Limits of detection and decision. Part 1

Extensive Monte Carlo studies of instrumental limits of detection were performed on a simple univariate chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing of tens of millions of independent calibration curve data sets. It was found that prediction interval-based experimental detection limits were significantly negatively biased, in both the net response domain and the chemical content domain, resulting in substantially higher rates of false negatives than specified via customary critical t values. The diagnostic fix for the bias problem provided clear proof that hypothesis-based detection limits need not be unique, even as distributions of random variates, if the alternate hypothesis is non-unique. It was also demonstrated that hypothesis-based decision and detection limits have finite support that does not include the region near zero analyte content, so that both have finite moments and finite confidence intervals.     

Limits of detection and decision. Part 4

Probability density functions (PDFs) have been derived for a number of commonly used limit of detection definitions, including several variants of the Relative Standard Deviation of the Background–Background Equivalent Concentration (RSDB–BEC) method, for a simple linear chemical measurement system (CMS) having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing. All of these detection limit definitions serve as both decision and detection limits, thereby implicitly resulting in 50% rates of Type 2 errors. It has been demonstrated that these are closely related to Currie decision limits, if the coverage factor, k, is properly defined, and that all of the PDFs are scaled reciprocals of noncentral t variates. All of the detection limits have well-defined upper and lower limits, thereby resulting in finite moments and confidence limits, and the problem of estimating the noncentrality parameter has been addressed. As in Parts 1–3, extensive Monte Carlo simulations were performed and all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Specific recommendations for harmonization of detection limit methodology have also been made.     

Statistical behavior of ten million experimental detection limits

Using a lab-constructed laser-excited fluorimeter, together with bootstrapping methodology, the authors have generated many millions of experimental linear calibration curves for the detection of rhodamine 6G tetrafluoroborate in ethanol solutions. The detection limits computed from them are in excellent agreement with both previously published theory and with comprehensive Monte Carlo computer simulations. Currie decision levels and Currie detection limits, each in the theoretical, chemical content domain, were found to be simply scaled reciprocals of the non-centrality parameter of the non-central t distribution that characterizes univariate linear calibration curves that have homoscedastic, additive Gaussian white noise. Accurate and precise estimates of the theoretical, content domain Currie detection limit for the experimental system, with 5% (each) probabilities of false positives and false negatives, are presented.     

Limits of detection and decision. Part 3

It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on ‘critical values of the non-centrality parameter of the non-central t distribution’, is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, “hockey stick” and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.     

True detection limits in an experimental linearly heteroscedastic system.: Part 2

Despite much different processing of the experimental fluorescence detection data presented in Part 1, essentially the same estimates were obtained for the true theoretical Currie decision levels (Y_C and X_C) and true Currie detection limits (Y_D and X_D). The obtained experimental values, for 5% probability of false positives and 5% probability of false negatives, were Y_C = 56.0 mV, Y_D = 125. mV, X_C = 0.132 μg/mL and X_D = 0.293 μg/mL. For 5% probability of false positives and 1% probability of false negatives, the obtained detection limits were Y_D = 158. mV and X_D = 0.371 μg/mL. Furthermore, by using bootstrapping methodology on the experimental data for the standards and the analytical blank, it was possible to validate previously published experimental domain expressions for the decision levels (y_C and x_C) and detection limits (y_D and x_D). This was demonstrated by testing the generated decision levels and detection limits for their performance in regard to false positives and false negatives. In every case, the obtained numbers of false negatives and false positives were as specified a priori.     

True detection limits in an experimental linearly heteroscedastic system. Part 1

Using a lab-constructed laser-excited filter fluorimeter deliberately designed to exhibit linearly heteroscedastic, additive Gaussian noise, it has been shown that accurate estimates may be made of the true theoretical Currie decision levels (Y_C and X_C) and true Currie detection limits (Y_D and X_D) for the detection of rhodamine 6 G tetrafluoroborate in ethanol. The obtained experimental values, for 5% probability of false positives and 5% probability of false negatives, were Y_C = 56.1 mV, Y_D = 125. mV, X_C = 0.132 μg/mL and X_D = 0.294 μg/mL. For 5% probability of false positives and 1% probability of false negatives, the obtained detection limits were Y_D = 158. mV and X_D = 0.372 μg/mL. These decision levels and corresponding detection limits were shown to pass the ultimate test: they resulted in observed probabilities of false positives and false negatives that were statistically equivalent to the a priori specified values.     

Uncertainty-based measurement quality control

According to a simple acceptance decision rule for measurement quality control, a measured value will be accepted if the expanded uncertainty of the measurements is not greater than a preset maximum permissible uncertainty. Otherwise, the measured value will be rejected. The expanded uncertainty may be calculated as the z-based uncertainty (the half-width of the z-interval) when the measurement population standard deviation σ is known or the sample size is large (30 or greater), or by a sample-based uncertainty estimator when σ is unknown and the sample size is small. The decision made based on the z-based uncertainty will be deterministic and may be assumed to be correct. However, the decision made based on a sample-based uncertainty estimator will be uncertain. This paper develops the mathematical formulations for computing the probability of acceptance for two sample-based uncertainty estimators: the t-based uncertainty (the half-width of the t-interval) and an unbiased uncertainty estimator. The risk of incorrect decision-making, in terms of the false acceptance probability and false rejection probability, is derived from the probability of acceptance. The theoretical analyses indicate that the t-based uncertainty may result in significantly high false rejection probability when the sample size is very small (especially for samples of size 2). For some applications, the unbiased uncertainty estimator may be superior to the t-based uncertainty for measurement quality control. Several examples from acoustic Doppler current profiler streamflow measurements are presented to demonstrate the performance of the t-based uncertainty and the unbiased uncertainty estimator.     

Metrological reference values for estimating measurement bias in clinical laboratory sciences

Clinical laboratory quantities are measured for monitoring or diagnostic purposes. In both cases, a modification of the measurement bias can generate a false interpretation of measurement results. On the other hand, in clinical laboratory sciences, one of the most frequently used metrological reference value for calculating measurement bias is a conventional value that corresponds to the called consensus value. But this selection probably is not the best one, and some clinical and biological considerations should be made to decide the requirement for maximum permissible measurement bias and to decide the more appropriate metrological reference value. In the clinical laboratory, the medical relevance of the measurement bias of any measurement system in use depends on the measurement bias with which the biological reference values were produced. This dependence is due to the necessity that, for interpretation purposes, the current measurement bias should be the same that is included in the biological reference limits. For this reason, it is necessary to control the changes of bias during the life span of a measuring system. Several scenarios are described for the different estimations of bias.     

Automatic screening method for the preconcentration and determination of N-nitrosamines in water

A screening method was developed to discriminate among water samples contaminated or uncontaminated with N-nitrosamines in order to reduce the use of expensive instruments such as chromatographs. The system is based on the preconcentration of the analytes onto a sorbent column, elution and derivatization to form nitrite, then formation of a coloured product (Griess reaction) and photometric detection. The limit of detection achieved for 100 ml of sample volume was 0.2 μg/l and the sample frequency 3 h⁻¹. The reliability of the proposed method of the N-nitrosamines was established at five concentrations (between 0.5 and 3 times the limit of detection). For a level concentration of 0.6 μg/l (three times the limit of detection), the percentage of false negatives is 0%. The method was applied to the screening of several water samples (river, pond, well, tap and waste) with a positive response only for waste water samples.     

Pulsed coulometric detection of carbohydrates at a constant detection potential at gold electrodes in alkaline media

A significant increase in the signal-to-noise ratio for the pulsed amperometric detection (PAD) of carbohydrates at gold electrodes is obtained by increasing the length of the current integration period (t_i) from the traditional value of 16.7 ms (i.e., $\text{1}\text{60}$ Hz). For t_i > 16.7 ms, the integrated response (q, coulombs) is plotted as the signal. This pulsed coulometric detection (PCD) is applied in a flow-injection system. For t_i = 500 ms, the detection limit with the instrumentation used is 1 μM (S/N = 2) for glucose which is a significant improvement on the value 35 μM found with PAD. The absolute detection limits for glucose and sucrose are ca. 50 pmol and 125 pmol, respectively, in 50-μl samples. Calibration plots (q_p vs. C^b) for PCD are linear over significantly larger dynamic ranges than those observed for PAD because of the lower detection limits.     

An inter-laboratory study of detection limits in the analysis of water and wastewater for organo-chlorine pesticides by liquid/liquid extraction and gas chromatography-electron capture detector (USEPA Method 608)

An inter-laboratory study was conducted to assess the Kaiser-Currie Model (KCM) for the determination of detection limits. Six laboratories participated in the analysis of samples prepared from distilled water, some containing organo-chlorine pesticides at a concentration of zero and other with a greater than zero concentration. The study consisted of three phases, the first of which was a study to assess the longer term variability of distilled water samples containing no organo-chlorine pesticides prepared by the participating laboratory analysed over a six month period. A second phase consisted of replicates of distilled water samples containing organo-chlorine pesticides prepared at a single concentration greater than zero by the laboratory and were analysed over several days. Finally, a third phase consisted of twelve distilled water samples, eleven containing organo-chlorine pesticides at a concentration of greater than zero and one with a concentration of zero prepared by a third party. Estimated detection limits were determined and then compared to the observed detection limits. Only in a minority of cases, where the distribution of results from samples containing a concentration of zero was normally distributed, did Currie's L _C accurately predict a concentration which corresponded to a 1% false positive rate in distilled water samples with a zero concentration of the study analyte. The USEPA's MDL performed more poorly. In the majority of cases, when any non-zero results were obtained from distilled water samples containing a concentration of zero, they were not normally distributed. Contrary to expectation, false negatives and false positives rarely occurred simultaneously on any given day. The variability between days of analysis and the use of noise reducing techniques proved to be a significant source of the observed non-normal distribution of distilled water samples. Conventional procedures based on the KCM and their underlying analytical and statistical assumptions did not provide useful predictions of laboratory sensitivity in most cases in this study.     

Validation of reducing-difference procedure for the interpretation of non-polarized infrared spectra of n-component solid mixtures

Validation of reducing-difference procedure based on subtracting of non-polarized infrared (IR) spectra of n-component solid mixtures is presented. The accuracy and precision are established. The limits of detection are 3.0, 2.5, 1.5 and 1.0 wt.% for 5-, 4-, 3-and 2-component mixtures, respectively. Smoothing procedures for IR spectral analysis, based on Savitzky-Golay or Fourier methods are applied as well. The mean values and relative standard deviations for peak position (ν_i) and integral absorbance (A_i) obtained by this data processing approach have been examined using Student's t-test.     

Selective cyclization of alkynols and alkynylamines catalyzed by potassium tert-butoxide

Potassium tert-butoxide (t-BuOK) was found to be an effective catalyst for the cyclization of aromatic alkynols and alkynylamines. In the presence of 10 mol % t-BuOK, a range of alkynols were converted to the corresponding exo-cyclic enol ethers as pure Z-stereoisomers with 100% selectivity and moderate to excellent yields. Moreover, the cyclization of alkynylamines was also achieved to afford indoles and isoindolin-1-ones in good yields.     

Ultrasensitive electrochemical sensor for p-nitrophenyl organophosphates based on ordered mesoporous carbons at low potential without deoxygenization

p-Nitrophenyl organophosphates (OPs) including paraoxon, parathion and methyl parathion, etc, are highly poisonous OPs, for which sensitive and rapid detection method is most needed. In this work, an ultrasensitive electrochemical sensor for the determination of p-nitrophenyl OPs was developed based on ordered mesoporous carbons (OMCs) modified glassy carbon electrode (GCE) (OMCs/GCE). The electrochemical behavior and reaction mechanism of p-nitrophenyl OPs at OMCs/GCE was elaborated by taking paraoxon as an example. Experimental conditions such as buffer pH, preconcentration potential and time were optimized. By using differential pulse voltammetry, the current response of the sensor at −0.085 V was linear with concentration within 0.01–1.00 μM and 1.00–20 μM paraoxon. Similar linear ranges of 0.015–0.5 μM and 0.5–10 μM were found for parathion, and 0.01–0.5 μM and 0.5–10 μM for methyl parathion. The low limits of detection were evaluated to be 1.9 nM for paraoxon, 3.4 nM for parathion and 2.1 nM for methyl parathion (S/N = 3). Common interfering species had no interference to the detection of p-nitrophenyl OPs. The sensor can be applicable to real samples measurement. Therefore, a simple, sensitive, reproducible and cost-effective electrochemical sensor was proposed for the fast direct determination of trace p-nitrophenyl OPs at low potential without deoxygenization.     

Copper(II) tetrafluoroborate as a novel and highly efficient catalyst for N-tert-butoxycarbonylation of amines under solvent-free conditions at room temperature

Commercially available copper(II) tetrafluoroborate hydrate was found to be a highly efficient catalyst for chemoselective N-tert-butoxycarbonylation of amines with di-tert-butyl dicarbonate under solvent-free conditions and at room temperature. Various aromatic amines were protected as their N-tert-butyl carbamates in high yields and in short times. No competitive side reactions such as isocyanate, urea, and N,N-di-t-Boc formation was observed. Chemoselective N-tert-butoxycarbonylation was achieved with substrates bearing OH and SH groups. Chiral α-amino acid esters afforded the corresponding N-t-Boc derivatives in excellent yields.     

Highly sensitive spectrophotometric methods for the determination, validation and thermogravimetric analysis of antiulcer drugs, nizatidine and ranitidine in pure and pharmaceutical preparations

Two sensitive, simple and rapid UV and second order derivative spectrophotometric methods were developed for the determination of nizatidine and ranitidine hydrochloride in pure form and pharmaceutical preparations. For the first method, UV spectrophotometic method, nizatidine was determined at 325 nm and ranitidine at 325.5 nm with detection limits of 0.07 and 0.04 μg/mL, respectively. For the second method, the distances between two extremum values (peak-to-peak amplitudes), 328/356.5 nm for nizatidine and 326/357 nm for ranitidine were measured in the second order derivative-spectra. The detection limits were found to be 0.02 μg/mL for nizatidine and 0.016 μg/mL for ranitidine, respectively. The thermal analysis of the two drugs was studied by Thermogravimetric Analysis-Differential Scanning Calorimetry (TGA-DSC) techniques. Enthalpy changes were obtained 121.9 and 124.15 J/g for nizatidine and ranitidine, respectively. The proposed method was successfully applied to the analysis of pharmaceutical preparations. The results were in good agreement with those obtained using the reference method; no significant difference were found in the accuracy and precision as revealed by the accepted values of t- and F-tests.     

Syntheses and structures of zinc and tin(II) compounds with hemilabile N-silyl-tert-butylamido and N-silyl-p-tolylamido ligands that contain pendent tert-butoxy groups

Syntheses and solid-state structures of zinc and tin(II) compounds, containing the N-silyl-amide ligands (O^tBu)(NR)SiMe₂, R = ^tBu (L^tBu), or R = p-tolyl (L^pTol), are reported. The N-silyl amines were synthesized by modified published procedures from commercially available Me₂SiCl₂, ^tBuOH, and ^tBuNH₂, or p-Me-C₆H₄NH₂, respectively. Treatment of SnCl₂ with LiL^pTol furnished Sn(L^pTol)₂, which was X-ray structurally characterized and shown to contain two covalent Sn-N bonds and two asymmetrical O → Sn donor bonds. The single-crystal X-ray structure of Sn(L^tBu)₂ revealed a much more symmetrically-coordinated, pseudo-trigonal-bipyramidal tin atom. Aminolysis of diethylzinc with HL^pTol produced [EtZn(L^pTol)]₂, which crystallized as a centrosymmetric dimer, containing four-coordinate zinc atoms connected by bridging amides. Zinc dichloride, by contrast, reacted with two equivalents of LiL^tBu to produce the homoleptic, pseudo-spirocyclic Zn(L^tBu)₂.     

Dynamic microwave-assisted extraction coupled with on-line spectrophotometric determination of safflower yellow in Flos Carthami

A rapid dynamic microwave-assisted extraction and on-line detection by spectrophotometry is proposed for the determination of safflower yellow in Flos Carthami. A high pressure and a peristaltic pump were used to deliver the solvent. A TM₀₁₀ microwave resonance cavity was applied to concentrate the microwave energy and the forward power about 60 W was enough for the extraction. Other extraction conditions also were examined and optimized. In this work, the extraction process can be monitored by measuring the absorption of safflower yellow in the extract, which would be convenient for rapid optimization of the extraction process. The detection and quantification limits are 8 and 27 μg mL⁻¹, respectively. The within-day and between-day precision (R.S.D.) are 1.6-3.2% and 2.8-4.2%, respectively. Compared with off-line detection, the proposed method may provide more rapid measurement and is more convenient for obtaining continuous measurements.     

Fluorescence detection of total count of Escherichia coli and Staphylococcus aureus on water-soluble CdSe quantum dots coupled with bacteria

The aim of this paper was to demonstrate a fluorescence measurement method for rapid detection of two bacterial count by using water-soluble quantum dots (QDs) as a fluorescence marker, and spectrofluorometer acted as detection apparatus, while Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) were as detection target bacteria. Highly luminescent water-soluble CdSe QDs were first prepared by using thioglycolic acid (TGA) as a ligand, and were then covalently coupled with target bacteria. The bacterial cell images were obtained using fluorescence microscopy. Our results showed that CdSe QDs prepared in water phase were highly luminescent, stable, and successfully conjugated with E. coli and S. aureus. The fluorescence method could detect 10²-10⁷ CFU/mL total count of E. coli and S. aureus in 1-2 h and the low detection limit is 10² CFU/mL. A linear relationship of the fluorescence peak intensity and log total count of E. coli and S. aureus have been established using the equation Y = 118.68X − 141.75 (r = 0.9907).     

Micellization behavior of diblock and triblock copolymers of poly(t-butyl methacrylate) bearing associating short polystyrene end-blocks

Anionic polymerization high vacuum techniques were employed for the synthesis of a diblock (PS-b-PtBuMA) and two triblock (PS-b-PtBuMA-b-PS) copolymers of polystyrene (PS) and poly(t-butyl methacrylate) (PtBuMA) bearing similar low molecular weight PS end-block(s). Dilute solution viscometry, as well as static and dynamic light scattering, were employed to assess whether the short PS end-blocks were able to promote association in t-amyl alcohol, a selective solvent for PtBuMA. The effect of macromolecular architecture on the association behavior of the copolymers was also examined.