Clinical Biochemistry of Domestic Animals (Sixth Edition) - UMK ...

6
Chapter | 1 Concepts of Normality in Clinical Biochemistry
Anderson-Darling normality test
A-squared 3.39
P-value 0.005
Mean 66.042
StDev 31.447
Variance 988.902
Skewness 0.929303
Kurtosis 0.549188
N 168
30
60
90
120
150
180
Minimum 18.000
1st quartile 43.000
Median 58.500
3rd quartile 83.750
Maximum 184.000
95% Confidence intervals
* *
95% Confidence interval for mean
61.252 70.832
95% Confidence interval for median
53.000 64.000
95% Confidence interval for StDev
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
Frequently, some transformation (such as the logarithmic or
square root transformation) of the analyte values will make
the distribution more Gaussian ( Kleinbaum et al. , 2008 ;
Neter et al. , 1996 ; Zar, 1999 ). The boundaries for the reference
values are two standard deviations above and below
the mean for the distribution of the transformed analyte
values. These boundaries then can be expressed in terms of
the original analyte values by retransformation. Figure 1-4
describes the distribution of the ALT analyte values after
transformation with natural logarithms. The reference
boundaries in logarithmic units are equal to 4.08013
(1.96 0.47591) or (3.14734, 5.01292), which correspond
to (23.3, 150.3U/liter), in the original units of the analyte.
2 . Use of Percentiles
The second approach that can be followed in the situation
where an assumption of a Gaussian distribution is not tenable
is to choose percentiles as boundaries ( Feinstein, 1977 ;
Herrera, 1958 ; Mainland, 1963 ; Massod, 1977 ; Reed et al. ,
1971 ; Solberg, 1999 ). For example, if we wanted to misclassify
only 5% of normal animals as being abnormal, the
2.5th and 97.5th percentiles could be chosen as the reference
boundaries. Thus, animals would be classified as abnormal
when having analyte values either below the value of the
analyte below which are 2.5% of all normal analyte values
or above the value of the analyte below which are 97.5% of
all normal analyte values. This method is attractive because
percentiles are reflective of the distribution involved.
The 97.5th percentile is estimated as the value of the
analyte corresponding to the ( n 1) 0.975th observation
in an ascending array of the analyte values for a sample of n
normal animals ( Dunn and Clark, 2001 ; Ryan et al. , 2001 ;
Snedecor and Cochran, 1989 ). For the ALT values from
the sample of n 168 animals, (n 1) 0.975 169
0.975 164.775. Because there is no 164.775th observation,
the 97.5th percentile is found by interpolating between
the ALT values corresponding to the 164th and 165th
observation in the ascending array commonly referred
to as the 164th and 165th order statistics ( Ryan et al .,
2001 ; Snedecor and Cochran, 1989 ). The 164th order statistic
is 138U/liter and the 165th order statistic is 140U/
liter and the interpolation is 138 0.775(140 138)
139.5U/liter. The 2.5th percentile is estimated similarly as
the ( n 1) 0.025th order statistic, which is the 4.225th
order statistic for the sample of ALT values. In this case,
the 4th and 5th order statistics are the same, 24 U/liter,
which is the estimate of the 2.5th percentile. Note that there
is reasonable agreement between this reference interval and