1010 USP39-NF34 ANALYTICAL DATA INTERPRETATION AND TREATMENT (ÖÐÓ¢ÎÄ)

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System Performance Verification

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Verifying an acceptable level of performance for an analytical system in routine or continuous use can be a valuable practice. This may be accomplished by analyzing a control sample at appropriate intervals, or using other means, such as, variation among the standards, background signal-to-noise ratios, etc. Attention to the measured parameter, such as charting the results obtained by analysis of a control sample, can signal a change in performance that requires adjustment of the analytical system. An example of a controlled chart is provided in Appendix A.

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Procedure Validation

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All analytical procedures are appropriately validated as specified in Validation of Compendial Procedures <1225>. Analytical procedures published in the USP¨CNF have been validated and meet the Current Good Manufacturing Practices regulatory requirement for validation as established in the Code of Federal Regulations. A validated procedure may be used to test a new formulation (such as a new product, dosage form, or process intermediate) only after confirming that the new formulation does not interfere with the accuracy, linearity, or precision of the method. It may not be assumed that a validated procedure could correctly measure the active ingredient in a formulation that is different from that used in establishing the original validity of the procedure. [NOTE ON TERMINOLOGY¡ªThe definition of accuracy in <1225> and in ICH Q2 corresponds to unbiasedness only. In the International Vocabulary of Metrology (VIM) and documents of the International Organization for Standardization (ISO), accuracy has a different meaning. In ISO, accuracy combines the concepts of unbiasedness (termed trueness) and precision. This chapter follows the definition in <1225>, which corresponds only to trueness.]

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MEASUREMENT PRINCIPLES AND VARIATION

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All measurements are, at best, estimates of the actual (¨Dtrue¡¬ or ¨Daccepted¡¬) value for they contain random

variability (also referred to as random error) and may also contain systematic variation (bias). Thus, the measured value differs from the actual value because of variability inherent in the measurement. If an array of measurements consists of individual results that are representative of the whole, statistical methods can be used to estimate informative properties of the entirety, and statistical tests are available to investigate whether it is likely that these properties comply with given requirements. The resulting statistical analyses should address the variability associated with the measurement process as well as that of the entity being measured. Statistical measures used to assess the direction and magnitude of these errors include the mean, standard deviation, and expressions derived therefrom, such as the percent coefficient of variation (%CV; also called the percent relative standard deviation, %RSD). The estimated variability can be used to calculate confidence intervals for the mean, or measures of variability, and tolerance intervals capturing a specified proportion of the individual measurements.

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The use of statistical measures must be tempered with good judgment, especially with regard to representative sampling. Data should be consistent with the statistical assumptions used for the analysis. If one or more of these assumptions appear to be violated, alternative methods may be required in the evaluation of the data. In particular, most of the statistical measures and tests cited in this chapter rely on the assumptions that the distribution of the entire population is represented by a normal distribution and that the analyzed sample is a representative subset of this population. The normal (or Gaussian) distribution is bell-shaped and symmetric about its center and has certain characteristics that are required for these tests to be valid. The data may not always be expected to be normally distributed and may require a transformation to better fit a normal distribution. For example, there exist variables that

have distributions with longer right tails than left. Such distributions can often be made approximately normal through a log transformation. An alternative approach would be to use ¨Ddistribution-free¡¬ or ¨Dnonparametric¡¬ statistical procedures that do not require that the shape of the population be that of a normal distribution. When the objective is to construct a confidence interval for the mean or for the difference between two means, for example, then the normality assumption is not as important because of the central limit theorem. However, one must verify normality of data to construct valid confidence intervals for standard deviations and ratios of standard deviations, perform some outlier tests, and construct valid statistical tolerance limits. In the latter case, normality is a critical assumption. Simple graphical methods, such as dot plots, histograms, and normal probability plots, are useful aids for investigating this assumption. ʹÓÃͳ¼ÆÁ¿±ØÐëÓÐÁ¼ºÃµÄÅжϼÓÒÔµ÷½Ú£¬ÌرðÊÇÒª¿¼Âǵ½³éÑùµÄ´ú±íÐÔ¡£Êý¾Ý±ØÐëÓë·ÖÎöÓõ½µÄͳ¼Æ¼ÙÉèÏàÒ»Ö¡£Èç¹ûÓÐÒ»¸ö»ò¶à¸ö¼ÙÉè³öÏÖ²»Ïà·û£¬ÔòÐèÒª²ÉÓÃÌæ´úµÄ·½·¨½øÐÐÊý¾ÝÆÀ¼Û¡£ÌرðÓ¦Ö¸³öµÄÊÇ£¬±¾ÕÂËùÒýÓõÄͳ¼ÆÁ¿ºÍ¼ìÑé¶¼ÊÇ»ùÓÚ¼ÙÉè×ÜÌå·ûºÏÕý̬·Ö²¼£¬²¢ÇÒ¼ÙÉèËù·ÖÎöµÄÑù±¾ÊÇÄÜ´ú±í×ÜÌåµÄÒ»¸öÑÇÌ壨Subset£©¡£Õý̬·Ö²¼£¨Ò²½Ð¸ß˹·Ö²¼£©ÊÇÒ»¸öÖÓÐÎÇÒ³ÊÖÐÐĶԳÆÐÎ×´µÄ·Ö²¼£¬²¢ÇÒÓÐһЩÓÃÓÚ¼ìÑéµÄÌØÕ÷ÐèÒª±»ÑéÖ¤¡£Êý¾Ý²¢·Ç×ÜÊÇ·ûºÏÕý̬·Ö²¼µÄ£¬ÕâʱÐèÒª½øÐÐÊʵ±×ª»»ÒÔ±ãÆä¸üºÃµØ·ûºÏÕý̬·Ö²¼¡£ÀýÈ磬´æÔÚ×ÅһЩ±äÁ¿¾ßÓг¤ÓÒβ·Ö²¼¡£ÕâÑùµÄ·Ö²¼¾­³£Í¨¹ý¶ÔÊýת»»½«Æä±äΪ·ûºÏ½üËÆÕý̬·Ö²¼¡£Ò²¿ÉʹÓá°²»ÒÀÀµÓÚ·Ö²¼¡±»ò¡°·Ç²ÎÊý¡±µÄÌæ´úͳ¼Æ·½·¨£¬¸ÃÀà·½·¨²»ÒªÇóÊý¾Ý·ûºÏÕý̬·Ö²¼¡£µ±Ä¿±êÊǼÆËã¾ùÖµ»òÁ½¾ùÖµ²îµÄÖÃÐÅÇø¼äʱ£¬ÄÇô£¬ÆäÕý̬ÐÔ¼ÙÉè¾ÍÒòÖÐÐļ«ÏÞ¶¨Àí£¨central limit theorem£©¶ø²»ÔÙÄÇÃ´ÖØÒª¡£µ«ÊÇ£¬ÈËÃDZØÐëÊ×ÏÈÑéÖ¤Êý¾ÝµÄÕý̬ÐÔ£¬²ÅÄܼÆËã³öÕýÈ·ÓÐЧµÄ±ê×¼²îµÄÖÃÐÅÇø¼äºÍ±ê׼ƫ²î±È¡¢½øÐÐÒì³£Öµ¼ì²â²¢ÇÒ¼ÆËã³öÕýÈ·ÓÐЧµÄͳ¼ÆÈÝÈÌÏ޵ȡ£¶ÔÓÚºóÕߣ¬Õý̬ÐÔÊÇÖÁ¹ØÖØÒªµÄ¼ÙÉ衣һЩ¼òµ¥µÄ×÷ͼ·¨£¨ÈçÉ¢µãͼ¡¢Öù״ͼºÍÕý̬¸ÅÂÊͼ£©¶ÔÓÚ·ÖÎöÕý̬ÐÔ¼ÙÉè·Ç³£ÓÐÓá£

A single analytical measurement may be useful in quality assessment if the sample is from a whole that has been prepared using a well-validated, documented process and if the analytical errors are well known. The obtained analytical result may be qualified by including an estimate of the associated errors. There may be instances when one might consider the use of averaging because the variability associated with an average value is always reduced as compared to the variability in the individual measurements. The choice of whether to use individual measurements or averages will depend upon the use of the measure and its variability. For example, when multiple measurements are obtained on the same sample aliquot, such as from multiple injections of the sample in an HPLC method, it is generally advisable to average the resulting data for the reason discussed above.

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Variability is associated with the dispersion of observations around the center of a distribution. The most

commonly used statistic to measure the center is the sample mean (x):

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Analytical procedure variability can be estimated in various ways. The most common and useful assessment of a procedure's variability is the determination of the standard deviation based on repeated independent1 measurements of a sample. The sample standard deviation, s, is calculated by the formula:

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in which xi is the individual measurement in a set of n measurements; and x is the mean of all the measurements. The percent relative standard deviation (%RSD) is then calculated as:

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and expressed as a percentage. If the data requires log transformation to achieve normality (e.g., for biological assays), then alternative methods are available2.

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1

Multiple measurements (or, equivalently, the experimental errors associated with the multiple measurements) are independent from one another when they can be assumed to represent a random sample from the population. In such a sample, the magnitude of one measurement is not influenced by, nor does it influence the magnitude of, any other measurement. Lack of independence implies the measurements are correlated over time or space. Consider the example of a 96-well microtiter plate. Suppose that whenever the

unknown causes that produce experimental error lead to a low result (negative error) when a sample is placed in the first column and these same causes would also lead to a low result for a sample placed in the second column, then the two resulting measurements would not be statistically independent. One way to avoid such possibilities would be to randomize the placement of the samples on the plate. µ±¿ÉÒÔ¼Ù¶¨ËûÃÇÊÇÀ´×ÔÓÚͬһÕûÌåµÄËæ»ú´ú±íÑù±¾£¬¶à´Î²âÁ¿ÊDZ˴˶ÀÁ¢µÄ£¬Í¬ÑùµÄÓë¶à´Î²âÁ¿Ïà¹ØµÄʵÑéÎó²îÒ²ÊDZ˴˶ÀÁ¢µÄ¡£ÔÚÕâÑùÒ»¸öÑù±¾ÖУ¬µ¥´Î²âÁ¿µÄÁ¿Öµ²»»á±»ÆäËûµÄ²âÁ¿Ëù¸ÉÈÅ£¬Ò²²»»á¸ÉÈÅÆäËû²âÁ¿µÄÁ¿Öµ¡£È±·¦¶ÀÁ¢ÐÔÒâζ×ŲâÁ¿ÖµÓëʱ¼ä»ò¿Õ¼äÏà¹Ø¡£ÏëÏóÏÂ96¿×°åµÄÀý×Ó¡£¼ÙÉèµ±ÑùÆ·ÖÃÓÚµÚÒ»¿×ÉÏʱδ֪µÄʵÑéÎó²îÒòËØÔÚÈκÎʱºò¶¼µ¼ÖÂÒ»¸öÆ«µÍµÄ½á¹û£¨ÒõÐÔ½á¹û£©£¬ÕâЩÏàͬµÄÒòËØÒ²¶ÔµÚ¶þ¿×ÉϵÄÑù±¾µ¼ÖÂÁËÆ«µÍ½á¹û£¬ÄÇôÕâÁ½¸ö²âÁ¿½á¹û¾Í²»ÄÜÂú×ã¶ÀÁ¢ÐÔµÄÒªÇó¡£±ÜÃâÕâÖÖ¿ÉÄÜÐÔµÄÒ»ÖÖ·½·¨ÊÇÔÚ°åÉÏËæ»ú·ÅÖÃÑù±¾¡£

2

When data have been log (base e) transformed to achieve normality, the %RSD is:

This can be reasonably approximated by: where s is the standard deviation of the log (base e) transformed data. µ±Êý¾Ý½øÐÐÁ˶ÔÊýת»»ÒÔ»ñµÃÕý̬ÐÔºó£¬%RSD¼ÆË㹫ʽΪ Ò²¿ÉÒÔºÏÀíµÄ¼ò»¯Îª ÆäÖÐsÊÇ×ÔÈ»¶ÔÊýת»»ºóÊý¾ÝµÄ±ê׼ƫ²î¡£

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