Preface It has been more than a decade since the publication of the We would also like to take this opportunity to extend our fifth edition, and understandably numerous changes have heartfelt thanks to Melissa Turner and Kristi Anderson, who come about, not the least of which are changes in authorship have ably shepherded us through the intricacies of dealing as well as rapid progress in the various fields of clinical scien- with a new publisher, Elsevier, who purchased Academic tific endeavor. First of all, we’d like to pay tribute to a num- Press, the publisher for the first five editions. Our thanks ber of our previous authors who have passed away since the also go to Julie Ochs who has ably guided us through the publication of the fifth edition. Notably, they are Drs. Duane final steps of the printing and publication process. They F. Brobst (Pancreas), Charles C. Capen (Calcium), Jens G. have all been extremely diligent, having been almost at our Hauge (Genetics), and Joseph E. Smith (Iron). All succumbed beck and call for assistance, clarification, guidance, and to cancers of various types except for Dr. Smith, who died in a encouragement at every step of the way. To all three of our tragic auto accident. Others have retired and chose not to con- publisher contacts, we are extremely grateful. tribute or to contribute in a secondary role. All of these authors Finally, we must acknowledge and express our thanks contributed greatly to previous editions and are sorely missed to our families who have been incredibly supportive in our as contributors at the forefront of their respective fields. It is almost single minded effort to bring this current edition to all these contributors that the editors of this current edition to fruition. Without their unqualified support, this work wish to dedicate this new volume. New lead authors have would have been most difficult to accomplish and perhaps been identified and have contributed ably to this edition. not even possible. As in previous editions, this edition continues to pro- J. Jerry Kaneko mote the concept of the Systeme International d’Unites (SI John W. Harvey units) with the hope and expectation that ultimately it may Michael L. Bruss be universally accepted. ix PPRREE--PP337700449911..iinndddd iixx 66//2255//22000088 44::3377::4488 PPMM Contributors Numbers in parentheses indicate the pages on which the authors ’ contributions begin. Håkan Andersson ( 635 ) Department of Integrative Biology, Laurel J. Gershwin (157) Department of Pathology, Umea University, SE-90187 Umea, Sweden Microbiology and Immunology, School of Veterinary Medicine, University of California, Davis, Davis, CA Cleta Sue Bailey (769) Department of Surgical and 95616 Radiological Sciences, School of Veterinary Medicine, University of California, Davis, Davis, CA 95616 Urs Giger (27, 731) School of Veterinary Medicine, Jean-Pierre Braun (485) Department of Physiopathology University of Pennsylvania, Philadelphia, PA 19104-6010 and Experimental Toxicology, National School of John W. Harvey (173, 259) Department of Physiological Veterinary Medicine of Toulouse, 31076 Toulouse, Sciences, College of Veterinary Medicine, University of France Florida, Gainesville, FL 32610 Michael L. Bruss (81, 529) Department of Anatomy, Mark Haskins (27, 731) Department of Pathology, School Physiology and Cell Biology School of Veterinary of Veterinary Medicine, University of Pennsylvania, Medicine, University of California, Davis, Davis, CA Philadelphia, PA 19104-6010 95616 Walter E. Hoffmann (351) Department of Veterinary Hilary Burgess (287) Department of Pathobiology, Pathobiology, College of Veterinary Medicine, Ontario Veterinary College, University of Guelph, University of Illinois, Urbana, IL 61801 Guelph, Ontario, N1G2W1, Canada William E. Hornbuckle (413) Department of Clinical Gary P. Carlson (529) Department of Medicine and Sciences, New York State College of Veterinary Epidemiology, School of Veterinary Medicine, Medicine, Cornell University, Ithaca, NY 14853 University of California, Davis, Davis, CA 95616 J. Jerry Kaneko (45, 241, 623) Department of Pathology, Stan W. Casteel (821) Medical Diagnostic Laboratory, Microbiology and Immunology, School of Veterinary College of Veterinary Medicine University of Missouri, Medicine, University of California, Davis, Davis, CA Columbia, MO 65205 95616 Sharon A. Center (379) Department of Clinical Sciences, Carl L. Keen (663) Department of Nutrition, College of New York State College of Veterinary Medicine, Cornell Agriculture and Environmental Sciences, University of University, Ithaca, NY 14853 California, Davis, Davis, CA 95616 P. David Eckersall (117) Division of Animal Production Kurt V. Kreutzer (821) Department of Biomedical and Public Health, Institute of Comparative Medicine, Sciences, College of Veterinary Medicine, University University of Glasgow, Glasgow G61-1QH, Scotland, UK of Missouri, Columbia, MO 65211 Thomas B. Farver (1) Department of Population Health and Reproduction, School of Veterinary Medicine, Herve P. Lefebvr e (485) Department of Physiopathology and University of California, Davis, Davis, CA 95616 Experimental Toxicology, National School of Veterinary Medicine of Toulouse, 31076 Toulouse, France Andrea J. Fascetti (663, 695) Department of Molecular Biosciences, School of Veterinary Medicine, University Michael D. Lucroy (751) VCA Veterinary Specialty of California, Davis, Davis, CA 95616 Center, Indianapolis, IN 46820 Patricia Gentry (287) Department of Biomedical J.T. Lumeij (839) Department of Clinical Sciences of Sciences, Ontario Veterinary College Guelph, Companion Animals, Faculty of Veterinary Medicine, University of Guelph, Ontario, N1G2W1, Canada Utrecht University, 3584 CM Utrecht, The Netherlands vii CCTTRR--PP337700449911..iinndddd vviiii 66//2255//22000088 44::3344::2211 PPMM viii Contributors Björn P. Meij (561, 605) Department of Clinical Sciences Stephanie J. Valberg (459) Department of Veterinary of Companion Animals, Faculty of Veterinary Medicine, Population Medicine College of Veterinary Medicine, Utrecht University, 3584 CM Utrecht, The Netherlands University of Minnesota, St. Paul, MN 55108 Jan A. Mol (561, 605) Department of Clinical Sciences of Karen A. Vernau (769) Department of Surgical and Companion Animals, Faculty of Veterinary Medicine, Radiological Sciences, School of Veterinary Medicine, Utrecht University, 3584 CM Utrecht, The Netherlands University of California, Davis, Davis, CA 95616 James G. Morris (695) Department of Molecular Biosciences, William Vernau (769) Department of Pathology, School of Veterinary Medicine, University of California, Microbiology and Immunology School of Veterinary Davis, Davis, CA 95616 Medicine, University of California, Davis, Davis, CA Robert B. Rucker (663, 695) Department of Nutrition, 95616 College of Agriculture and Environmental Sciences, Bruce Walcheck (331) Department of Veterinary and University of California, Davis, Davis, CA 95616 Biomedical Sciences, College of Veterinary Medicine, Kenneth W. Simpson (413) Department of Clinical University of Minnesota, St. Paul, MN 55108 Sciences, College of Veterinary Medicine, Cornell University, Ithaca, NY 14853-6401 Douglas J. Weiss (331) Department of Veterinary Pathobiology, College of Veterinary Medicine, Philip F. Solter (351) Department of Veterinary Pathobiology, University of Minnesota, St. Paul, MN 55108 College of Veterinary Medicine, University of Illinois, Urbana, IL 61801 Petra Werner (27) Department of Medicine, Section of Medical Genetics, School of Veterinary Medicine, Bud C. Tennant (379, 413) Department of Clinical University of Pennsylvania, Philadelphia, PA 19104-6010 Sciences, New York State College of Veterinary Medicine, Cornell University, Ithaca, NY 14853 Darren Wood (287) Department of Pathobiology, Ontario James R. Turk (821) Department of Biomedical Sciences, Veterinary College, University of Guelph, Guelph, College of Veterinary Medicine, University of Missouri, Ontario, N1G2W1, Canada Columbia, MO 65211 CCTTRR--PP337700449911..iinndddd vviiiiii 66//2255//22000088 44::3344::2222 PPMM Chapter 1 Concepts of Normality in Clinical Biochemistry Thomas B. Farver Department of Population Health and Reproduction School of Veterinary Medicine University of California, Davis Davis, California of disease. Whether a given dog belongs to the population I. POPULATIONS AND THEIR DISTRIBUTIONS of healthy dogs depends on someone’s ability to determine II. R EFERENCE INTERVAL DETERMINATION if the dog is or is not free of disease. Populations may be AND USE finite or infinite in size. A. Gaussian Distribution A population can be described by quantifiable charac- B. Evaluating Probabilities Using a Gaussian Distribution teristics frequently called o bservations or measures . If it C. Conventional Method for Determining Reference were possible to record an observation for all members in Intervals the population, one most likely would demonstrate that not D. Methods for Determining Reference Intervals for Analytes all members of the population have the same value for the Not Having the Gaussian Distribution given observation. This reflects the inherent variability in E. Sensitivity and Specifi city of a Decision Based on a populations. For a given measure, the list of possible val- Reference Interval ues that can be assumed with the corresponding frequency F. Predictive Value of a Decision Based on a with which each value appears in the population relative to Reference Interval the total number of elements in the population is referred G. ROC Analysis to as the distribution of the measure or observation in the III. ACCURACY IN ANALYTE MEASUREMENTS IV. PRECISION IN ANALYTE MEASUREMENTS population. Distributions can be displayed in tabular or V. INFERENCE FROM SAMPLES graphical form or summarized in mathematical expressions. A. Simple Random Sampling Distributions are classified as discrete distributions or con- B. Descriptive Statistics tinuous distributions on the basis of values that the mea- C. Sampling Distributions sure can assume. Measures with a continuous distribution D. Constructing an Interval Estimate of the can assume essentially an infinite number of values over Population Mean, μ some defined range of values, whereas those with a dis- E. Comparing the Mean Response of crete distribution can assume only a relatively few values Two Populations within a given range, such as only integer values. F. Comparing the Mean Response of Three or Each population distribution can be described by quan- More Populations Using Independent Samples tities known as p arameters . One set of parameters of a G. Effi ciency in Experimental Designs population distribution provides information on the center H. Nesting Designs of the distribution or value(s) of the measure that seems REFERENCES to be assumed by a preponderance of the elements in the population. The mean, median, and mode are three mem- bers of the class of parameters describing the center of the I . POPULATIONS AND THEIR distribution. Another class of parameters provides informa- DISTRIBUTIONS tion on the spread of the distribution. Spread of the distri- bution has to do with whether most of the values that are A population is a collection of individuals or items having assumed in the population are close to the center of the something in common. For example, one could say that the distribution or whether a wider range of values is assumed. population of healthy dogs consists of all dogs that are free The standard deviation, variance, and range are examples Copyright © 2008, Elsevier Inc. Clinical Biochemistry of Domestic Animals, 6th Edition 1 All rights reserved. CCHH000011--PP337700449911..iinndddd 11 66//2277//22000088 1100::3366::0077 AAMM 2 Chapter | 1 Concepts of Normality in Clinical Biochemistry of parameters that provide information on the spread of the distribution. The shape of the distribution is very important. Some distributions are symmetric about their center, whereas other distributions are asymmetric, being N (m, s2) skewed (having a heavier tail) either to the right or to 68.26% the left. II . REFERENCE INTERVAL 13.59% 13.59% DETERMINATION AND USE m(cid:3)2s m(cid:3)1s m m(cid:5)1s m(cid:5)2s One task of clinicians is determining whether an animal FIGURE 1-1 The Gaussian distribution. that enters the clinic has blood and urine analyte values that are in the normal interval. The conventional method of establishing normalcy for a particular analyte is based on the assumption that the distribution of the analyte in the values, the frequency distribution is Gaussian. Figure 1-2 , population of normal animals is the “ normal ” or Gaussian adapted from the printout of MINITAB, Release 14.13,1 distribution. To avoid confusion resulting from the use of gives an example of the distribution of glucose values given a single word having two different meanings, the “ nor- in Table 1-1 for a sample of 168 dogs from a presumably mal ” distribution henceforth is referred to as the Gaussian healthy population. distribution. [To produce this figure, place the glucose values for the 168 dogs in one column of a MINITAB worksheet and give the following commands: A . Gaussian Distribution Understanding the conventional method for establishing Stat (from the main menu)→ Basic Statistics normalcy requires an understanding of the properties of → GGraphical Summary the Gaussian distribution. Theoretically, a Gaussian distri- bution is defined by the equation In the Graphical Summary dialog box, select the column of the worksheet containing the glucose values and place it y(cid:2) 1 e(cid:3)(x(cid:3)μ)2/2σ2 in the Variables: box. Hit OK . 2πσ Though not perfectly Gaussian, the distribution is rea- sonably well approximated by the Gaussian distribution. where x is any value that a given measurement can Support for this claim is that the distribution has the char- assume, y is the relative frequency of x , μ is the center acteristic bell shape and appears to be symmetric about of the distribution, σ is the standard deviation of the the mean. Also, the mean [estimated to be 96.4 mg/dl distribution, π is the constant 3.1416, and e is the constant (5.34 mmol/liter)] of this distribution is nearly equal to the 2.7183. median [estimated to be 95.0 mg/dl (5.27 mmol/liter)], which Theoretically, x can take on any value from (cid:3) (cid:4) to (cid:5) (cid:4) . is characteristic of the Gaussian distribution. The estimates Figure 1-1 gives an example of a Gaussian distribution of the skewness and kurtosis coefficients are close to zero, and demonstrates that the distribution is symmetric around also characteristic of a Gaussian distribution ( Daniel, 2005 ; μ and is bell shaped. Figure 1-1 also shows that 68% of Schork and Remington, 2000 ; Snedecor and Cochran, the distribution is accounted for by measurements of x that 1989 ). have a value within 1 standard deviation of the mean, and 95% of the distribution includes those values of x that are within 2 standard deviations of the mean. Nearly all of the B . Evaluating Probabilities Using distribution (97.75%) is contained by the bound of 3 stan- a Gaussian Distribution dard deviations of the mean. All Gaussian distributions can be standardized to the ref- Most analytes cannot take on negative values and so, erence Gaussian distribution, which is called the s tandard strictly speaking, cannot have Gaussian distributions. However, the distribution of many analyte values is approxi- mated well by the Gaussian distribution because virtually all the values that can be assumed by the analyte are within 1 MINITAB, Inc., Quality Plaza, 829 Pine Hall Road, State College, PA 4 standard deviations of the mean and, for this range of 16801-3008. CCHH000011--PP337700449911..iinndddd 22 66//2277//22000088 1100::3366::0088 AAMM II. Reference Interval Determination and Use 3 Anderson-Darling normality test A-squared 0.51 P-value 0.190 Mean 96.429 StDev 14.619 Variance 213.707 Skewness (cid:3)0.0944703 Kurtosis 0.0706586 N 168 Minimum 57.000 1st quartile 87.000 Median 95.000 3rd quartile 107.000 60 75 90 105 125 135 Maximum 136.000 95% Confidence interval for mean 94.202 98.655 95% Confidence interval for median 94.000 98.177 95% Confidence interval for StDev 95% Confidence intervals 13.205 16.374 Mean Median 94 95 96 97 98 99 FIGURE 1-2 Distribution and summary statistics for the sample of canine glucose values (mg/dl) in Table 1-1. Printout of MINITAB, Release 14.13. Gaussian distribution . Standardization in general is accom- are traditionally designated by the letter z so that it can be plished by subtracting the center of the distribution from said that z is N (0,1). That all Gaussian distributions can be a given element in the distribution and dividing the result transformed to the standard Gaussian distribution is con- by the standard deviation of the distribution. The distri- venient in that just a single table is required to summarize bution of a standardized Gaussian distribution—that is, a the probability structure of the infinite number of Gaussian Gaussian distribution that has its elements standardized distributions. Table 1-2 provides an example of such a in this form—has its center at zero and has a variance of table and gives the percentiles of the standard Gaussian unity. The elements of the standard Gaussian distribution distribution. Example 1 Suppose the underlying population of elements is N (4,16) 40th percentile. Thus, the probability of observing a z value and one element from this population is selected. We want less than or equal to (cid:3) 0.25 is approximately 0.40. The prob- to find the probability that the selected element has a value ability of observing x (cid:7) 6.1 is equivalent to the probability less than 3.0 or greater than 6.1. In solving this problem, the of observing z (cid:7) (6.1 (cid:3) 4)/(4) (cid:2) (cid:5) 0.525. Table 1-2 gives the relevant distribution is specified: x is N (4,16). The probabil- probability of observing a z (cid:6) 0.525 as approximately 0.70, so ity of observing x (cid:6) 3.0 in the distribution of x is equivalent the probability of observing a z (cid:7) 0.525 approximately equals to the probability of observing z (cid:6) (3.0 (cid:3) 4)/4 (cid:2) (cid:3) 0.25 in the 1 (cid:3) 0.70 or 0.30. The desired probability of observing a sample standard Gaussian distribution. Going to Table 1-2 , z (cid:2) 0.25 is observation less than 3.0 or greater than 6.1 is the sum of 0.40 approximately the 60th percentile of the standard Gaussian and 0.30, which is approximately 0.7 or 7 chances in 10. distribution and by symmetry z (cid:2) (cid:3) 0.25 is approximately the CCHH000011--PP337700449911..iinndddd 33 66//2277//22000088 1100::3366::0099 AAMM 4 Chapter | 1 Concepts of Normality in Clinical Biochemistry TABLE 1-1 Glucose (Glu, mg/dl) and Alanine Aminotransferase (ALT,U/l) for a Sample of 168 Dogs from the Population of Healthy Dogsa Dog Glu ALT Dog Glu ALT Dog Glu ALT Dog Glu ALT 1 88 60 43 86 53 85 110 54 127 108 105 2 104 79 44 86 50 86 78 54 128 90 32 3 89 138 45 115 72 87 95 37 129 100 25 4 99 58 46 98 59 88 111 25 130 96 46 5 63 34 47 98 80 89 116 115 131 86 95 6 97 43 48 99 42 90 108 60 132 100 99 7 94 47 49 94 42 91 76 36 133 122 115 8 105 77 50 104 116 92 111 102 134 109 60 9 86 102 51 107 98 93 86 62 135 77 67 10 124 34 52 107 78 94 101 43 136 88 83 11 118 64 53 119 56 95 106 73 137 94 118 12 112 184 54 114 38 96 92 99 138 92 44 13 85 82 55 94 50 97 67 50 139 121 64 14 109 35 56 109 47 98 75 24 140 86 19 15 96 46 57 110 32 99 127 110 141 84 68 16 72 29 58 99 53 100 87 65 142 86 74 17 91 117 59 105 97 101 136 44 143 105 86 18 94 132 60 102 97 102 94 40 144 91 47 19 90 68 61 100 54 103 89 18 145 92 56 20 68 50 62 83 36 104 72 30 146 89 49 21 84 95 63 83 32 105 87 75 147 123 78 22 94 140 64 108 111 106 96 66 148 109 93 23 91 38 65 114 63 107 85 113 149 117 46 24 90 146 66 105 58 108 95 63 150 115 31 25 72 68 67 74 24 109 96 61 151 83 65 26 87 42 68 92 96 110 117 62 152 94 55 27 94 43 69 97 42 111 106 33 153 92 52 28 97 84 70 85 101 112 113 99 154 109 64 29 103 44 71 83 46 113 107 97 155 92 59 30 70 84 72 86 58 114 96 131 156 93 49 31 91 108 73 110 29 115 94 44 157 92 29 32 58 28 74 121 115 116 100 68 158 101 66 33 89 75 75 87 62 117 127 37 159 113 53 34 81 38 76 88 40 118 106 52 160 92 79 35 106 38 77 114 78 119 93 113 161 110 47 36 94 26 78 96 83 120 99 142 162 116 46 37 57 89 79 107 26 121 94 45 163 111 137 38 67 35 80 101 19 122 82 80 164 111 57 39 93 69 81 90 105 123 130 53 165 70 49 40 89 44 82 110 133 124 76 87 166 94 80 41 80 47 83 65 56 125 99 36 167 106 53 42 112 41 84 95 70 126 81 31 168 102 128 a These data were provided by Dr. J. J. Kaneko, Department of Pathology, Microbiology and Immunology, School of Veterinary Medicine, University of California, Davis. CCHH000011--PP337700449911..iinndddd 44 66//2277//22000088 1100::3366::1100 AAMM II. Reference Interval Determination and Use 5 2.5% of the animals would have an analyte value above 2 TABLE 1-2 Percentiles of the Standard Gaussian (z) standard deviations above the mean. So with this classi- Distributiona ,b fication scheme, there is a 5% chance that a true normal z (cid:2) 0 z (cid:2) 1.282 z (cid:2) 1.960 animal would be classified as being abnormal. Clinicians, 0.50 0.90 0.975 by choosing 2 as the multiple, are willing to designate nor- z (cid:2) 0.126 z (cid:2) 1.341 z (cid:2) 2.054 0.55 0.91 0.98 mal animals with extreme values of a particular analyte as z 0.60 (cid:2) 0.253 z0 .92 (cid:2) 1.405 z0 .99 (cid:2) 2.326 being abnormal as the trade-off for not accepting too many z (cid:2) 0.385 z (cid:2) 1.476 z (cid:2) 2.576 abnormal animals as normals. With this methodology, no 0.65 0.93 0.995 z (cid:2) 0.524 z (cid:2) 1.555 z (cid:2) 3.090 consideration is given to the distribution of abnormal ani- 0.70 0.94 0.999 mals because in fact there would be multiple distributions z (cid:2) 0.674 z (cid:2) 1.645 z (cid:2) 3.719 0.75 0.95 0.9999 corresponding to the many types of abnormalities. The z (cid:2) 0.842 z (cid:2) 1.751 z (cid:2) 4.265 0.80 0.96 0.99999 assumption is that for those cases where an analyte would z 0.85 (cid:2) 1.036 z0 .97 (cid:2) 1.881 be useful in identification of abnormal animals, the value of the analyte would be sufficiently above or below the a This table was generated with MINITAB Release 14.13 as follows: The indicated cumulative probabilities 0.5 to 0.99999 were placed in a column of a MINITAB center of the distribution of the analyte for normal animals. worksheet and the following commands given: The reference interval for glucose based on the distribution Calc (from the main menu of MINITAB) → Probability Distributions → Normal from the sample of 168 normal dogs is 96.42857 mg/dl (cid:8) Distribution. Within the Normal Distribution dialog box, Inverse cumulative probability was selected, Mean was set to 0.0, Standard deviation was set to 1.0, (1.96 (cid:9) 14.61873 mg/dl) or 67.8 mg/dl (3.76 mmol/liter) to and the column of the worksheet containing the cumulative probabilities was selected 125.1 mg/dl (6.94 mmol/liter). and placed in the Input column: followed by hitting OK. Solberg (1999) gave 1/ α as the theoretical minimum b Example: The 75th percentile, or the z value below, which is 75% of the Gaussian distribution, equals 0.674, z (cid:2) 0.674. Percentiles smaller than the 50th percentile sample size for estimation of the 100 α and 100(1 (cid:3) α ) 0.75 can be found by noting that the Gaussian distribution is symmetric about zero so that, percentiles. Thus, a minimum of 40 animals is required to for example, z (cid:2) (cid:3) 0.524. 0.30 estimate the 2.5th and 97.5th percentiles but many more than 40 is recommended. C . Conventional Method for Determining D . Methods for Determining Reference Reference Intervals Intervals for Analytes Not Having the Gaussian Distribution The first step in establishing a normal interval by the con- ventional method involves determining the mean and stand- The conventional procedure for assessing normalcy ard deviation of the distribution of the analyte. This can works quite well provided the distribution of the analyte be accomplished by taking a representative sample (using is approximately Gaussian. Unfortunately, for many ana- a sampling design that has a random component such as lytes a Gaussian distribution is not a good assumption. For simple random sampling) from the population of normal example, Figure 1-3 describes the distribution of alanine animals and computing the mean and standard deviation of aminotransferase (ALT) values given in Table 1-1 for the the sample. same sample of 168 normal dogs. This distribution is vis- Once these estimates of μ and σ are obtained, an animal ibly asymmetric. The distribution has a longer tail to the coming into the clinic in the future is classified as being right and is said to be skewed to the right or positively normal for a particular analyte if its value for the analyte is skewed. The skewness value (0.93) exceeds the approxi- within the bound of some multiple of the standard deviation mate 99th percentile of the distribution for this coefficient below the mean and some multiple of the standard deviation for random samples from a population having a Gaussian above the mean. The multiple is determined by the degree distribution. That the distribution is not symmetric and of certainty that one desires to place on the classification hence not Gaussian is also evidenced by the lack of agree- scheme. For example, if the multiple chosen is 2, which is ment between the mean and median as shown in Figure 1- the conventional choice, any animal entering the clinic with 3 . Application of the conventional procedure for computing an analyte value within 2 standard deviations of the mean reference intervals [x (cid:8) (1.96 (cid:9) SD)] reveals a reference would be classified as normal, whereas all animals with a interval of 4.4 to 127.7U/liter so that all the low values of value of the analyte outside this boundary would be classi- the distribution fall above the value, which is 2 standard fied as abnormal. Because 95% of the Gaussian distribution deviations below the mean of the distribution, and more is located within 1.96 or approximately 2 standard devia- than 2.5% of the high values fall above the value, which is tions of the mean, with this classification scheme, 2.5% of 2 standard deviations above the mean. The following sec- the normal animals would have a value of the analyte that tions give two approaches that can be followed in such a would be below 2 standard deviations below the mean, and situation to obtain reference intervals. CCHH000011--PP337700449911..iinndddd 55 66//2277//22000088 1100::3366::1100 AAMM 6 Chapter | 1 Concepts of Normality in Clinical Biochemistry Anderson-Darling normality test A-squared 3.39 P-value (cid:6) 0.005 Mean 66.042 StDev 31.447 Variance 988.902 Skewness 0.929303 Kurtosis 0.549188 N 168 Minimum 18.000 1st quartile 43.000 Median 58.500 3rd quartile 83.750 30 60 90 120 150 180 Maximum 184.000 95% Confidence interval for mean * * 61.252 70.832 95% Confidence interval for median 53.000 64.000 95% Confidence interval for StDev 95% Confidence intervals 28.406 35.223 Mean Median 55 60 65 70 FIGURE 1-3 Distribution and summary statistics for the sample of canine alanine aminotransferase values (U/liter) in Table 1-1 . Printout of MINITAB, Release 14.13. 1 . Use of Transformations when having analyte values either below the value of the analyte below which are 2.5% of all normal analyte values Frequently, some transformation (such as the logarithmic or or above the value of the analyte below which are 97.5% of square root transformation) of the analyte values will make all normal analyte values. This method is attractive because the distribution more Gaussian ( Kleinbaum e t al. , 2008 ; percentiles are reflective of the distribution involved. Neter et al. , 1996 ; Zar, 1999 ). The boundaries for the ref- The 97.5th percentile is estimated as the value of the erence values are two standard deviations above and below analyte corresponding to the ( n (cid:5) 1) (cid:9) 0.975th observation the mean for the distribution of the transformed analyte in an ascending array of the analyte values for a sample of n values. These boundaries then can be expressed in terms of normal animals ( Dunn and Clark, 2001 ; Ryan e t al. , 2001 ; the original analyte values by retransformation. Figure 1-4 Snedecor and Cochran, 1989 ). For the ALT values from describes the distribution of the ALT analyte values after the sample of n (cid:2) 168 animals, (n (cid:5) 1) (cid:9) 0.975 (cid:2) 169 (cid:9) transformation with natural logarithms. The reference 0.975 (cid:2) 164.775. Because there is no 164.775th observa- boundaries in logarithmic units are equal to 4.08013 (cid:8) tion, the 97.5th percentile is found by interpolating between (1.96 (cid:9) 0.47591) or (3.14734, 5.01292), which correspond the ALT values corresponding to the 164th and 165th to (23.3, 150.3U/liter), in the original units of the analyte. observation in the ascending array commonly referred to as the 164th and 165th order statistics ( Ryan e t al ., 2 . Use of Percentiles 2001 ; Snedecor and Cochran, 1989 ). The 164th order sta- The second approach that can be followed in the situation tistic is 138U/liter and the 165th order statistic is 140U/ where an assumption of a Gaussian distribution is not ten- liter and the interpolation is 138 (cid:5) 0.775(140 (cid:3) 138) (cid:2) able is to choose percentiles as boundaries ( Feinstein, 1977 ; 139.5U/liter. The 2.5th percentile is estimated similarly as Herrera, 1958 ; Mainland, 1963 ; Massod, 1977 ; Reed e t al. , the ( n (cid:5) 1) (cid:9) 0.025th order statistic, which is the 4.225th 1971 ; Solberg, 1999) . For example, if we wanted to mis- order statistic for the sample of ALT values. In this case, classify only 5% of normal animals as being abnormal, the the 4th and 5th order statistics are the same, 24 U/liter, 2.5th and 97.5th percentiles could be chosen as the reference which is the estimate of the 2.5th percentile. Note that there boundaries. Thus, animals would be classified as abnormal is reasonable agreement between this reference interval and CCHH000011--PP337700449911..iinndddd 66 66//2277//22000088 1100::3366::1100 AAMM II. Reference Interval Determination and Use 7 Anderson-Darling normality test A-squared 0.33 P-value 0.514 Mean 4.0801 StDev 0.4759 Variance 0.2265 Skewness (cid:3)0.078280 Kurtosis (cid:3)0.475771 N 168 Minimum 2.8904 1st Quartile 3.7612 Median 4.0690 3rd Quartile 4.4278 2.8 3.2 3.6 4.0 4.4 4.8 5.2 Maximum 5.2149 95% Confidence interval for mean 4.0076 4.1526 95% Confidence interval for median 3.9703 4.1589 95% Confidence interval for StDev 95% Confidence intervals 0.4299 0.5331 Mean Median 3.95 4.00 4.05 4.10 4.15 FIGURE 1-4 Distribution and summary statistics for the natural logarithm of the sample of canine alanine ami- notransferase values (U/liter) in Table 1-1 . Printout of MINITAB, Release 14.13. that obtained using the logarithmic transformation. This 0.03 method of using percentiles as reference values can also be used for analytes having a Gaussian distribution. The 2.5th y and 97.5th percentiles for the sample of glucose values are nc 0.02 e 65.4 mg/dl (3.63 mmol/liter) and 126.3 mg/dl (7.01 mmol/ u q e liter), respectively. This interval agrees very well with that e fr calculated earlier using the conventional method. v ati 0.01 el Normal dogs R Type III diabetes mellitus dogs E . Sensitivity and Specifi city of a Decision Based on a Reference Interval 0.00 0 50 100 150 200 250 As alluded to earlier, in addition to the “ normal ” or healthy Glucose (mg/dl) population, several diseased populations may be involved, FIGURE 1-5 Overlapping Gaussian distributions of one analyte for each with its own distribution. Figure 1-5 depicts the dis- a diseased dog population and a healthy, nondiseased dog population. tributions of one analyte for a single diseased population Decision (threshold) point is the upper limit of the reference interval for and for a normal healthy, nondiseased population. Note the normal dogs. The magnitude of the vertically shaded area is the prob- that there will be some overlap of these distributions. Little ability of misclassifying a diseased dog as being normal and the magni- overlap may occur when the disease has a major impact tude of the horizontally shaded area is the probability of misclassifying a normal dog as being diseased. on the level of the analyte, whereas extensive overlap could occur if the level of the analyte is unchanged by the disease. would be classified as nondiseased, the false negatives. Using the upper limit of the reference interval for the Second, normal patients with values above the normal normal dogs as the decision (threshold) point could lead to interval would be classified incorrectly as diseased and two types of mistakes in diagnosis of patients. First, dis- would be the false positives. The probabilities associated eased patients having values within the normal interval with making these two kinds of mistakes in classifying CCHH000011--PP337700449911..iinndddd 77 66//2277//22000088 1100::3366::1111 AAMM