\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\"eq2\"\u00a0(Eq 2)\u00a0(3)<\/a>\r\n\t\t\t\t<\/h6>\r\n\r\n\t\t\t\t
\r\n\t\t\t\t\t\"eq3\"\u00a0(Eq 3)\u00a0(4)<\/a>\r\n\t\t\t\t<\/h6>\r\n\t\t\t<\/td>\r\n\t\t\t
\r\n\t\t\t\t

\r\n\t\t\t\t\tBias takes into account the effects influencing the result\u00a0that are systematic over a long term, (5)<\/a>\u00a0occurring at any stage of the analytical process.\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tBias can be expressed as an absolute or relative bias.\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tAbsolute bias is useful when it is either constant over the used concentration range or if it is evaluated separately at different concentrations.\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tRelative bias is useful when the absolute bias is proportional to the analyte concentration and it is desired that the same bias estimate could be used at different concentration levels.\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tProcess efficiency (2)<\/a>, PE<\/em>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t
\r\n\t\t\t\t\t\u00a0<\/em>\"eq4\"\u00a0<\/em>(Eq 4)\u00a0(6)<\/a>\r\n\t\t\t\t<\/h6>\r\n\r\n\t\t\t\t
\r\n\t\t\t\t\t\"eq5\"(Eq 5)\r\n\t\t\t\t<\/h6>\r\n\t\t\t<\/td>\r\n\t\t\t
\r\n\t\t\t\t

\r\n\t\t\t\t\tProcess efficiency (PE<\/em>) refers to the joint effect of possible losses during sample preparation and ionization suppression\/enhancement in the ion source.\u00a0PE<\/em>\u00a0is a useful parameter for characterizing the analysis method when it is either required for the characterization of the method or when it is intended to carry out correction with\u00a0PE<\/em> (more generally: bias correction).\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tRecovery (2)<\/a>,\u00a0R<\/em>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t
\r\n\t\t\t\t\t\"eq6\"\u00a0(Eq 6)\r\n\t\t\t\t<\/h6>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tRecovery\u00a0(7)<\/a>\u00a0expresses the efficiency of the sample preparation step: the proportion of an analyte obtained from the sample during sample preparation (see also (4)<\/a>).\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tIonization suppression\/enhancement (matrix effect), ME<\/em>ionization\u00a0<\/sub>(2)<\/a>,\u00a0(8)<\/a>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t
\r\n\t\t\t\t\t\"eq7\"\u00a0(Eq 7)\r\n\t\t\t\t<\/h6>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tIn LC-MS the term matrix effect refers to the suppression (usually) or enhancement (rarely) (9)<\/a>\u00a0of analyte ionization in the ion source\u00a0by co-eluting compounds originating from the sample matrix.\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tm<\/em>analyte detected<\/sub> \u2013 analyte amount detected in the sample\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\tm<\/em>analyte extracted<\/sub> \u2013 analyte amount actually extracted from the sample.\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tStability, B<\/em>stab<\/sub>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tSee section 8<\/a> for discussion\r\n\t\t\t\t<\/p>\r\n\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tThis bias constituent takes into account losses due to the analyte decomposition. Depending at which stage of the sample preparation the decomposition occurs, there are different types of stability (see section 8<\/a> below).\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tB<\/em>other<\/sub>\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\t\u00a0\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t\t

\r\n\t\t\t\t

\r\n\t\t\t\t\tThis bias constituent takes into account other bias sources (e.g. calibration of glassware) that are not connected to the above mentioned factors.\r\n\t\t\t\t<\/p>\r\n\t\t\t<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n

\r\n\t(1)\u00a0X<\/em>lab<\/sub>: average of results obtained by the laboratory;\u00a0X<\/em>ref<\/sub>: reference value.\u00a0\r\n<\/p>\r\n\r\n

\r\n\t(2)\u00a0Can be expressed as a simple ratio or as a percentage (in the latter case the ratio is multiplied by 100).\r\n<\/p>\r\n\r\n

\r\n\t(3)\u00a0This bias is expressed as a percentage. Absence of bias corresponds to 0%. Negative bias values indicate negative and positive bias values positive bias.\r\n<\/p>\r\n\r\n

\r\n\t(4)\u00a0This way of expressing relative bias differs from the one in Eq 2. The absence of bias in this case corresponds to 1. Bias values below 1 indicate a negative bias and values above 1 indicate a positive bias. In many areas the ratio X<\/em>lab<\/sub>\/X<\/em>ref<\/sub> is interpreted as recovery, i.e. the four bias components in this equation would combine into recovery. However, in LC-MS it is useful to make a distinction between recovery \u2013 relating specifically to sample preparation \u2013 and other bias components.\r\n<\/p>\r\n\r\n

\r\n\t(5)\u00a0Bias can also be determined as the short-term i.e. within-day bias (see below), but the long-term bias is more useful, e.g. for measurement uncertainty estimation, as is explained in section 7<\/a>.\u00a0\r\n<\/p>\r\n\r\n

\r\n\t(6)\u00a0This equation holds, if B<\/em>stab<\/sub> and B<\/em>other<\/sub> are insignificantly different from 1.\r\n<\/p>\r\n\r\n

\r\n\t(7) In the case of most other analytical techniques recovery would also include the possible matrix effects, so that it would effectively be equal to\u00a0PE<\/em>\u00a0as defined above.\r\n<\/p>\r\n\r\n

\r\n\t(8) There are different ways of expressing the matrix effect. We use the way which is similar to expressing recovery and process efficiency.\r\n<\/p>\r\n\r\n

\r\n\t(9)\u00a0In the case of alleged ionization enhancement it may under closer examination turn out that the reason for the enhanced signal is not the analyte signal enhancement but the interference from some other compound in the matrix, which accidentally gives precursor and product ions with the same m\/z value as the analyte [ref 23] i.e. apparent ionization enhancement may in fact be caused by insufficient selectivity.\r\n<\/p>\r\n\r\n

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