Statistical validation precision

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... 

Compared with conventional impurities measurements, trace analyses caimot be expected to achieve the same linearity and precision values. This is due to the lower signal-to-noise ratios inevitable at low levels. Hence, while the same approaches can be used, greater latitude will be necessary in the acceptance criteria. What must be demonstrated is that the data is statistically valid to show that the levels of toxic analytes are below their specification limits. 

Determination Determine the precision of an analytical method by assaying a sufficient number of aliquots of a homogeneous sample to be able to calculate statistically valid estimates of standard deviation or relative standard deviation (coefficient of variation). Assays in this context are independent analyses of samples that have... 

This hypothesis leads to a simpler and more general Topo-Information relationship. The choice of an average antmor environment Eji rather than a minimal anterior environment as reference for estimating the pertiirbation term, is dictated by criteria of precision, statistic validity and reliability. These qualities... 

As a multiparametric equation, it requires more precise measurements and larger samples to attain statistical validity. The variations in oR obtained from different molecular systems and their small values indicate the inadequacy of such separations to construct a reliable aR. 

An indicator must also be reasonably amenable to measurement. Just what one measures is likely to depend on the facilities one has, and which types of figures are most likely to be complete, representative, accurate, rapidly available and statistically valid [23]. Some types of data can be (and often are) captured in large administrative data bases however these, as pointed out in Chapter 2, may have been designed for uses other than cost containment and policy review, and lack precisely the variables which one now needs. Data from such an information system may therefore prove disappointing when one puts questions which the system was not designed to answer. If one has any reason to doubt the rehability of the data in such a system, some form of peer review at the source will be advisable, for example to ensure that data are being entered consistently and in fine with prescribed procedures. 

Such a procedure would require a very large analytical effort and the assumption is usually made that the distribution curve at this second stage can be described either as a normal curve or as a curve. The statistical validity of this second stage estimate of precision is based on the form of the first Stage distribution curve, i.e. Figure 2.1. An estimate of the precision of mixture quality is only possible if the sample distribution curve described in Figure 2.1 is that of a normal distribution. The test for normality can be carried out by an adaptation on the test and is illustrated in section 2.3. 

Unless the variances of the two results are equal, it is not statistically valid to take a simple mean. This is not unreasonable. A simple mean accords equal importance to each result. A result with a larger variance is less precise and should not be taken as much notice of. The correct procedure is to calculate a weighted mean, a ... 

The raw data collected during the experiment are then analyzed. Frequently the data must be reduced or transformed to a more readily analyzable form. A statistical treatment of the data is used to evaluate the accuracy and precision of the analysis and to validate the procedure. These results are compared with the criteria established during the design of the experiment, and then the design is reconsidered, additional experimental trials are run, or a solution to the problem is proposed. When a solution is proposed, the results are subject to an external evaluation that may result in a new problem and the beginning of a new analytical cycle. 

The specification development process is a data-driven activity that requires a validated analytical method. The levels of data needed include assay precision, replicate process results (process precision), and real-time stability profiles. A statistical analysis of these data is critical in setting a realistic specification. Most often, aggregation and fragmentation degradation mechanisms are common to protein and peptide therapeutics. Therefore, the SE-HPLC method provides a critical quality parameter that would need to be controlled by a specification limit. 

Figure 4.31. Key statistical indicators for validation experiments. The individual data files are marked in the first panels with the numbers 1, 2, and 3, and are in the same sequence for all groups. The lin/lin respectively log/log evaluation formats are indicated by the letters a and b. Limits of detection/quantitation cannot be calculated for the log/log format. The slopes, in percent of the average, are very similar for all three laboratories. The precision of the slopes is given as 100 t CW b)/b in [%]. The residual standard deviation follows a similar pattern as does the precision of the slope b. The LOD conforms nicely with the evaluation as required by the FDA. The calibration-design sensitive LOQ puts an upper bound on the estimates. The XI5% analysis can be high, particularly if the intercept should be negative.

Precision estimates are key method performance parameters and are also required in order to carry out other aspects of method validation, such as bias and ruggedness studies. Precision is also a component of measurement uncertainty, as detailed in Chapter 6. The statistics that are applied refer to random variation and therefore it is important that the measurements are made to comply with this requirement, e.g. if change of precision with concentration is being investigated, the samples should be measured in a random order. 

The first precise or calculable aspect of experimental design encountered is determining sufficient test and control group sizes to allow one to have an adequate level of confidence in the results of a study (that is, in the ability of the study design with the statistical tests used to detect a true difference, or effect, when it is present). The statistical test contributes a level of power to such a detection. Remember that the power of a statistical test is the probability that a test results in rejection of a hypothesis, H0 say, when some other hypothesis, H, say, is valid. This is termed the power of the test with respect to the (alternative) hypothesis H. ... 

II the difference approach, which typically utilises 2-sided statistical tests (Hartmann et al., 1998), using either the null hypothesis (H0) or the alternative hypothesis (Hi). The evaluation of the method s bias (trueness) is determined by assessing the 95% confidence intervals (Cl) of the overall average bias compared to the 0% relative bias value (or 100% recovery). If the Cl brackets the 0% bias then the trueness that the method generates acceptable data is accepted, otherwise it is rejected. For precision measurements, if the Cl brackets the maximum RSDp at each concentration level of the validation standards then the method is acceptable. Typically, RSDn> is set at <3% (Bouabidi et al., 2010),... 

III the equivalence approach, which typically compares a statistical parameters confidence interval versus pre-defined acceptance limits (Schuirmann, 1987 Hartmann et al., 1995 Kringle et al., 2001 Hartmann et al., 1994). This approach assesses whether the true value of the parameter(s) are included in their respective acceptance limits, at each concentration level of the validation standards. The 90% 2-sided Cl of the relative bias is determined at each concentration level and compared to the 2% acceptance limits. For precision measurements, if the upper limit of the 95% Cl of the RSDn> is <3% then the method is acceptable (Bouabidi et al., 2010) or,... 

As noted in the last section, the correct answer to an analysis is usually not known in advance. So the key question becomes How can a laboratory be absolutely sure that the result it is reporting is accurate First, the bias, if any, of a method must be determined and the method must be validated as mentioned in the last section (see also Section 5.6). Besides periodically checking to be sure that all instruments and measuring devices are calibrated and functioning properly, and besides assuring that the sample on which the work was performed truly represents the entire bulk system (in other words, besides making certain the work performed is free of avoidable error), the analyst relies on the precision of a series of measurements or analysis results to be the indicator of accuracy. If a series of tests all provide the same or nearly the same result, and that result is free of bias or compensated for bias, it is taken to be an accurate answer. Obviously, what degree of precision is required and how to deal with the data in order to have the confidence that is needed or wanted are important questions. The answer lies in the use of statistics. Statistical methods take a look at the series of measurements that are the data, provide some mathematical indication of the precision, and reject or retain outliers, or suspect data values, based on predetermined limits. 

The statistical prediction errors for the validation samples in this example are plotted in Figure 5.11. The maximum statistical prediction error for component A (Figure 5.1 la) is 0.025, which must be compared to the precision requirements of the application. For component B (Figure 5.life), maximum statistical prediction error is —0.019. In addition, no samples appear to have unusually large statistical prediction errors which would indicate an outlier. 

Statistical Prediction Errors (Model and Sample Diagnostic) From the S matrix it is possible to predict all four components (caustic, salt, water concentration, and temperature). However, in this application the interest is only in caustic and, therefore, only the results for this component are presented. The statistical prediction errors for the caustic concentration for the validation data vary from 0.006 to 0.028 wt.% (see Figure 5-54). The goal is to predict the caustic concentration to 0.1 wt.% (lo), and the statistical prediction errors indicate that the precision of the method is adequate. Also, there do not appear to be any sample(s) that have an unusual error when compared to the rest of the samples. 

A clinical trial is an experiment and not only do we have to ensure that the clinical elements fit with the objectives of the trial, we also have to design the trial in a tight scientific way to make sure that it is capable of providing valid answers to the key questions in an unbiased, precise and structured way. This is where the statistics comes in and statistical thinking is a vital element of the design process for every clinical trial. 

The most important aspects of data handling for potency assays and low-precision assays are that the data is handled by validated computer programs and that the acceptance and rejection criteria incorporated are clear and based upon statistical or proven (at validation) limits. 

The basic criterion for successful validation was that a method should come within 25% of the "true value" at the 95% confidence level. To meet this criterion, the protocol for experimental testing and method validation was established with a firm statistical basis. A statistical protocol provided methods of data analysis that allowed the accuracy criterion to be evaluated with statistical parameters estimated from the laboratory test data. It also gave a means to evaluate precision and bias, independently and in combination, to determine the accuracy of sampling and analytical methods. The substances studied in the second phase of the study are summarized in Table I. 

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