a multivariate analysis of certain biochemical components of … · 2016-06-02 · cnco o co m en...

A MULTIVARIATE ANALYSIS OF CERTAIN BIOCHEMICALCOMPONENTS OF EQUINE AND FELINE SERUM SAMPLES

AS REPORTED BY AN AUTO-ANALYZER SYSTEM

By

Robert Rothnick Jorgensen

United StatesNaval Postgraduate School

rsnrHESISA MULTIVARIATE ANALYSIS OF CERTAIN BIOCHEMICAL

COMPONENTS OF EQUINE AND FELINE SERUM SAMPLES

AS REPORTED BY AN AUTO--ANALYZER SYSTEM

by

Robert Rothni ck Jo rgensen, Sr.

Thesis Advisor A. F . Andrus

March 1971

Apptiovnd faon. public A.e£ea.6c; cUAtnlbiition 'Mitlmltzd.

T.1 37477

A Multivariate Analysis of Certain Biochemical Components

of Equine and Feline Serum Samples

as Reported by an Auto-analyzer System

by

Robert Rothnick Jorgensen, Sr.Lieutenant Colonel, United States Army

B.S., University of Minnesota, 1957D.V.M. , University of Minnesota, 1959M.P.H., University of Minnesota, 1965

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN OPERATIONS RESEARCH

from the

NAVAL POSTGRADUATE SCHOOLMarch 19 71

LibraryJJAVAL POSTGRADUATE SCHOOLMONTLT . 93940

ABSTRACT

This thesis contains a multivariate statistical analysis

of the results of an automated analysis of serum samples

from the horse and cat. In the horse, 12 biochemical com-

ponents plus body weight and age are recorded; thus,

observations are made on 14 random variables. In the case

of the cat there are observations on 13 random variables.

Ninety-one (91) pair-wise correlation coefficients are

computed from the equine data and 78 pair-wise correlation

coefficients are computed from the feline data. Extensive

hypothesis testing concerning these correlation coefficients

is conducted and the results are presented. A discriminant

analysis for 2 groups, male and female, is conducted for

each species. In this analysis the vector of sample means

of the biochemical components plus body weight and age for

males is contrasted with the corresponding vector from

females. Tolerance limits for each biochemical component

measured are presented for both . species

.

TABLE OF CONTENTS

I. • INTRODUCTION 6

II. A BRIEF CONSIDERATION OF THE AUTOANALYZER 8

III. THE MAMMALIAN SPECIES UNDER STUDY ANDCOLLECTION OF SAMPLES 9

IV. TABULAR PRESENTATION OF DATA 10

V. SAMPLE STATISTICS 16

VI. HYPOTHESES TESTED 30

VII. TOLERANCE LIMITS 44

VIII. SUMMARY 48

IX. RECOMMENDATIONS 56

LIST OF REFERENCES 57

INITIAL DISTRIBUTION LIST 59

FORM DD 1473 60

LIST OF TABLES

Table

I - Serum Biochemical Values in 44 Horses asReported by an Auto-analyzer System 11

II - Serum Biochemical Values in 30 Cats asReported by an Auto-analyzer System 14

III - Table of Sample Mean Vectors 20

IV - A Variance-covariance Matrix for 44 Horses 22

B Variance-covariance Matrix for 21 FemaleHorses 23

C Variance-covariance Matrix for 21 FemaleHorses 24

D Variance-covariance Matrix for 30 Cats 25

E Variance-covariance Matrix for 15 MaleCats 26

F Variance-covariance Matrix for 15 FemaleCats 27

V - Critical Values r-j ^ for the Specified afor 44 Horses and 30 Cats 31

VI - A Correlation Matrix for 44 Horses 32

B Correlation Matrix for 30 Cats 33

VII - Critical Values of r j ^ for the Specifieda for 23 Male Horses and 15 Male Cats 34

VIII-A Correlation Matrix for 23 Male Horses 35

B - Correlation Matrix for 15 Male Cats 36

IX Critical Values of r j ^ for the Specifieda for 21 Female Horses and 15 FemaleCats 37

Table

X - A Correlation Matrix for 21 Female Horses 38

B Correlation Matrix for 15 Female Cats 39

XI - Statistically Significant Differences inSample Correlation Coefficients in Maleand Female Horses 41

XII - Discriminant Analysis Between Males andFemales 43

XIII-A Tolerance Limits in the Horse 46

B Tolerance Limits in the Cat 47

I. INTRODUCTION

There is a basic oneness of the human and veterinary

medical professions [1] . Many diagnostic and therapeutic

devices developed for use in one of these professions have

sooner or later found equally significant application in

the other. In particular, the advent of automated devices

for the analysis of human serum has greatly facilitated

biochemical profiling [2]. However, as Coffman reports,

restricted availability of these devices in the past has

limited their practicality in clinical veterinary medicine

[3]. Coffman goes on to point out, and this writer has

encountered no statement to the contrary, that the appli-

cability of these devices, in enhancing the diagnostic

capabilities of the clinician, will be cause for their

increased utilization by the veterinary medical profession

[4] . It is therefore logical to assume that automated

biochemical profiling will be of increasing value in

describing the normal intervals about the true biochemical

parameters in the serum of domestic animals.

Although the auto-analyzer devices are capable of

generating a large volume of data concerning biochemical

values in human and animal sera, the proper analysis of

these data should not be treated superficially. The lack of

proficiency in statistical methodology by members of the

bio-medical professions is an unfortunate fact [5].

Additionally, qualified statisticians are often asked to

make meaningful conclusions from biological data that have

been generated in meaningless fashion [6] . The increased

reliance of the veterinary medical profession upon automated

analyzing devices will yield little addition to our

knowledge of serum biochemical parameters and their con-

comitant physiological significance unless the data are

meaningfully collected and analyzed by sophisticated

statistical techniques. It is this conclusion which has

motivated the research effort reported herein.

II. A BRIEF CONSIDERATION OF THE AUTOANALYZER

The autoanalyzer used in this study was a Technicon

Sequential Multiple Analyzer, SMA 12/60, which was first

introduced in 1967 as a successor to the widely used

SMA 12 [7] . The SMA 12/60 analyzes a serum sample

quantitatively and reports on the concentration of 12 of

the serum biochemical components on an easily interpreted

pre-calibrated chart paper. The 12 biochemical components

quantitatively analyzed are: calcium, inorganic phosphate,

glucose, blood urea nitrogen (BUN), uric acid, cholesterol,

total protein, albumen, total bilirubin, alkaline phos-

phatase, lactic dehydrogenase (LDH) , and glutamic oxalacetic

transaminase (SGOT)

.

The primary value of the autoanalyzer is that it provides

a reasonable biochemical profile of the subject from a

single serum sample within 60 seconds; it is invaluable as

a screening device in that certain metabolic aberrations,

whether suspected or unsuspected, will be manifested in

abnormal serum chemistry charts.

III. THE MAMMALIAN SPECIES UNDER STUDYAND COLLECTION OF SAMPLES

The horse has recently enjoyed a resurgence of popu-

larity although it is more in demand as a pleasure and

recreation animal rather than a source of agricultural

power. It was selected for this study because it was felt

that the economic value of the horse justifies the most

sophisticated diagnostic techniques by consulted veterin-

arians. While some data are available as to equine

biochemical parameters the work thus far reported does not

fully exploit the statistical potential of these data [8].

In this study, 44 horses of various breeds, 23 males

and 21 females, were selected. All were clinically in

good health. Blood samples were obtained by vena puncture;

the serum was separated from the clot and was then centri-

fuged, frozen, and maintained in a frozen state until

submitted to the laboratory.

The cat was selected for this study because information

concerning biochemical parameters in the serum of this ani-

mal is particularly lacking [9]. Thirty (30) cats, 15 males

and 15 -females, all of mixed breed but of varying ages were

included in this study. All were free of clinical illness.

Blood samples were obtained by cardiac puncture and the

samples were then processed as described above.

IV. TABULAR PRESENTATION OF DATA

In consideration of the equine data 14 variables were

under consideration; in addition to the 12 serum biochemical

components reported by the autoanalyzer , body weight and

age were also considered. A previous report indicates

that equine serum albumen is not reliably reported by the

autoanalyzer [10] . Albumen is nonetheless included in this

study to form a basis for substantiation or repudiation of

this fact as may be justified by further research.

A similar approach was employed with the feline data

with the exception that 13 variables were under considera-

tion; inasmuch as no cat demonstrated measurable total

bilirubin it was deleted from consideration.

The data as reported by the SMA 12/60 Auto-analyzer for

the 44 horses and 30 cats are presented in Table I and

Table II respectively.

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V. SAMPLE STATISTICS

The analysis of the data is amenable to multivariate

methodology. In the case of the equine data we have obser-

vations on 14 random variables:

X. . 1 = 1,2,.... ,44

where "i" refers to the identification of the animal and j

refers to a variable.

In particular we have:

Random Variable Definition

X. , Calcium Level of Horse Number "i"1/1

X. _ Inorganic Phosphate Level of Horse "i"l , z

X. - Glucose Level of Horse "i"l , j

X. „ BUN Level of Horse "i"

X. _ Uric Acid Level of Horse "i"i/5

X. c Cholesterol Level of Horse "i"i / o

X. _ Total Protein Level of Horse "i"i / '

X. Albumen Level in Horse "i"I/O

X. n Total Bilirubin Level of Horse "i"i/9

X. , A Alkaline Phosphatase Level of Horse "i"1,10 v

X. ,, LDH Level of Horse "i"i/ll

X. , SGOT Level of Horse "i"

X. , .. Body Weight of Horse "i"1 / 1 J

X, ,

4Age of Horse "i"

16

In the case of the cat we have observations on 13 random

variables

:

Y. . i = 1,2, ,301 1 J

j = 1,2, ,13

where "i" and "j" again refer to the identification of the

animal and the characteristic respectively.

In particular we have:

Random Variable Definition

Y.,1

Y.,2

Y.1 ,3

Y.l ,4

Y.l ,5

Y.1 ,6

Y.l ,7

Y.l ,8

Y.l ,9

Y.1 ,10

Y.l ,11

Y.l ,12

Y.1 ,13

Calcium Level of Cat "i"

Inorganic Phosphate Level of Cat "i'

Glucose Level of Cat "i"

BUN Level of Cat "i"

Uric Acid Level of Cat "i"

Cholesterol Level of Cat "i"

Total Protein Level of Cat "i"

Albumen Level of Cat "i"

Alkaline Phosphatase Level of Cat "i'

LDH Level of Cat "i"

SGOT Level of Cat "i"

Body Weight of Cat "i"

Age of Cat "i"

In the description of sample statistics that follow, the

computational formulae are given for x. .. The same formulae

apply for y. and it is understood that N = 44 and N = 30

for the horse and cat respectively.

17

In multivariate terminology, each horse may be repre-

sented as a 14 dimensional vector X . For example,

referring to Table I we see that horse number 1 is repre-

sented as follows: "

X (1) _

— — — —xl,l

11.2

Xl,2 3.3

31,3

86.

Xl,4

10.

Xl,5

0.5

*1,6 110.

Xl,7 = 6.4

Xl,8

0.6

Xl,9

0.9

Xl,10

87.

Xl,ll

211.

Xl,12

460.

Xl,13

850.

Xl,14

13.

The sample mean, x..

, is required for each of the set of

observations on the 14 variables and is computed as follows:

Nx. . = Z

3 i=l

2-1N

The sample means of the observations on the j variables

may be represented as a j -dimensional sample mean vector,

x, where

18

X.

X.

X.

X.

X.

_1_

N

NEx

i=l lfl

NEx. ~

1=1 1*2

NE x. -.

i=l L ' 3

NE x. .

i=lX '=>

NE x.

i=l X 'P

The 6 sample mean vectors representing 44 horses, 23 male

horses , 21 female horses, 30 cats, 15 male cats, 15 female

cats, are presented in Table III.

2The sample variance, s . or s . .is computed for each

3 3 i 3

set of observations on the j variables as follows:

3 N" 1 i=l

NE (X_. i - x. .)

The sample standard deviation is computed by simply obtain-

ing the square root of the sample variance:

s . = Jl

The sample covariance, s. , , between the observations x. .

and x. , , i = 1,...,N, is computed as follows:1 , K

19

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20

s .

N(x. . - X. . ) (x. ,

- X.. )J,k N-l i=1 i,D 3 i/k k'

In multivariate analysis the sample variances of the

observation on the variables and the sample covariances

between each pair of these variables is presented as a

sample variance-covariance matrix (S) with dimensions p by

p. The elements of the sample variance-covariance matrix

are as follows:

(S) =

Sl,l

sl,2

Sl,3

•** Sl,k

s2,l

S2,2

S2,3

**• S 2,k

'1,P

;

2,p

3,1 2,2 3,3 D,k j ,p

p 7 l p,2 p,3 p,k P/P

In the main diagonal of the matrix j is equal to k and the

main diagonal elements represent the sample variances for

each of the j variables. Since s . , = s, ., for the sample

variance-covariance matrices computed, those elements above

the main diagonal will be deleted and the matrices will be

lower triangular. The variance-covariance matrices for 44

horses, 23 male horses, 21 female horses, 30 cats, 15 male

cats, and 15 female cats are presented in Tables IV, A

thru F.

21

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27

The primary purpose of computing the sample variance-

covariance matrix is in computing the Pearson Product

Moment Correlation Coefficient, r. . . This statistic is a3 /*

measure of the tendency of 2 variables to vary together in

linear fashion. It is described as the ratio of the sample

covariance between 2 variables to the square root of the

product of the sample variances of the 2 variables; that is,

s . ,

3 /kr . . =D/k

V (s:,:

)(s*,k>

/l4\For the equine data there are _ I =91 pair-wise correla-

tion coefficients to be computed and for the feline data

there are I „ 1 = 78 pair-wise correlation coefficients to

compute and consider.

The tests of hypotheses conducted in this research

effort rely on certain assumptions concerning the sample

statistics. The central limit theorem, which permits us to

a2

assume a normal (y, — ) distribution of sample means in the

univariate case [11] , also permits us to make the assumption

of normality in the multivariate case; namely, the distri-

bution of the sample mean vectors, x, is normal with mean y_

and variance-covariance matrix -=- Z [12] . This assumption

will be employed in testing the notion that the vector of

sample means of the males of a given species does not differ

significantly from that of females of the same species.

Additionally, if the population correlation coefficient,

p. , , between 2 variables equals zero, then the sample3 r&

28

correlation coefficient, r. , is distributed as3 r*.

t(N-2) v/(l- r* )

/N-2

where "t,„2 v represents the Student "t" distribution with

N-2 degrees of freedom [13] . Equivalently , the statistic

r. , /N-23' k

is distributed according to the Student "t" distribution

with N-2 degrees of freedom, provided that the hypothesis

that p . , = is true.3 /-K

29

VI. HYPOTHESES TESTED

A "null" hypothesis, denoted as H , can be defined as a

statement or notion for which it is possible to compute a

statistic and the corresponding probability of a more extreme

value of that statistic. Alternatively, it is common to

establish a probability corresponding to the risk of

rejecting H when, in fact, it is true and denoting this

probability as a. H is then rejected only when the test

statistic is more extreme than that associated with a.

In this study the following null hypotheses were tested:

1. H : The true correlation coefficient (p . . ) betweeno H D,k'

variables j and k is equal to zero. This hypothesis was

tested for both equine and feline data irrespective of the

sex of the animal.

Since the sample correlation coefficient can be converted

into a "t,„ ox " statistic, providing H is true, it is(N-2) e o

possible to solve for the "critical" value of r . , by3 / K

establishing a type I error (a) and locating the appropriate

"t., „ " value from a statistical table. In fact, this(N-2)

critical value of r. . , denoted r . , , is obtained asJ , K CCJ ,K

follows

:

ta

raj,k r~2

V< + (N " 2)

where t is the 1-a percentile point of the "t" distribu-

tion with N-2 degrees of freedom. Conveniently, values of

30

r . kare already tabulated [14]. Those appropriate to the

testing of this null hypothesis are presented in Table V.

TABLE V

CRITICAL VALUES OF r . , FOR SPECIFIED aD_rk

N a = 0.05 a= 0.01

44 (Horses) 0.298 0.385

30 (Cats) 0.367 0.470

Triangular matrices of sample correlation coefficients

for the 44 horses and 30 cats are presented in Tables VI-A

and VI-B respectively. In these tables those values of r . ,

3 / K

for which H : p. , = can be rejected at a = 0.05 areo H j,k J

indicated by a* and those for which the hypothesis can be

rejected at a = 0.01 are indicated with **.

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33

m2. H : The true coefficient of correlation, p . . ,

between variables j and k for the males is zero. This

hypothesis is tested separately for horses and cats.

The critical values of r . , are presented in Table VII.3 /K

TABLE VII

CRITICAL VALUE OF r. . FOR THE SPECIFIED a3>k

N a = 0.05

0.413

0.514

a = 0.01

23 (Male Horses)

15 (Male Cats)

0.526

0.641

Triangular matrices of sample correlation coefficients for

the 23 male horses and 15 male cats are presented in

Tables VIII-A and VIII-B respectively. Significant values

are indicated as previously described.

34

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3. H : The true correlation coefficient, p. ., betweenO ] fK

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TABLE IX

CRITICAL VALUE OF r. . FOR THE SPECIFIED aLdS

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21 (Female Horses) 0.433 0.549

15 (Female Cats) 0.514 0.641

Triangular matrices of sample correlation coefficients for

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Tables X-A and X-B. Significance is indicated as pre-

viously specified.

37

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39

4. H mj.k pja = P j/k

This hypothesis states that the sample correlation

coefficients between variables j and k for males and

females, considered as separate entities, are actually

estimating a common population correlation coefficient,

p. . [15]. Alternatively, the hypothesis states thatJ * K

P- v " P- u= 0. Note that there is no assumption that

p j,k = °-

To test this hypothesis Fisher's Z transformation is

employed where

.m

j,k \ in1 + r

mj.k

1 - rmj»k

and

j,k I-1 + r

j rk

1 - rj,k

It will be noted that each Z . , is the inverse hyperbolic3 /K

tangent of rjrk

[16]. If H is true, then

1/k i ,k

vNm~ 3

+

Nm-3 N

f-3

has a standard normal distribution [17] . In the equine data,

thereforeNm = 23 and N

f = 21. The quantity

becomes

/-±_ + i

"VNm-3 N

r-3

./•^r + ^r - /0. 10555. . . - 0.325. To reject H atV 20 18 J o

40

the a = 0.05 level (|z. . - Z. ,| ) , must be greater than

or equal to (1. 96) (0 . 325) = 0.637. To reject H at the

a = 0.01 level this absolute difference must be greater than

or equal to (2.575) (0.325) = 0.837. It should be recalled

that 1.96 and 2.575 represent the (1-a) =0.95 and

(1-a) = 0.99 percentile points of the standard normal

distribution, respectively.

In the equine data, statistically significant differences

between male and female sample correlation coefficients are

presented in Table XI.

TABLE XI

Paired Variables rm

. Z™ . rf

, Z? . I Zm

. - Z? . I

SSS^ri^-I "°- 254 -°' 260 °' 515 °' 570 °' 830 *phate & Glucose

Glucose and Age 0.195 -0.198 -0.517 -0.572 0.770*

Tota/protein °* 216 °- 220 "°- 534 "0-596 0.816*

TotalS

protein °* 301 * 311 -°' 506 "0-557 0.868**

* - significant at a = 0.05** - significant at a = 0.01

In the feline data there were no statistically signifi-

cant differences between any of the male and female corre-

lation coefficients. Therefore, H cannot be rejected ino J

the case of the cat, at a = 0.05.

41

5. H : y - y =0; that is, the samole mean vectoro — —

for males and the sample rear, vector for females car.e frcr.

the same parent population with mean vector u. To test

2the validity of H , Ma:.= l = r.:c:3' D statistic is computed

as follows

:

Um - xf

]

Ts'

1^ - xf

] = D2

— — — — _where [x — x ] is the trar.sccse cf the 14 by 1 vector o:

cr s a z z—— a z z ~ z z z z — z — ~ z a b s "*e s **

~""" e z a 1 a a *~ c f e— a 1 —

vectors of sample r.ear.s , S is the inverse cf the ceded

variance-covariance matrix S,

where S = (/-DS 111

+ (Nf-l)S

f

n™ + h* - 2

arc.r.S"

-

is the variar.ce-ccvariar.ee matrix fcr male data

S~ is the variar.ce-ccvariar.ee rr.atrix fcr ferale fata

w is the male sample size

N~ is the female sample size.

2If H is true, then D' is distributee"

z ::"-::- .:r-vr -2)~- —

in acczrcar.zs v;izh the T cistributicr. chat has ~ >"-" -::~-p-l)

degrees of freezzr. [IS]. The results cf this hype thesis

test are presented in Table XII.

42

TABLE XII

DISCRIMINANT ANALYSIS BETWEEN MALES AND FEMALES

Species ComputedD2

Degrees ofFreedom

ComputedF Value

F ata = 0.05

Equine

Feline

2.537

5.748

(14,29)

(13,16)

1.374

1.895

2.10

2.40

Thus, for each species, the computed F statistic is not

significant at a = 0.05 and H cannot be rejected at that

level of significance.

43

VII. TOLERANCE LIMITS

Upper and lower tolerance levels based on the observed

data are determined as follows: each x. . is estimating a

2population mean, y . ; each s. is estimating a population

2 2variance, a., u . and a. are fixed but unknown parameters.3 3 3

r

2The statistics x. . and s. are random variables. It is3 3

possible to determine a constant, K, such that in a large

series of samples from a normal distribution, a fixed pro-

portion, y, of the intervals x. . ± K Is . will include

100 (l-a )% or more of the distribution. Thus, statistical

tolerance limits for a normal random variable, X. ., are

given by the following:

- K Is2. and U = x. . + K Is

2

«V ] 3 <*v :

These limits have the property that the probability that

the interval includes at least a specified proportion (1-a)

of the distribution is equal to a preassigned value a [19]

In this paper, values of 0.95 and 0.05 were assigned to y

and a respectively. The following K. _,. values such that

the probability is 0.95 that at least 95% of the distribu-

n~tion will be included between x. . ± K- ._ Is. arej 0.05V ]

presented:

44

NK0.05

44 2.415

38 2.464

30 2.549

24 2.651

21 2.723

These values are employed in constructing the tolerance

limits for the biochemical components of each species.

These limits are presented in Tables XIII-A and XIII-B.

45

TABLE XI I I-

A

TOLERANCE LIMITS IN THE HORSE

BiochemicalComponent N x. .

3S.J

K *05 x. . ±

J: K.

Q5S

Calcium 44 11.78 0.61 2.415 10.31 - 13.25

InorganicPhosphate

44 3.62 0.92 2.415 1.40 5.84

Glucose 44 86.77 12.47 2.415 56.65 - 116.89

BUN 44 14.55 3.72 2.415 5.57 - 23.53

Uric Acid ' 44 0.45 0.15 2.415 0.09 0.81

Cholesterol 44 112.70 15.31 2.415 75.73 - 149.67

TotalProtein 44 6.49 0.40 2.415 5.52 7.46

Albumen 44 0.48 0.09 2.415 0.26 0.70

TotalBilirubin 44 1.40 0.90 2.415 3.57

AlkalinePhosphatase 44 145.39 77.39 2.415 - 332.29

LDH 44 223.57 67.51 2.415 60.53 - 386.61

SGOT 44 786.36 433.77 _ _ — —

38 636 05 127.80 2.464 321.15 - 950.95

46

TABLE XIII-B

TOLERANCE LIMITS IN THE CAT

Variable N X S K *05 KS x ± KS

Calcium 30 9.27 0.81 2.549 2.06 7.21 - 11.33

InorganicPhosphate 30 7.23 1.13 2.549 2.88 4.35 - 10.11

Glucose 30 78.53 27.35 2.549 69.72 8.81 - 148.25

BUN 30 25.50 5.01 2.549 12.77 12.73 - 38.27

Uric Acid 30 0.90 0.16 2.549 0.41 0.49 - 1.31

Choles-terol

302421

79.6091.7997.33

36.6429.9127.76

2.5492.6512.723

93.4079.2975.59

12.50 -

21.74 -

173.00171.08172.92

TotalProtein 30 6.78 0.52 2.549 1.33 5.45 - 8.11

Albumen 30 1.53 0.18 2.549 0.46 1.07 - 1.99

AlkalinePhos

.

30 60.67 30.86 2.549 78.66 139.33

LDH 30 271.03 121.49 2.549 309.68 580.71

SGOT 30 86.37 32.35 2.549 82.46 3.91 - 168.83

47

VIII. SUMMARY

-

A summary of the significant findings of this study will

be presented according to species. In this summary,

"significant," as applied to sample correlation coefficients,

refers to an ability to reject H: p • , = at a ! 0.05.2 J o K j,k

A. EQUINE DATA

In the case of the data pertaining to the 44 horses,

significant positive correlation coefficients were obtained

for the 2 3 males in the following pair-wise observa ions:

Calcium and Albumen

Inorganic Phosphate and Alkaline Phosphatase

Cholesterol and Alkaline Phosphatase

Total Protein and Body Weight

Total Protein and Age

Significant negative correlation coefficients for the 23

male horses were obtained in the following paired obser-

vations :

Calcium and Total Bilirubin

Inorganic Phosphate and Total Protein

Inorganic Phosphate and Body Weight

Inorganic Phosphate and Age

Cholesterol and Age

Total Protein and Alkaline Phosphatase

Albumen and Total Bilirubin

48

Alkaline Phosphatase and Body Weight

Alkaline Phosphatase and Age

LDH and Age

Significant positive correlation coefficients were

observed in the sample of 21 female horses between the

following paired variables:

*Inorganic Phosphate and Glucose

Inorganic Phosphate and Uric Acid


Glucose and Alkaline Phosphatase

Uric Acid and Albumen

Total Protein and Total Bilirubin

Body Weight and Age

Significant negative correlation coefficients were observed

in the sample of 21 female horses between the following

paired variables:

Calcium and BUN



Glucose and Body Weight

*Glucose and Age

*Uric Acid and Total Protein

Uric Acid and Age

Glucose and Total Protein



50

Those correlation coefficients in the female found to be

significantly different from the corresponding correlation

coefficient in the male are indicated with a *.

Significant positive correlation coefficients in all 44

horses as a group that were not significant in either of the

sub-groups considered separately were observed between the

following paired variables:

Inorganic Phosphate and Cholesterol

Uric Acid and Cholesterol

Inorganic Phosphate and LDH

Significant positive correlation coefficients in all 44

horses as a group that were also significant in both the

male and female sub-groups were observed between the follow-

ing paired variables:


Significant negative correlation coefficients in all 44

horses that were also significant in both the male and

female sub-groups are as follows:





All other positive and negative correlation coefficients

that were observed to be significant in all 44 horses appear

to have reached significant levels only because of a very

high correlation coefficient in one of the sub-groups.

51

In considering the fifth hypothesis, it is concluded

from this study that there is no difference between male

and female with respect to the mean values of the 12 serum

biochemical parameters as reported by the autoanalyzer in

the population of horses from which this sample of 44 horses

is a representative sample.

B. FELINE DATA

With respect to 15 female cats, the following positive

bivariate correlation coefficients were found to be

significant:

BUN and Uric Acid



The following negative bivariate correlation coefficients

were found to be significant in the data obtained from the

15 female cats:

Calcium and Age

LDH and Age

The 15 male cats showed the following positive correla-

tion coefficients that were statistically significant:

Calcium and Inorganic Phosphate



Glucose and Age

BUN and Uric Acid

52

Cholesterol and SGOT


Albumen and Body Weight

Body Weight and Age

The following statistically significant bivariate cor-

relation coefficients were demonstrated from the male data:

Calcium and Glucose




None of the correlation coefficients in one sex differed

significantly from the corresponding coefficient in the other

sex. Admittedly, the relatively small size of the sub-groups

is a limiting factor.

The influence of the number of observations on the sig-

nificance of correlation coefficients is evidenced when we

consider the 30 cats as a single group. Significant posi-

tive correlation coefficients in all 30 cats were obtained

for the following paired variables:

Calcium and Inorganic Phosphate

*Calcium and Cholesterol

*Calcium and Alkaline Phosphatase

Calcium and LDH



Glucose and Age

53

BUN and Uric Acid

Cholesterol and SGOT



Albumen and Body Weight

Body Weight and Age

The following significant negative correlation coeffi-

cients between paired variables were observed in the 30 cats:

Calcium and Glucose

Calcium and Total Protein

Calcium and Age



Glucose and LDH




LDH and Age

Significant correlation coefficient in the combined sample

of 30 cats that were not significant in either males or

females considered separately are indicated with a *.

Certainly, it would appear that additional observations

in both male and female cats could result in an increased

number of bivariate correlation coefficients attaining

significance; this is particularly true of the female group.

54

With respect to the fifth hypothesis of equality of the

mean vectors, it is concluded that there is no difference

between males and females in the means of the 12 biochemical

components in the feline population from which this sample

of 30 is representative.

55

IX. RECOMMENDATIONS

The analysis of the equine biochemical data suggests

future work is desirable, particularly in the measurement

of albumen, LDH, and SGOT as reported by the autoanalyzer

.

The significant bivariate correlation coefficients , par-

ticularly as they occur in the female, should be exploited

for possible diagnostic significance.

The analysis of the feline biochemical data demonstrates

that animals in apparent robust health can nonetheless be

hypercholesterolemic , at least as reported by the auto-

analyzer. Even when the 9 most extreme cases were ignored

the lower limit of the cholesterol tolerance was consider-

ably below those values previously reported by Cornelius

and Kaneko [20]

.

This work has been undertaken as a pilot study in

multivariate analysis of biochemical components of the serum

of two of the common species of domestic animals. Emphasis

has been placed on tolerance interval estimations, possibly

significant bivariate linear association as measured by the

Pearson Product Moment Correlation Coefficient, and a

discriminant analysis of the male and female sample mean

vectors. With the increased use of the autoanalyzer and

increased availability of data, this method of statistical

analysis can and should be expanded.

56

LIST OF REFERENCES

1. S.chwabe, C. W. , Veterinary Medicine and Human Health ,

p. 3, Williams and Wilkins, 1964.

2. Technicon Corporation, SMA 12/60 , p. 1, 1967.

3. Coffman, J. R. , "A Perspective on Clinical Chemistriesin the Horse ,

" Veterinary Medicine/Small AnimalClinician , vol. 65, No. 11, p. 1092, Nov., 1970.

4. Ibid, p. 1092.

5. Schor, S. S., "The Mystic Statistic," Journal of theAmerican Medical Association , vol. 95, No. 8, p. 615,1966.

6. Worcester, J., "The Statistical Method," New EnglandJournal of Medicine , vol. 274, No. 1, p. 27, 1966.

7. Technicon, Op. Cit. , p. 1.

8. Wolff, W. A., Tumbleson, M. E. , and Littleton, C. A.,"Serum Chemistry in Normal and Diseased Horses,"Advances in Automated Analysis , vol. Ill, Mediad, Inc.,White Plains, N.Y., pp 179-135, 1970.

9. Kaneko, J. J., Personal Communication, October 22, 1970.

10. Coffman, Op. Cit., p. 1024.

11. Mood, A. M. , and Graybill, F. A. , Introduction to theTheory of Statistics , pp. 149-150, McGraw-Hill, 1963.

12. Anderson, T. W. , An Introduction to MultivariateStatistical Analysis , p. 2, Wiley, 1958.

13. Ostle, B. , Statistics in Research , p. 225, Iowa StateUniversity Press, 1963.

14. Snedecor, G. W. , and Cochran, W. G. , StatisticalMethods , p. 557, Iowa State University Press, 1967.

15. Sokal, R. R. , and Rohlf, F. J., Biometry , p. 520,Freeman, 1969.

16. Ibid, p. 519.

17. Ibid, p. 521.

57

18. Dixon, W. J., BMP Biomedical Computer Programs , p. 190,University of California Press, 1970.

19. Bowker, A. H. , and Lieberman, G. J., EngineeringStatistics , p. 228, Prentice-Hall, 1964.

20. Cornelius, C. E. , and Kaneko , J. J., Clinical Bio-chemistry of Domestic Animals , p. 100, Academic Press,1963.

58

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 0212 2

Naval Postgraduate SchoolMonterey, California 9 3940

3. Department of Operations Analysis, Code 55 1

Naval Postgraduate SchoolMonterey, California 93940

4. Assoc. Professor A. F. Andrus , Code 55As 1

Department of Operations AnalysisNaval Postgraduate SchoolMonterey, California 93940

5. LTC Robert R. Jorgensen 1

246 Ardennes CircleFort Ord, California 93941

6. Office of the Surgeon General 1

Attn: MEDVSDepartment of the ArmyWashington, D. C. 20314

7. Dr. J. J. Kaneko 1Professor and ChairmanDepartment of Clinical PathologySchool of Veterinary MedicineUniversity of California - DavisDavis, California 95616

59

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA -R&D^Security classification ol title, body ol abstract and indexing annotation must be entered when the overall report is classitied)

I originating ACTIVITY (Corporate author)


Za. REPORT SECURITY CLASSIFICATION

Unclassified2b. GROUP

3 REPQR T TITLE

A MULTIVARIATE ANALYSIS OF CERTAIN BIOCHEMICAL COMPONENTS OF EQUINEAND FELINE SERUM SAMPLES AS REPORTED BY AN AUTO-ANALYZER SYSTEM

4 DESCRIPTIVE NOTES (Type ol report end, inc. I us i »t dares;

Master's Thesis; March 19715 AUTHOR(S) (First name, middle initial, last name)

Robert Rothnick Jorgensen, Sr. ; Lieutenant Colonel, United States Army

6 REPOR T D A TE

March 1971la, TOTAL NO. OF PAGES

617b. NO. OF REFS

20Be CONTRACT OR GRANT NO.

6. PROJEC T NO.

9a. ORIGINATOR'S REPORT NUMBER(S)

9b. OTHER REPORT NOISI (Any other numbers that may be assignedthis report)

10 DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

II. SUPPLEMENTARY NOTES

13. ABSTRACT

12. SPONSORING MILITARY ACTIVITY


This thesis contains a multivariate statistical analysisof the results of an automated analysis of serum samplesfrom the horse and cat. In the horse, 12 biochemical com-ponents plus body weight and age are recorded; thus,observations are made on 14 random variables. In the caseof the cat there are observations on 13 random variables.Ninety-one (91) pair-wise correlation coefficients arecomputed from the equine data and 78 pair-wise correlationcoefficients are computed from the feline data. Extensivehypothesis testing concerning these correlation coefficientsis conducted and the results are presented. A discriminantanalysis for 2 groups, male and female, is conducted foreach species. In this analysis the vector of sample meansof the biochemical components plus body weight and age formales is contrasted with the corresponding vector fromfemales. Tolerance limits for each biochemical componentmeasured are presented for both species.

DD FORMi nov es

S/N 01 01 -807-681 1

1473 (PAGE 1)

60UNCLASSIFIEDSecurity Classification

1-31408

UNCLASSIFIEDSecurity Classification

key wo ROSROUE *T ROLE W T ROLE W T

MULTIVARIATE ANALYSIS

SERUM - EQUINE AND FELINE,AUTOMATED ANALYSIS

DD ,

Fr»"..1473 'back, UNCLASSIFIED

S/N 0101-807-6921 61 Security Classification 4-3 1409

Thesis

J825c.l

2 2 2 7 ti

126356|

jorgensen

A multivariate

^nalvsis of certain

^hemica! components

of equine and feline

serum samples as re-

ported by an auto-ana

lyzer system.?

g

? ft

ts

Thesis 126356J825 Jorgensenc.l A multivariate

analysis of certainbiochemical componentsof equine and felineserum samples as re-ported by an auto-ana-lyzer system.

thesJ825

A multivariate analysis of certain bioch

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