Quantitative assays statistical methods

Incubate at least four series, cells with three or more different concentrations of the preparation to be examined and the reference preparation in a microtitre plate and include in each series appropriate controls of untreated cells. Choose the concentrations of the preparations such that the lowest concentration produces some protection and the largest concentration produces less than maximal protection against the viral cytopathic effect. At a suitable time add the cytopathic virus to the wells with the exception of a sulScient number of wells in ah series, which are left with uninfected control cells. Determine the cytopathic effect of virus quantitatively with a suitable method. Calculate the potency of the preparation to be examined by the usual statistical methods for a parallel line assay. 

An important extension of our large validation studies involves the use of data bases from field studies in the development of improved statistical methods for a variety of problems in quantitative applications of immunoassays. These problems include the preparation and analysis of calibration curves, treatment of "outliers" and values below detection limits, and the optimization of resource allocation in the analytical procedure. This last area is a difficult one because of the multiple level nested designs frequently used in large studies such as ours (22.). We have developed collaborations with David Rocke and Davis Bunch (statisticians and numerical analysts at Davis) in order to address these problems within the context of working assays. Hopefully we also can address the mathematical basis of using multiple immunoassays as biochemical "tasters" to approach multianalyte situations. 

Sensitivity refers to the lower limit of detection (LOD) of the assay (i.e., the lowest concentration of the analyte that the assay can distinguish from the blank). Limit of quantitation (LOQ) is another parameter related to the use of quantitative assays, which is the lowest concentration of the analyte that can be measured with an acceptable level of precision. Levels below LOQ have an increased degree of statistical uncertainty, which affects the accuracy of the method. 

Statistical methods provide an approach that yields quantitative estimates of the random uncertainties in the raw data measurements themselves and also in the conclusions drawn from them. Statistical methods do not detect systematic errors (e.g. bias) present in an assay nor do they give a clear-cut answer to the question as to whether or not a particular experimental result is acceptable. An acceptability criterion must be chosen a priori based on the underlying assumption that the data follow a Gaussian (normal) distribution. A common acceptability criterion is the 95 % confidence level, corresponding to a p-value of 0.05. Because work is with small data sets in trace quantitative analyses, as opposed to the infinitely large data sets required for idealized statistical theory, use is mode of tools and tests based on the (t) distribution (Sudent s t distribution) developed specifically for the statistical analysis of small data sets. 

The literature abounds with assay statistics but perhaps the most statistically interesting publication, based solely on the vast number of samples analyzed, is an epidemiological study of the effects of exposure to secondhand cigarette smoke conducted by the U.S. Center for Disease Control. This assay employed APCI LC/MS/MS for the determination of cotinine, a nicotine metabolite, in semm using a stable isotope internal standard. At the time of the publication, data on >32,000 samples utilizing a single mass spectrometer had been amassed. Precision and accuracy of the method was approximately 6% except at the limit of quantitation (25 pg/mL), which had a C Vof 12%. It is appropriate to point out here that these statistics provide the variation in the entire method. The previous discussion on reproducibility (see Section 13.3.1 and 13.3.2) dealt only with variabihtyhmits imposed by the mass spectrometer based on ion current stability measurements that establish the theoretical limits. 

Part—I has three chapters that exclusively deal with General Aspects of pharmaceutical analysis. Chapter 1 focuses on the pharmaceutical chemicals and their respective purity and management. Critical information with regard to description of the finished product, sampling procedures, bioavailability, identification tests, physical constants and miscellaneous characteristics, such as ash values, loss on drying, clarity and color of solution, specific tests, limit tests of metallic and non-metallic impurities, limits of moisture content, volatile and non-volatile matter and lastly residue on ignition have also been dealt with. Each section provides adequate procedural details supported by ample typical examples from the Official Compendia. Chapter 2 embraces the theory and technique of quantitative analysis with specific emphasis on volumetric analysis, volumetric apparatus, their specifications, standardization and utility. It also includes biomedical analytical chemistry, colorimetric assays, theory and assay of biochemicals, such as urea, bilirubin, cholesterol and enzymatic assays, such as alkaline phosphatase, lactate dehydrogenase, salient features of radioimmunoassay and automated methods of chemical analysis. Chapter 3 provides special emphasis on errors in pharmaceutical analysis and their statistical validation. The first aspect is related to errors in pharmaceutical analysis and embodies classification of errors, accuracy, precision and makes... 

The procedure for GLC analysis gave a lower limit for quantitation of 1 in plasma of approximately 1 ng/ml from twice the standard deviation (0.32 ng) obtained for the amount of 1 recovered from 2.25 ng in 2 ml of plasma. Similarly, the procedure for radiochemical analysis gave a lower limit of approximately 0.2 ng/ml from twice the standard deviation (0.084 ng). A statistical analysis of the apparent differences between the tetrahydrocannabinol assays at a given time from both analytical methods showed no significance. 

The similar method using nickel (II) instead of cobalt, cadmium and manganese was also investigated by Salem et al. [49] for the quantitative determination of flufenamic, mefenamic and tranexamic acids, furose-mide, diclofenac sodium and thiaprofenic acid. Statistical analysis of the results compared to assays used in pharmacopoeias and the Amax methods revealed equal precision and accuracy. Furthermore, the assays were also applied for the determination of these drugs in pharmaceutical preparations. 

Determination of Assay Sensitivity with Replication and Statistics. Sensitivity can be defined as the ability of a test to discriminate between adjacent levels or concentrations of test analyte. There are other definitions of sensitivity, but the one specified is sufficiently general to serve several needs in residue analysis. For example, the definition recognizes that test sensitivity can vary with the point on the standard curve. If one of the points used is zero, then the sensitivity estimate can be either the level of smallest quantitation or the level of detectability of the method. The... 

The quantitation of enzymes and substrates has long been of critical importance in clinical chemistry, since metabolic levels of a variety of species are known to be associated with certain disease states. Enzymatic methods may be used in complex matrices, such as serum or urine, due to the high selectivity of enzymes for their natural substrates. Because of this selectivity, enzymatic assays are also used in chemical and biochemical research. This chapter considers quantitative experimental methods, the biochemical species that is being measured, how the measurement is made, and how experimental data relate to concentration. This chapter assumes familiarity with the principles of spectroscopic (absorbance, fluorescence, chemi-and bioluminescence, nephelometry, and turbidimetry), electrochemical (poten-tiometry and amperometry), calorimetry, and radiochemical methods. For an excellent coverage of these topics, the student is referred to Daniel C. Harris, Quantitative Chemical Analysis (6th ed.). In addition, statistical terms and methods, such as detection limit, signal-to-noise ratio (S/N), sensitivity, relative standard deviation (RSD), and linear regression are assumed familiar Chapter 16 in this volume discusses statistical parameters. 

Quantitative methods are assays that result in meaningful numeric measurements for a characteristic of a product. Quantitative methods are used in assessing whether final product meets specifications. They are also used to measure product quality (or quantity) in various stages of manufactuiing and the results are often used in quality control charts. Validation is an objective process used to determine whether a quantitative method is performing as expected and is appropriate for its intended use. This chapter provides the motivation behind validation, some terms and definitions used in validation, a consolidated statistically sound approach to validation, along with appropriate statistical analysis, and reporting of validation results. A hypothetical but realistic example is presented and is used to illustrate the validation process. 

In addition to laboratoiy glassware and equipment necessary fOT cleanup of the extract, traditional pesticide residue methods require expensive chromatogrsqihic instrumentation for identification and quantitation of residues. EIA methods require minimal amounts of glassware, disposable plasticware, or other supplies. Quantitative EIAs often make use of 96-well microtiter plates fOT multiple simultaneous assays of about a dozen extracts and associated reference standard. Major equipment consists of a plate reader, which automatically measures the absorbance of each well. Plate readers can be used alone or in conjunction with a personal computer, which can correlate replicate measurements, construct the calibration curve, calculate results, and provide a complete statistical analysis. Such an EIA workstation can be obtained for roughly half the cost of the GC or HPLC system typically used for pesticide residue analysis. 

These results dearly demonstrate that FDMS, in conjunction with a multichannel analyzer, represents a powerful method for the trace analysis of metals. Obviously, the unavoidable statistical fluctuations in the FD ion currents have lost then-detrimental effect on the FD assay and the signal-to-noise ratio of the signals in question has been improved considerably by spectra accumulation. In addition, it can be expected that by use of the isotope dilution technique quantitative determinations of high sensitivity and accuracy can be accomplished without prior treatment of the original biological or environnmntal sample. 

The next section deals with method validation of quantitative TLC methods. Two questions should, however, be answered prior to discussing the validation experiments namely, whether the statistical evaluation of data elements, such as precision, accuracy, and reproducibility should be calculated on the basis of measured peak heights or peak areas, and whether the internal or external standard methods, or area normalization should be used to yield quantitative results for the assay. Without going into detail, the most important advantages and limitations of peak height and peak area measurements, and those of the different methods of quantification are summarized in Table 4. 

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