End-point analysis

Cohen M, Adams PC, Parry G, Xiong J, Chamberlain D, Wieczorek 1 et al. Combination antithrombotic therapy in unstable rest angina and non-Q-wave infarction in nonprior aspirin users. Primary end points analysis from the ATACS trial. Antithrombotic Therapy in Acute Coronary Syndromes Research Group. Circulation 1994 89(l) 81-8. 

Neophobia to the presence of multiple water bottles and to the taste of sucrose may also confound behavioral results in this model. To avoid this problem, acclimate mice by giving them two bottles, each with the sucrose solution, for 72 h before the test, or with one water and one sucrose bottle for 1 h per day for 1 week. Also, consider lengthening the period of the test to at least 24 h. Researchers may choose to utilize video recording to document all water intake, however, end point analysis of overall sucrose consumption (as described earlier) is acceptable. 

It is usually required to perform an intent-to-treat analysis that will include data on all patients who were enrolled and began treatment, regardless of whether they followed protocol, finished the study, violated protocol, or dropped out.The purpose here is to ensure the safety of the investigational substance, because substantial bias would be built into the overall analysis with the exclusion of patients who could not tolerate medication and dropped out, or who were not helped by the medication and switched to another treatment. In addition, of course, there might be an analysis of the results from all patients who followed the entire protocol properly.The intent-to-treat analysis should include patients who withdrew from the study the last clinical measurements taken for these patients should be carried forward as the last observation or final score—the so-called end point analysis. 

Two basic procedures seem called for compare the dropout rates and time-to-dropout across all treatment groups, and analyze the intent-to-treat group (all randomized patients). Beyond this, consider two analyses (in addition to intent-to-treat) to assess the impact of the dropouts on the final results an end point analysis (the last clinical and laboratory observations of each patient) and an analysis of all patients actually evaluated at each of the scheduled patient visits. 

An equilibrium method utilizes end-point analysis. Obviously, the greater the extent of conversion, the more accurate the measurement. Because the majority of enzymatic reactions involve two substrates (or one substrate and one coenzyme), it is possible to achieve enhanced conversion by using high concentration of the second reactant X. 

The discussions of pK, log P, and log D above all pertain to the end point analysis of the solubility of a drug candidate. A correlation exists between log P of neutral immiscible liquids with their solubility in water however, for solids solubility also depends on the energy required to break the crystal lattice where log P is related to solubility. It is therefore possible to have compounds with high log P values, which are stiU soluble on account of their low melting point. Similarly, it is possible to have a low log P compound with a high melting point, which is very insoluble. 

Because enzymatic reactions are usually not completely selective, it is important to note that end-point analysis of the reaction mixture does not reveal enzyme selectivity if the reaction has proceeded to high conversion. The selectivity can only be determined by analyzing the concentrations of the products as the conversion of substrates proceeds. An example is given in Figure 4.9-5. 

The primary end point was the proportion of subjects in each treatment group who achieved treatment success after 8 weeks, analysed on an intension to treat (ITT) basis. In the primary end point analysis, subjects missing 8-weeks outcomes data were classified as treatment failures regardless of their outcomes at earlier evaluations. Secondary end points included treatment success as a function of baseline ISGA score (mild or moderate), ISGA score of 0 or 1 (clear or almost clear) and effects of treatment on target lesions. 

One of the main outcomes of the analysis so far is that the topological matrix D, presented in Eq. (38), is identical to an adiabatic-to-diabatic transformation matrix calculated at the end point of a closed contour. From Eq. (38), it is noticed that D does not depend on any particular point along the contour but on the contour itself. Since the integration is carried out over the non-adiabatic coupling matrix, x, and since D has to be a diagonal matrix with numbers of norm 1 for any contour in configuration space, these two facts impose severe restrictions on the non-adiabatic coupling terms. 

In this experiment students standardize a solution of HGl by titration using several different indicators to signal the titration s end point. A statistical analysis of the data using f-tests and F-tests allows students to compare results obtained using the same indicator, with results obtained using different indicators. The results of this experiment can be used later when discussing the selection of appropriate indicators. 

Derivative methods are particularly well suited for locating end points in multi-protic and multicomponent systems, in which the use of separate visual indicators for each end point is impractical. The precision with which the end point may be located also makes derivative methods attractive for the analysis of samples with poorly defined normal titration curves. 

Under these conditions some OH is consumed in neutralizing CO2. The result is a determinate error in the titrant s concentration. If the titrant is used to analyze an analyte that has the same end point pH as the primary standard used during standardization, the determinate errors in the standardization and the analysis cancel, and accurate results may still be obtained. 

CO2 is determined by titrating with a standard solution of NaOH to the phenolphthalein end point, or to a pH of 8.3, with results reported as milligrams CO2 per liter. This analysis is essentially the same as that for the determination of total acidity, and can only be applied to water samples that do not contain any strong acid acidity. 

Procedure. Select a volume of sample requiring less than 15 mL of titrant to keep the analysis time under 5 min and, if necessary, dilute the sample to 50 mL with distilled water. Adjust the pH by adding 1-2 mL of a pH 10 buffer containing a small amount of Mg +-EDTA. Add 1-2 drops of indicator, and titrate with a standard solution of EDTA until the red-to-blue end point is reached. 

In a titrimetric method of analysis the volume of titrant reacting stoichiometrically with the analyte provides quantitative information about the amount of analyte in a sample. The volume of titrant required to achieve this stoichiometric reaction is called the equivalence point. Experimentally we determine the titration s end point using a visual indicator that changes color near the equivalence point. Alternatively, we can locate the end point by recording a titration curve showing the titration reaction s progress as a function of the titrant s volume. In either case, the end point must closely match the equivalence point if a titration is to be accurate. Knowing the shape of a titration... 

The following experiments may he used to illustrate the application of titrimetry to quantitative, qtmlitative, or characterization problems. Experiments are grouped into four categories based on the type of reaction (acid-base, complexation, redox, and precipitation). A brief description is included with each experiment providing details such as the type of sample analyzed, the method for locating end points, or the analysis of data. Additional experiments emphasizing potentiometric electrodes are found in Chapter 11. 

This experiment outlines a potentiometric titration for determining the valency of copper in superconductors in place of the visual end point used in the preceding experiment of Harris, Hill, and Hewston. The analysis of several different superconducting materials is described. 

Tartaric acid, H2C4H4O6, is a diprotic weak acid with a pK i of 3.0 and a pK 2 of 4.4. Suppose you have a sample of impure tartaric acid (%purity > 80) and that you plan to determine its purity by titrating with a solution of 0.1 M NaOH using a visual indicator to signal the end point. Describe how you would carry out the analysis, paying particular attention to how much sample you would use, the desired pH range over which you would like the visual indicator to operate, and how you would calculate the %w/w tartaric acid. 

The purity of a synthetic preparation of methylethyl ketone (C4H8O) can be determined by reacting the ketone with hydroxylamine hydrochloride, liberating HCl (see Table 9.10). In a typical analysis, a 3.00-mL sample was diluted to 50.00 ml and treated with an excess of hydroxylamine hydrochloride. The liberated HCl was titrated with 0.9989 M NaOH, requiring 32.68 ml to reach the end point. Report the percent purity of the sample, given that the density of methylethyl ketone is 0.805 g/mL. 

The concentration of cyanide, CN, in a copper electroplating bath can be determined by a complexometric titration with Ag+, forming the soluble Ag(CN)2 complex. In a typical analysis a 5.00-mL sample from an electroplating bath is transferred to a 250-mL Erlenmeyer flask, and treated with 100 mL of H2O, 5 mL of 20% w/v NaOH, and 5 mL of 10% w/v Kl. The sample is titrated with 0.1012 M AgN03, requiring 27.36 mL to reach the end point as signaled by the formation of a yellow precipitate of Agl. Report the concentration of cyanide as parts per million of NaCN. 

End Point Determination Adding a mediator solves the problem of maintaining 100% current efficiency, but does not solve the problem of determining when the analyte s electrolysis is complete. Using the same example, once all the Fe + has been oxidized current continues to flow as a result of the oxidation of Ce + and, eventually, the oxidation of 1T20. What is needed is a means of indicating when the oxidation of Fe + is complete. In this respect it is convenient to treat a controlled-current coulometric analysis as if electrolysis of the analyte occurs only as a result of its reaction with the mediator. A reaction between an analyte and a mediator, such as that shown in reaction 11.31, is identical to that encountered in a redox titration. Thus, the same end points that are used in redox titrimetry (see Chapter 9), such as visual indicators, and potentiometric and conductometric measurements, may be used to signal the end point of a controlled-current coulometric analysis. For example, ferroin may be used to provide a visual end point for the Ce -mediated coulometric analysis for Fe +. 

Scale of Operation Coulometric methods of analysis can be used to analyze small absolute amounts of analyte. In controlled-current coulometry, for example, the moles of analyte consumed during an exhaustive electrolysis is given by equation 11.32. An electrolysis carried out with a constant current of 100 pA for 100 s, therefore, consumes only 1 X 10 mol of analyte if = 1. For an analyte with a molecular weight of 100 g/mol, 1 X 10 mol corresponds to only 10 pg. The concentration of analyte in the electrochemical cell, however, must be sufficient to allow an accurate determination of the end point. When using visual end points, coulometric titrations require solution concentrations greater than 10 M and, as with conventional titrations, are limited to major and minor analytes. A coulometric titration to a preset potentiometric end point is feasible even with solution concentrations of 10 M, making possible the analysis of trace analytes. 

Accuracy The accuracy of a controlled-current coulometric method of analysis is determined by the current efficiency, the accuracy with which current and time can be measured, and the accuracy of the end point. With modern instrumentation the maximum measurement error for current is about +0.01%, and that for time is approximately +0.1%. The maximum end point error for a coulometric titration is at least as good as that for conventional titrations and is often better when using small quantities of reagents. Taken together, these measurement errors suggest that accuracies of 0.1-0.3% are feasible. The limiting factor in many analyses, therefore, is current efficiency. Fortunately current efficiencies of greater than 99.5% are obtained routinely and often exceed 99.9%. 

Note that the method of end group analysis is inapplicable to copolymers, since the presence of more than one repeat unit adds extra uncertainty as to the nature of chain ends. The above example included the remark that the molecular weights calculated in the example were average values. In the next section we shall examine this point in greater detail. 

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