Introduction

Pharmaceutical analysis procedures may be used to answer any of the questions outlined in Box 1.1. The quality of a product may deviate from the standard required but in carrying out an analysis one also has to be certain that the quality of the analysis itself is of the standard required. Quality control is integral to all modern industrial processes and the pharmaceutical industry is no exception. Testing a pharmaceutical product involves chemical, physical and sometimes microbiological analyses. It has been estimated that £10 billion is spent each year on analyses in the UK alone and such analytical processes can be found in industries as diverse as those producing food, beverages, cosmetics, detergents, metals, paints, water, agrochemicals, biotechnological products and pharmaceuticals. With such large amounts of money being spent on analytical quality control, great importance must be placed on providing accurate and precise analyses (Box 1.2). Thus it is appropriate to begin a book on the topic of pharmaceutical analysis by considering, at a basic level, the criteria which are used to judge the quality of an analysis. The terms used in defining analytical quality form a rather elegant vocabulary that can be used to describe quality in many fields, and in writing this book the author would hope to describe each topic under consideration with accuracy, precision and, most importantly, reproducibility, so that the information included in it can be readily assimilated and reproduced where required by the reader. The following sections provide an introduction to the control of analytical quality. More detailed treatment of the topic is given in the reference cited at the end of the chapter.¹

Control of errors in analysis

A quantitative analysis is not a great deal of use unless there is some estimation of how prone to error the analytical procedure is. Simply accepting the analytical result could lead to rejection or acceptance of a product on the basis of a faulty analysis. For this reason it is usual to make several repeat measurements of the same sample in order to determine the degree of agreement between them. There are three types of errors which may occur in the course of an analysis: gross, systematic and random. Gross errors are easily recognised since they involve a major breakdown in the analytical process such as samples being spilt, wrong dilutions being prepared or instruments breaking down or being used in the wrong way. If a gross error occurs the results are rejected and the analysis is repeated from the beginning. Random and systematic errors can be distinguished in the following example:

A batch of paracetamol tablets are stated to contain 500 mg of paracetamol per tablet; for the purpose of this example it is presumed that 100% of the stated content is the correct answer. Four students carry out a spectrophotometric analysis of an extract from the tablets and obtain the following percentages of stated content for the repeat analysis of paracetamol in the tablets:

The means of these results can be simply calculated according to the formula:

     [Equation 1]

where is the arithmetic mean, x_i is the individual value and n is the number of measurements.

These results can be seen diagrammatically in Figure 1.1.

Fig. 1.1 Diagrammatic representation of accuracy and precision for analysis of paracetamol in tablet form.

Student 1 has obtained a set of results which are all clustered close to 100% of the stated content and with a mean for the five measurements very close to the correct answer. In this case the measurements made were both precise and accurate, and obviously the steps in the assay have been controlled very carefully.

Student 2 has obtained a set of results which are closely clustered, but give a mean which is lower than the correct answer. Thus, although this assay is precise, it is not completely accurate. Such a set of results indicates that the analyst has not produced random errors, which would produce a large scatter in the results, but has produced an analysis containing a systematic error. Such errors might include repeated inaccuracy in the measurement of a volume or failure to zero the spectrophotometer correctly prior to taking the set of readings. The analysis has been mainly well controlled except for probably one step, which has caused the inaccuracy and thus the assay is precisely inaccurate.

Student 3 has obtained a set of results which are widely scattered and hence imprecise, and which give a mean which is lower than the correct answer. Thus the analysis contains random errors or, possibly, looking at the spread of the results, three defined errors which have been produced randomly. The analysis was thus poorly controlled and it would require more work than that required in the case of student 2 to eliminate the errors. In such a simple analysis the random results might simply be produced by, for instance, a poor pipetting technique, where volumes both higher and lower than that required were measured.

Student 4 has obtained a set of results which are widely scattered yet a mean which is close to the correct answer. It is probably only chance that separates the results of student 4 from those of student 3 and, although the answer obtained is accurate, it would not be wise to trust it to always be so.

The best assay was carried out by student 1, and student 2 produced an assay that might be improved with a little work.

In practice it might be rather difficult to tell whether student 1 or student 2 had carried out the best analysis, since it is rare, unless the sample is a pure analytical standard, that the exact content of a sample is known. In order to determine whether student 1 or 2 had carried out the best assay it might be necessary to get other analysts to obtain similar sets of precise results in order to be absolutely sure of the correct answer. The factors leading to imprecision and inaccuracy in assay results are outlined in Box 1.3.

Accuracy and precision

The most fundamental requirements of an analysis are that it should be accurate and precise. It is presumed, although it cannot be proven, that a series of measurements (y) of the same sample will be normally distributed about a mean (μ), i.e. they fall into a Gaussian pattern as shown in Figure 1.2.

Fig. 1.2 The Gaussian distribution.

The distance σ shown in Figure 1.2 appears to be nearly 0.5 of the width of distribution; however, because the function of the curve is exponential it tends to zero and does not actually meet the x axis until infinity, where there is an infinitesimal probability that there may be a value for x. For practical purposes approximately 68% of a series of measurements should fall within the distance σ either side of the mean and 95% of the measurements should lie with 2σ of the mean. The aim in an analysis is to make σ as small a percentage of the value of μ as possible. The value of σ can be estimated using Equation 2:

     [Equation 2]

where:

Sometimes n rather than n – 1 is used in the equation but, particularly for small samples, it tends to produce an underestimate of σ. For a small number of values it is simple to work out s using a calculator and the above equation. Most calculators have a function which enables calculation of s directly and σ estimated using the above equation is usually labelled as σ_{n – 1}. For instance, if the example of results obtained by student 1, where the mean is calculated to be 99.9%, are substituted into equation 2, the following calculation results:

s = 0.46% of stated content

The calculated value for s provides a formal expression of the scatter in the results from the analysis rather than the visual judgement used in Figure 1.1. From the figure obtained for the standard deviation (SD), we can say that 68% of the results of the analysis will lie within the range 99.9 ± 0.46% (± σ) or within the range 99.44–100.36%. If we re-examine the figures obtained by student 1, it can be seen that 60% of the results fall within this range, with two outside the range, including one only very slightly below the range. The range based on ± σ defines the 68% confidence limits; for 95% confidence ± 2σ must be used, i.e. 95% of the results of student 1 lie within 99.9 ± 0.92% or 98.98–100.82%. It can be seen that this range includes all the results obtained by student 1.

The precision of an analysis is often expressed as the ± relative standard deviation (± RSD) (Equation 3).

     [Equation 3]

The confidence limits in this case are often not quoted but, since it is the SD that is an estimate of σ which is being used, they are usually 68%. The advantage of expressing precision in this way is that it eliminates any units and expresses the precision as a percentage of the mean. The results obtained from the assay of paracetamol tablets are shown in Table 1.1.

Table 1.1 Results obtained for the analysis of paracetamol tablets by four analysts

Validation of analytical procedures

The International Conference on Harmonisation (ICH) has adopted the following terms for defining how the quality of an assay is controlled.

Repeatability

Repeatability expresses the precision obtained under the same operating conditions over a short interval of time. Repeatability can also be termed intra-assay precision. It is likely that the assay would be repeated by the same person using a single instrument. Within repeatability it is convenient to separate the sample preparation method from the instrument performance. Figure 1.3 shows the levels of precision including some of the parameters which govern the system precision of a high-pressure liquid chromatography (HPLC) instrument. It would be expected that the system precision of a well-maintained instrument would be better than the overall repeatibility where sample extraction and dilution steps are prone to greater variation than the instrumental analysis step.

Fig. 1.3 Parameters involved in three levels of precision.

An excellent detailed summary of levels of precision is provided by Ermer. For example Figure 1.4 shows the results obtained from five repeat injections of a mixture of the steroids prednisone (P) and hydrocortisone (H) into a HPLC using a manual loop injector. The mixture was prepared by pipetting 5 ml of a 1 mg/ml stock solution of each steroid into a 100 ml volumetric flask and making up to volume with water.

Fig. 1.4 Repeat injection of a mixture of prednisone (0.05 mg/ml) and hydrocortisone (0.05 mg/ml) into a high-pressure liquid chromatography (HPLC) system.

The precision obtained for the areas of the hydrocortisone peak is ± 0.3%; the injection process in HPLC is generally very precise and one might expect even better precision from an automated injection system, thus this aspect of system precision is working well. The precision obtained for the prednisone peak is ± 0.6%; not quite as good, but this is not to do with the injector but is due to a small impurity peak (I) which runs closely after the prednisone causing some slight variation in the way the prednisone peak is integrated. The integration aspect of the system precision is not working quite as well when challenged with a difficulty in the integration method but the effect is really only minor. For the repeat, analysis is carried out on a subsequent day on a solution freshly prepared by the same method. The injection precision for hydrocortisone was ± 0.2%. The variation for the means of the areas of hydrocortisone peaks obtained on the 2 days was ± 0.8%; this indicates that there was small variation in the sample preparation (repeatability) between the 2 days since the variation in injection precision is ± 0.2%–± 0.3%. Usually it is expected that instrument precision is better than the precision of sample preparation if a robust type of instrument is used in order to carry out the analysis. Table 1.2 shows the results for the repeat absorbance measurement of the same sample with a UV spectrophotometer in comparison with the results obtained from measurement of five samples by a two-stage dilution from a stock solution. In both cases the precision is good but, as would be expected, the better precision is obtained where it is only instrumental precision that is being assessed. Of course instruments can malfunction and produce poor precision, for example a spectrophotometer might be nearing the end of the useful lifetime of its lamp and this would result in poor precision due to unstable readings.

Table 1.2 Comparison of precision obtained from the repeat measurement of the absorbance of a single sample compared with the measurement of the absorbance of five separately prepared dilutions of the same sample

Sample	Absorbance readings	RSD%
Repeat measurement	0.842, 0.844, 0.842, 0.845, 0.841	± 0.14
Repeat dilution/measurement	0.838, 0.840, 0.842, 0.845, 0.847	± 0.42

A target level for system precision is generally accepted to be < ± 1.0%.

This should be easily achievable in a correctly functioning HPLC system but might be more difficult in, for instance, a gas chromatography assay where the injection process is less well controlled. The tolerance levels may be set at much higher RSD in trace analyses where instruments are operated at higher levels of sensitivity and achieving 100% recovery of the analyte may be difficult.