Statistical methods detection limit

The method detection limit is, in reality, a statistical concept that is applicable only in trace analysis of certain types of substances, such as organic pollutants by gas chromatographic methods. The method detection limit measures the minimum detection limit of the method and involves all analytical steps, including sample extraction, concentration, and determination by an analytical instrument. Unlike the instrument detection limit, the method detection limit is not confined only to the detection limit of the instrument. 

The concentration of analytes that can be measured in various materials has been decreasing over the years as sensitivity and detection limits of analytical techniques have improved. The method detection limit (MDL) is the order of magnitude of the smallest quantity or concentration of substance which can be detected in principle the limit of detection (LOD), on the contrary, is a precisely calculable statistical value for a particular, defined analytical procedure. The instrument detection limit (IDL) is the smallest signal above background noise that an instrument can detect reliably. It is expressed either as an absolute limit (in units of mass, eg, ng), or as a relative limit (in terms of concentration, eg, g mL 1). 

Limit of Detection fLODl. "The limit of detection (1X)D) is defined as the lowest concentration level that can be determined to be statistically different from a blank. The concept is reviewed in [ref. 38) together with the statistical basis for its evaluation. Additional concepts include method detection limit (MDL), which refers to the lowest concentration of analyte that a method can detect reliably in either a sample or blank, and the Instrument detection limit (IDL), which refers to the smallest signal above background noise that an Instrument can detect reliably. Sometimes, the IDL and LOD are operationally the same. In practice, an indication of whether an analyte is detected by an Instrument is sometimes based on the extent of which the analyte signal exceeds peak-to-peak noise" (16). 

The process of statistical inference requires us to select an hypothesis (fancy VK>rd for assumption) about the result, and then prove that this hypothesis was incorrect. In the case of Method Detection Limit, we assume that the result belongs to a distribution whose mean is centered on "zero". Based on a one-tailed test, if the analytical result is far enough away from zero we then conclude that such a result must come from some other distribution, in which case there is some likelihood that the sample contains the target analyte. MDL is conventionally set at 3 SD. 

REM IT ALSO FINDS DETECTION LIMITS USING CONCEPTS FROM Hubaux and Vos, Analytical Chemistry, 1970, 42(8), 849-855 and from Koehn and Zimmerman, "Method Detection Limits, or How Low Can You Really Go Estimation of Analytical Method Reporting Limits by Statistical Procedures", paper presented at the EPA Conference on Analysis of Pollutants in the Environment Norfolk, VA May 13-14, 1987. 

Methods for determining the LOD that are based on the analysis of a field blank that does not contain the analyte of interest are problematic in many real-world applications because either such samples do not exist, or would be impossibly difficult to create. As such a circumstance is frequently encountered in environmental analysis, the USEPA adopted a detection limit procedure, termed the method detection limit (MDL), which focuses on an operational definition of detection limit. Specifically, the MDL is defined as the minimum concentration of a substance that can be measured and reported with 99% confidence that the analyte concentration is greater than zero. The MDL is determined from a replicate analysis of a sample of a specified matrix. Specifically, at least seven aliquots of sample, spiked to contain a concentration of from one to five times the method s estimated MDL, are analyzed. The MDL calculated from these results is statistically tested to determine its reasonableness. If the result fails the testing, this iterative process begins again with a new estimate of the MDL. 

Method detection limit (MDL) Involves measuring and LOD using blank matrix samples spiked with known amounts of the cahbration standard and taken through the entire extraction-clean-up-analysis procedure. MDL measures the ability of a specified measurement method to determine an analyte in a sample matrix, with data interpretation using a specified statistical method. The term MDL is often taken to mean the particular single point estimate determined using the prescription of the US EPA. 

The ability to demonstrate that two samples have different amounts of analyte is an essential part of many analyses. A method s sensitivity is a measure of its ability to establish that such differences are significant. Sensitivity is often confused with a method s detection limit. The detection limit is the smallest amount of analyte that can be determined with confidence. The detection limit, therefore, is a statistical parameter and is discussed in Chapter 4. 

A method s detection limit is the smallest amount or concentration of analyte that can be detected with statistical confidence. The International Union of Pure and Applied Chemistry (lUPAC) defines the detection limit as the smallest concentration or absolute amount of analyte that has a signal significantly larger than the signal arising from a reagent blank. Mathematically, the analyte s signal at the detection limit, (Sa)dl, is... 

St John PA, McCarthy WJ, Winefordner JD (1967) A statistical method for evaluation of limiting detectable sample concentrations. Anal Chem 39 1495... 

Statistical evaluation of HPLC UV MS[19] and CE UV MS[20] methods proves that MS detection of anthraquinone dyes is more sensitive than UV, especially in the case of chromatographic analysis of laccaic acids (almost 20 times) and purpurin (almost 40 times). However, detection limits of HPLC ESI MS determination of alizarin and purpurin (0.03 gg ml ) are about 20 times lower than those of CE ESI MS (0.52 0.58 gg ml x). 

The validation of a new method is more involved. A method may introduce a totally new system to the analysis, or it may introduce only new components to an established system. In any case, there may be several new techniques, several new pieces of equipment, several new standard materials, all of which need to be validated, both individually and as a unit. All of the method selection parameters mentioned above (detection limit, accuracy, etc.) are part of the validation process. Also, an important part of validation is the establishment of statistical control (see below). 

The strategies nsed in traditional statistical analyses to handling snch censoring range from simple snbstitntion methods (e.g., replace each censored valne by half the detection limit) to rather elaborate distributional models that attempt to reconstrnct the now dnbions valnes based on the patterns shown by the remaining valnes. Helsel (1990) reviews these strategies and points out the limitations of each. He notes that the cnrrent statistical methods... 

Verapamil and its active metabolite norverapamil were assayed from serum (frozen at -18°C) using a gas chromatographic-mass spectrometric method [5]. The detection limit of the method was 1 ng/ml. The areas under the concentration-time curves (AUC 0-32 h) were calculated by the trapezoidal method. Statistical evaluation was carried out using the paired Wilcoxon test and paired Student s t test. 

What does optimization mean in an analytical chemical laboratory The analyst can optimize responses such as the result of analysis of a standard against its certified value, precision, detection limit, throughput of the analysis, consumption of reagents, time spent by personnel, and overall cost. The factors that influence these potential responses are not always easy to define, and all these factors might not be amenable to the statistical methods described here. However, for precision, the sensitivity of the calibration relation, for example (slope of the calibration curve), would be an obvious candidate, as would the number of replicate measurements needed to achieve a target confidence interval. More examples of factors that have been optimized are given later in this chapter. 

J. Vial and A. Jardy, Experimental Comparison of the Different Approaches to Estimate LOD and LOQ of an HPLC Method, Anal. Chem. 1999, 71, 2672 G. L. Long and J. D. Winefordner, Limit of Detection, Anal. Chem. 1983,55, 713 A W. R. Porter, Proper Statistical Evaluation of Calibration Data, Anal. Chem. 1983,55, 1290A S. Geiss and J. W. Einmax, Comparison of Detection Limits... 

Slope, standard potential, linear concentration range and limit of detection should be determined using statistic methods, using data obtained for the calibration graph E vs. pSCpt (pSCpt — -log[SCpt]). 

The calibration graph at 510 nm is a straight line and Beer s law is obeyed from 0.5 to 5 [xg/ml of boron in the final measured solution (corresponding to 10-110 xg of boron in the aqueous phase). The molar absorptivity, calculated from the slope of the statistical working calibration graph at 510 nm, was 29051/mol/cm. The Sandell sensitivity was 0.011 xgcm2 of boron. The precision of the method for ten replicate determinations was 0.6%. The absorbance of the reagent blank solution at 510 nm was 0.010 d= 0.003 for ten replicate determinations. Therefore, the detection limit was 0.04 xg/ml of boron in the final measured solution. 

Note that f-statistics should be followed when the sample size is small, i.e., <30. In the MDL measurements, the number of replicate analyses are well below 30, generally 7. For example, if the number of replicate analyses are 7, then the degrees of freedom, i.e., the ( -1) is 6, and, therefore, the t value for 6 should be used in the above calculation. MDL must be determined at the 99% confidence level. When analyses are performed by GC or GC/MS methods, the concentrations of the analytes to be spiked into the seven aliquots of the reagent grade water for the MDL determination should be either at the levels of their IDL (instrument detection limit) or five times the background noise levels (the noise backgrounds) at or near their respective retention times. 

Helsel, D.R. (1990). Less than obvious-statistical treatment of data below the detection limits. Environ. Sci. Technol., 24 1766-1774. Helsel, D.R. and R.M. Hirsch (1992). Statistical Methods in Water Resources. New York Elsevier Science. 

There are often data sets used to estimate distributions of model inputs for which a portion of data are missing because attempts at measurement were below the detection limit of the measurement instrument. These data sets are said to be censored. Commonly used methods for dealing with such data sets are statistically biased. An example includes replacing non-detected values with one half of the detection limit. Such methods cause biased estimates of the mean and do not provide insight regarding the population distribution from which the measured data are a sample. Statistical methods can be used to make inferences regarding both the observed and unobserved (censored) portions of an empirical data set. For example, maximum likelihood estimation can be used to fit parametric distributions to censored data sets, including the portion of the distribution that is below one or more detection limits. Asymptotically unbiased estimates of statistics, such as the mean, can be estimated based upon the fitted distribution. Bootstrap simulation can be used to estimate uncertainty in the statistics of the fitted distribution (e.g. Zhao Frey, 2004). Imputation methods, such as... 

---