New Indices for Thyroid Functional Status, Hormone Binding, and Peripheral Hormone Metabolism

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1 New Indices for Thyroid Functional Status, Hormone Binding, and Peripheral Hormone Metabolism Principal Component Analysis of 24,000 Clinical Data KIYOSHI ICHIHARA, M.D., KIYOSHI MIYAI, M.D., NOBUYUKI ASHIDA, M.S., KEIKO TAKEOKA, M.T., AKEMI KAISO, B.S., AND NOBUYUKI AMINO, M.D. Principal component analysis of three thyroid function tests, thyroxine (T 4 ), 3,5,3'-triiodothyronine ( ), and uptake ( U), was done using 24,000 data obtained from patients with a wide range of pathophysiologic conditions related to the thyroid. The three component scores were obtained as follows: Zx = 2.62Vfi Vf^ +3.8Vfjlu ; ^ = 0.9 VT, VT^ VT3TJ ; and Z 3 = -3.94VT^ + O.95VT3" + 0.8VTW -.53 (T, Mg/dL, ng/dl, U%). The first component (Z,) represents an apparent axis to the direction of thyroid functional status. It provides a new metabolic index putting conventional free T 4 and free indices together. The second component (Z 2 ) was found to be a sensitive indicator of abnormal hormone binding. It showed a close correlation with serum concentration of thyroxine-binding globulin. The third component (Z 3 ) represents the degree of predominance over T 4. Computation of these scores will facilitate the diagnosis of atypical cases in which hyper- or is complicated by abnormal peripheral hormone binding and/or metabolism. (Key words: Thyroid; Thyroxin; 3,5,3'-triiodothyronine; uptake; Thyroxin-binding globulin; Principal component analysis) Am J Clin Pathol 986, 85: A LARGE NUMBER of thyroid function tests are now available for the laboratory diagnosis of thyroid disorders. Their interpretation, however, has become more complicated because various extrathyroid conditions cause inconsistencies among those test results. Even using the most common tests such as the measurements of serum concentration of thyroxine (T 4 ), 3,5,3-triiodothyronine ( ), and uptake ( U), there are various combinations of changes among them. Abnormality in thyroid-hormonebinding proteins causes a dissociation between the values of T 4 and T3U. 32 Abnormal peripheral metabolism of the thyroid hormones can lead to a lowering or elevation of relative to T 4.,2 ' 8,0, These conditions can be di- Received October 6, 984; received revised manuscript and accepted for publication October 3, 985. Supported in part by grant-in-aid from the Ministry of Health and Welfare, and the Ministry of Education, Science and Culture of Japan. Address reprint requests to Dr. Ichihara: Central Laboratory for Clinical Investigation, Osaka University Hospital, --50 Fukushima, Fukushimaku, Osaka 553, Japan. Central Laboratory for Clinical Investigation and Department of Laboratory Medicine, Osaka University Medical School, Osaka, Japan agnosed easily in typical cases. However, they tend to be overlooked in the presence of a functional abnormality or they mask its presence instead. There is also difficulty in determining the relative contribution of over T 4 to the peripheral hormonal activity. Actually, there is no comprehensive metabolic index representing both factors together. In this study, we applied principal component analysis to 24,000 clinical data with a set of three measurements T 4,, and U and tried to extract a main component axis that best represents the thyroid functional activity of those data covering a wide range of pathophysiologic conditions, f The diagnostic value of the main component score was assessed in reference to cases of well-defined thyroid disorders. The clinical implication of the two other components also was examined. One of them was found to be closely associated with an abnormal hormone binding and the other with a degree of predominance over T 4. Materials and Methods Analyses were made of 24,5 clinical data with a set of three measurements:, T 4, and U. Among them, 752 samples were also measured for serum thyroxinebinding globulin (TBG). All of the data were obtained from patients who visited our hospital over a four-year period between 980 and 984, and who had a wide-range of pathophysiologic conditions. The following groups of data were obtained separately as typical untreated cases with well-established clinical diagnosis: Graves' disease (n t The conventional units for T 4 (/jg/dl) and (ng/dl) are converted to molar units by use of the formulae: Mg/dL =.29 X 0" 8 mol/l and ng/dl =.54 X 0"" mol/l, respectively. 469 Downloaded from on 29 June 208

2 470 ICHIHARA ET AL. A.J.C.P. April 986 = ); subacute thyroiditis in its thyrotoxic phase (); postpartum transient thyrotoxicosis (2); latent primary caused by Hashimoto's thyroiditis (25); overt primary (7); familial TBG increment (9); normal pregnancy (9); familial TBG deficiency (0); TBG deficiency secondary to systemic illness (5); and low syndrome resulting from anorexia nervosa 8 (2). Ninety-three normal adults also were analysed to obtain normal reference ranges. and TBG were measured by double antibody radioimmunoassays (RA) ( -Eiken and TBG-Eiken, Eiken Immunochemical Laboratory, Tokyo, Japan). T 4 was measured by a double antibody RIA (T 4 -Eiken ) in the first two years, and later by RIA using an antibodycoated tube (Ab-tube T 4 -Eiken ). There was no significant bias in the measurement during those two periods. U was measured by use of a resin-sponge as an adsorbent (Triosorb, Dainabot, Tokyo, Japan) in the first year and then by macroaggregated albumin ( uptake MAA Kit, Amersham International, Buckinghamshire, England). Because there was significant difference between the two measurements, the former was transformed to the latter making use of their very close linear relationship. Yearly distributions of all the test values were drawn for each variable x ; (i =,2, 3; Xi = T 4, x 2 =, x 3 = U) with and without a square root or logarithmic transformation. The transformation that gave the closest approximation to normal distribution was chosen on a probability paper. Each value Xy (j =, 2,..., n) was transformed further to a standardized value Xy = (xy X;)/ Sj, where X; and Sj represent a mean and a standard deviation calculated from all n data. A 3 X 3 correlation matrix was then derived and served to obtain the following principal components 9 designated as z t, z 2, and z 3 in the order of their relative contribution: z, = A,, XX, + A 2 X X 2j + A, X X 3 z 2 A 2I X X,j + A 22 X X 2j + A 23 X X*-3j 3 XX 3j z 3 = A 3 X X,j + A 32 X X 2j + A 33 Here, A ip (p =, 2, 3) corresponds to the correlation coefficient between the original variables and a new component. The computation was iterated after rejecting data whose scores for the previous z 2 or z 3 were outside the mean ± 2.6 times the standard deviation of the respective score, whereas z t was allowed to have any value so that U 980 n=2586.::: ::::::::.:::t:i:i:i:t:i:t:: 98 n*4804 ill: Mi 982 n=68h i.l! X!!:: -Jl-J: j :i:5»»!!. \ *.: : : :.. HI;: HI II..* «il: :l: :«:l:j:l:«= «:«. ::::: : : :I:i:::::x... r. 983 n=7788 iiiii a * * tm t S I»»»i_«t» X»I*»««OOOOOOOOOIX^^^WDBOOOOOOOOOOOOOOOOOOOOOO V NCWM IMCKDM)aNOO^B MO OOOOOCOOOODOOOOOOOOOCIOOOOOOOOOOOOOOOOOOO :: :: :::::::::::::::::;:::: :::::::::::::':;::::::l:;'::::t:::t:::::: D«B IM<WOSNO<D'0'r<VO<0>Oir<MCMI><Miri>Oa><IirMO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO "ooooooooooooooooooooooooooooooooooooooooo FIG.. Yearly distribution of all patients test results for T, > and U. The n represents the number of data for the given year, and the black strip below each histogram represents a normal range for the measurement. Downloaded from on 29 June 208

3 Vol. 85 No. 4 PC ANALYSIS AND THREE NEW THYROID INDICES 47 FIG. 2. Correlation coefficients between principal components and original variables. The characteristic vector root of each component is also shown. It represents a proportion of information that each component acquired. The sum of the three roots is equal to the number of parameters analyzed; here, that is three. T - " T 3 u J 0 '. wmm\ i i i i i i > m O characteristic root its axis would stay in the direction of the thyroid functional status. After the fourth iteration, all the characteristic root remained almost unchanged. Original programs were made for all the analyses and graphical presentations using a microcomputer system (Wang model 2200 VP series) with peripherals of a floppy disk apparatus, plotting typewriter, and high-speed serial printer. Descriptions of assay procedures and data analyses are given in our previous papers. 6,7 Results Distribution of Test Results Yearly distributions of all the test results are shown in Figure l. None of the measurements showed clinically significant between-year variation. With any variable, the square : root transformation gave the closestfitof the data to normal distribution judged from a linearity on the ' " S '/ >< :"N'.r."".'. - : -.-.-»..... T H V '...: U * 34r 26' -""".--""" \y 3 "^ >ls^ ^ ^ M0 5, ^ T 4 jg/dl ^~---" z, z 2..-'-"' FIG. 3. Three-dimensional scatter of original data points and principal component axes. Shown are 0,000 points out of 24,5 original data before iterative truncation. Axes for the original variables underwent square-root transformation. Ranges of the measurements and normal ranges (strips with shadow) are indicated in the box on the right. The three principal component axes after the final iteration are superimposed on the graph. / " " '., ' ' " " ^--'" Downloaded from on 29 June 208

4 472 ICHIHARA ET AL. A.J.C.P. April 986 Zi 0 o Normal **- Graves' disease 'T**"»«H Subacute thyroiditis Post-partum thyrotoxicosis Latent primary Overt primary Increased TBG Increased TBG (Pregnancy) Decreased TBG Decreased TBG (secondary) Low syndrome» 9}»» %» MIHIHHI mii»"i - W0*> *> 9 m * M I I m*t»v»**» »» %» «%»»» Z2-0 0 Normal Graves' disease Subacute thyroiditis 'HP »#» Post-partum thyrotoxicosis WW f» Latent primary Overt primary Increased TBG» 0 - increased TBG (Pregnancy) M «^ '» Decreased TBG Decreased TBG (secondary) r» - *- Low syndrome m t FIG. 4. Typical thyroid-related disorders and principal component scores. Each component score was standardized so that its normal range is set between -2 and 2, as shown by the vertical strip of shadow. The first component score (Z,) corresponds to a metabolic index (Fig. 4A. upper). The second score (Z 2 ) represents an index of thyroid hormone binding in blood (Fig. 45, lower). The third score (Z 3 ) represents an index of predominance over T 4 (Fig. AC. opposite page). Downloaded from on 29 June 208

5 Vol. 85 No. 4 PC ANALYSIS AND THREE NEW THYROID INDICES Normal Graves' disease Subacute thyroiditis Post-partum thyrotoxicosis Latent primary Overt primary Increased TBG Increased TBG (Pregnancy) Decreased TBG Decreased TBG (secondary) Low syndrome -** >«*««M<M IMI IIW i M> m- $ : +m»*» m». y «w»t»i«:;; * %» I»l H'fl»»»»»»» i i i i I i I I I I I I FIG. 4. (Continued) probability paper. On the other hand, the distribution of each measurement in our normal adults was regarded as normal. Principal Component Scores and Three-Dimensional Scatter of Original Data Points The correlation coefficients between the extracted components and original variables are shown in Figure 2, together with the characteristic root that represents a proportion of original information each new component acquired. The first component showed strong positive correlation with all of the three original variables. The second component showed weak negative correlations with T 4 and, and close positive correlation with U. The third component showed moderate negative correlation with T 4, moderate positive correlation with, and no correlation with U. The principal component scores Z,, Z 2, and Z 3 were obtained from original variables by the following formulae (see Appendix): Z, = 2.62Vf^ VT VT3U Z 2 = 0.9 IVT^ ^ VlW Z 3 = -3.94VT^ Vf^ + O.lgVT^U -.53 where units of measurement for T 4,, and U are ng/ dl, ng/dl, and %, respectively. The distribution pattern of each score in the normal adults was regarded as normal on probability paper. Thus, each score above was standardized (as indicated by capital letter Z) so that the normal adults take values between 2 and 2, with a mean of zero and a unit standard deviation. The standardized scores can be approximated in other institutions by adjusting the center and the spread of the distribution of each score by use of the following formulas that require a mid-point (M[x]) and a half width (S[x]) of normal range for each variable x in a given institution (see Appendix): Z, = 4.53 X TJ X T? + 6. X U* +0.8 Z 2 =.57 X TJ +.62 XT? X U* Z 3 = X TJ X Tf X U* T 4 * = (VT^ -.02VM(T 4 ) )/VS(T 4 ) * = (Vt7- I.OIVM( ) yvscro U* = (VXjU VM( U) )/VS( U) where units of measurement for T 4,, and U are /xg/ dl, ng/dl, and %, respectively. These scores will be required to be restandardized by use of normals in each institution. Downloaded from on 29 June 208

6 474 ICHIHARA ET AL. A.J.C.P. April 986 Zo diagnosis of hyper- and/or (Fig. 4A). The decreased TBG states, however, tended to have lower scores and the increased TBG states have higher scores. The cases of low syndrome showed low scores almost equivalent to the level of mild. The second score (Z 2 ) is very specific with only welldefined cases of TBG abnormalities showing scores outside of the normal reference range (Fig. 4B). The third score (Z 3 ) was significantly higher than normal in Graves' disease, latent, and decreased TBG states, while it was significantly lower in thyrotoxic phase of subacute thyroiditis and in low syndrome (Fig. 4C). TBG pg/ml FIG. 5. The relationship between the second principal component and serum concentration of TBG. The simple correlation coefficient was The broken lines indicate the normal limits. Shown in Figure 3 is a three-dimensional scatter-diagram of the first 0,000 points out of 24,5 original data before the iterative truncation. The three axes superimposed on the figure correspond to Zi, z 2, and z 3 after the final iteration. Typical Thyroid-Related Disorders and Principal Component Scores Principal component scores are shown in Figure 4 for typical thyroia>related disorders without treatment. The first component score (Z t ) was closely related to clinical Correlation Between Z 2 and TBG Samples from 752 cases with measurement of TBG together with T 4,, and U were analyzed. The correlation coefficient between Z 2 and TBG was 0.82 (Fig. 5). There were some outlying points that may indicate abnormality in binding proteins other than TBG. Discrimination of Clinical Cases with Complex Abnormalities The three principal component scores were calculated from data of five selected cases with complex thyroidrelated abnormalities (Fig. 6), which were not easily detected from the original set of variables (T 4,, and U). In case, the presence of is apparent from low T 4,, and U values, but the coexistence of binding abnormality may be overlooked unless one notices atypically low U values for the level of T 4 and. By the new score system, however, the two conditions clearly are separated from each other, and Z, provides a quantitative measure of the severity of the in comparison with that in a reference case, case ', with typical Case T h H*=i U Case r T4 3.2 I mvfwl i J -r I tfzm H -< ZT -8. i i i EED ' ' * Z2 3.9 i i ES ' Z 3.0, EH] ' ' Zt -6. t i EE) FIG. 6. Discrimination of cases with complex thyroid-related abnormalities. Cases through 5 represent complex thyroid-related abnormalities, while those with a prime symbol correspond to reference cases with functional abnormality only I E3 i 600 I Z2 -Q.9 EHS T3U 24.5 i «W._ 50 -f- Z 3.2. i dh3 ' Downloaded from on 29 June 208

7 Vol. 85 No. 4 PC ANALYSIS AND THREE NEW THYROID INDICES 475 Case 2 T H o t U 44.8 l -ESI I I 600 i Zi m'h"m i i i Z i m Eg -i i i * i z 3.8* r~ri i i i i i Case 2' T4 4.0 I F^l * I m i U 35.0 'EZEfr- 600 I Zi ^ \=tm - Z2 0.2 i p«a Z 3.7 H i EEi Case 3 T i F^h I ^ *-* 600 I Z 5.3 " I I I I ' ' '' Z < I I ) ' '» ' L) Z ' K B FIG. 6. (Continued) Case 3' 0 0 T I E3=*- 326 I E3 I 20 H Zi.0 ' i rsra Z2-0.9 rfl= 20 U 40.0 'EZ' t Z 3 -. i i fggl Case Z -3.6 «i:::xr~::i Z «- Z * r~t~i t I I I I I Case T4 0.5 i f*mm- 20 t -I ZT.8 ' nst^i I EH 400 t 600 I Z EIS T3II 39.8 < <r^m. m - Z *-«aa * * Downloaded from on 29 June 208

8 476 ICHIHARA ET AL. A.J.C.P. April 986 value. Similarly, the co-existence of hyperthyroidism and increased hormone binding in case 2 is better identified by the new score system. Case 3 represents hyperthyroidism during pregnancy with prominent discrepancy of U value from the concentrations of T 4 and. Here again, the severity of the hyperthyroidism can be compared by the score of Z, with that of case 3' showing no such discrepancy. The patient in case 4 showed clinical signs of together with laboratory evidence of circulating auto-antibody to. The condition is characterized by abnormally high scores for Z 2 and Z 3. The patient in case 5 presented with metastatic esophageal cancer. A low Z 2 value indicates the presence of hypoproteinemia and a low Z 3 value represents the chronic debilitating condition or low syndrome. Discussion The following assumptions were made in the present analysis to derive new thyroid-related indices from laboratory database. There should emerge certain central tendencies in the directions of specific pathologic changes corresponding to those indices when we analyze a large number of data obtained from patients with a wide range of pathologic conditions. The data may have any values as long as they are, as a whole, unbiased and pathologically and physiologically attainable. Possible influence of unusually deviated points may well be excluded when the number of data points is large enough. We can never, however, be very sure about the validity of this assumption. Nevertheless, the following points may be taken into account in interpreting our results: () The yearly distribution of each measurement was almost constant, indicating the stability of both patient population and test results over the study periods. (2) The samples were ordered as routine tests for thyroid function mainly from four open clinics for thyroid diseases. Thus, it is unlikely that there was any specific bias in the selection of patients. The mathematical procedures used to derive the principal components were simple, with only three parameters involved, but a few steps were essential to pursue the original attempt of extracting a possible linear axis that would best represent a natural direction of change in thyroid function. First, we needed to normalize the data using square-root transformation since inspection of the threedimensional scatter diagram had revealed a relatively large variation in the hyperthyroid range with resultant nonlinearity in the relation. Second, correlation matrix rather than variance-covariance matrix was chosen to derive the principal components since each of the three variables has different unit of measurement. Third, iterative truncation of outlying points was done only in the direction of the second and the third principal components so that the main axis would keep to the expected direction of functional change. In reference to the well-documented cases of thyroidrelated disorders, the first principal component clearly represents thyroid functional status. The higher the score (Z,) the more active is the function. It appears to provide a new metabolic index combining conventional free T 4 and free indices (FT 4 I, F I) together. Our preliminary observation revealed that separation of values among different groups of patients by use of Z, score was, as a whole, almost identical to that by FT 4 I. Small differences between the two functional indices, however, were noticed in cases of latent and familial TBG deficiency, both of which showed closer to normal value by use of the new index. Meanwhile, cases of low syndrome tended to have greater deviation from normals by the new index, although metabolic implication of this finding is not evident. Anyway, when we consider three to five times higher serum concentration of FT 4 than that of F, 5 and if we accept a hypothesis of T 4 being about four times less potent biologically than, 4 it may be said that overall biologic impact of FT 4 is not so different from that of F. This reasoning, in turn, suggests that the new index, Z l5 virtually possessing both factors together, provides a more comprehensive measure of thyroid function than does FT 4 I or F I alone. The second component appeared to provide a useful information on the status of hormone binding. The higher the score, the more increased was the serum thyroxinebinding activity. Actually, it showed a very close correlation with serum level of TBG. The score appears specific since it is not affected by the status of thyroid function. Furthermore, the score may be superior to the immunologic measurement of TBG in that it also can reflect the presence of other forms of abnormality in binding proteins such as auto-antibody to the thyroid hormones. The third and smallest component appears to represent the degree of predominance over T 4, hence, abnormal T 4 metabolism in the peripheral tissues or in the thyroid. The current principal component analysis was very efficient in that it did not merely summarize data in terms of thyroid functional status, but provided information on the status of peripheral hormone binding and metabolism. In this sense, we were able to make the maximal use of the original information, extracting useful information from the minor components as well. The derivation of these three scores will facilitate the diagnosis of atypical cases in which hyper- or hypo-thyroidism is complicated by an abnormal peripheral hormone binding and/or metabolism whose presence tends to be overlooked. The present study also opens up a new approach to make use of laboratory database and to find out an unknown data structure of pathophysiologic im- Downloaded from on 29 June 208

9 Vol. 85 No. 4 PC ANALYSIS AND THREE NEW THYROID INDICES 477 plication. Such a structure can be elucidated only from a large number of actual clinical data. Acknowledgments. The authors are grateful to Mrs. Kiyomi Katsumaru, Mrs. Mariko Yasuhara, and Miss Mild Azushima for their kind help in collecting data. They also are grateful to Miss Junko Nishimura and Miss Fumie Moriwaki for their secretarial assistance. References. Amino N, Yabu Y, Kuro R, Miyai K, Kumahara Y: /T 4 ratio in thyroid disease. Lancet 979; :07 2. Amino N, Yabu Y, Miki T, et al: Serum ratio of triiodothyronine to thyroxine, and thyroxine binding globulin and calcitonin concentrations in Graves' disease and destruction-induced thyrotoxicosis. J Clin Endocrinol Metab 98;53: Bellabarba D, Inada M, Varsanoaharon N, Sterling K: Thyroxine transport and turnover in major nonthyroidal illness. J Clin Endocrinol Metab 968; 28: Brown J, Chopra IJ, Cornell JS, et al: Thyroid physiology in health and disease. Ann Intern Med 974; 8: Carayon P, Castanas E, Guibout M, Condaccioni JL: Assessment of clinical significance of free thyroid hormone ratio-immunoassays, Free Thyroid Hormones. Edited by R Ekins, G Faglia, F Pennisi, A Pinchera. Amsterdam, Excerpta Medica, 978, pp Ichihara K, Yamamoto T, Kumahara Y, Miyai K: An improved processing of radioimmunoassay data by means of a desktop calculator. () Comparison of regression procedures applied to selected kinds of radioimmunoassay. Clin Chim Acta 977; 79: Ichihara K, Miyai K, Takeoka K, Katsumaru K, Yasuhara M: Distribution of patients' test values and applicability of "average of normals" method to quality control of radioimmunoassays. Am J Clin Pathol 985;83: Miyai K, Yamamoto T, Azukizawa M, Ishibashi K, Kumahara Y: Serum thyroid hormones and thyrotropin in anorexia nervosa. J Clin Endocrinol Metab 975; 40: Morrison DF: The structure of multivariate observations: I. Principal component analysis, Multivariate Statistical Methods, 2nd ed. New York, McGraw-Hill, 976, pp Utiger RD: Decreased extrathyroidal triiodothyronine production in non-thyroidal illness: Benefit or harm? Am J Med 980; 69: Wartofsky L, Burman KD: Alterations in thyroid function in patients with systemic illness: The "euthyroid sick syndrome." Endocrinol Rev 982;3: Yabu Y, Amino N, Nakatani K, Ichihara K, Azukizawa M, Miyai K: Graves' disease associated with elevated serum thyroxinebinding globulin concentrations. J Clin Endocrinol Metab 980; 5: APPENDIX. Derivation and Standardization of Principal Component Scores Standardized values for T 4,, and U were computed from the following formulae: Ti = (VT^ )/0.64 T' 3 = (VT7-2.6)/2.63 U' = (VT3TJ )/0.37^ () T 4 U Table J. Correlation Matrix before and after Iterative Truncation T, *n = 24,5. f n = 22,704. Raw Data* U T 4 After Iterative Truncationf U sponding variable under square-root transformation. The values shown are those calculated from data after the final truncation. Each mean was found to correspond closely to the midpoint of the normal range. The principal component scores z,, z 2, and z 3 were obtained solving 3X3 correlation matrix consisting of T 4, T' 3, and T3U' shown in Table. The formulae for the scores at the end of the iteration are as follows: z, = 0.88 X T X X U' z 2 = X T X T' X U' z 3 = X T X T' X U' where figures in the parenthesis and those in the denominator are mean and standard deviation, respectively, for the correwhere each coefficient by definition corresponds to a correlation coefficient between a given component and each original variable. Putting equations () and (2) together, we can obtain the scores with respect to T 4,, and U. z, =.38/^ /^+ I.67I/T3TJ- 7.5 z 2 =0.4 Vf^ + 0./Tj"- 2.2VT3TJ f (3) z 3 = -0.6VT^ + 0.5^ VlW-0.24 where the sign of z 2 was reversed so that a positive value represents increased hormone binding rather than decreased binding. Means (and standard deviations) of z,, z 2, and z 3 calculated from data of 93 normal adults were (0.523), (0.454), and (0.54), respectively. By use of these parameters, each score in equations (3) was standardized as follows, so that the distribution of each new score would have a mean of zero and unit standard deviation: Z, = 2.62Vf^ + O.63VT3" + 3.I8I/T3TJ "" (2) Z 2 = 0.9l/f^ l/T^-4.68l/f3Tj > (4) Z 3 = -3.94Vfl Vf^ + O.I8VT3U -.53^ Conversion of the Principal Component Scores in Other Institutions Each score can be approximated in other laboratories by use of a midpoint (M[x]) and a half width (S[x]) of a given normal range for each variable x as follows: Downloaded from on 29 June 208

10 478 ICHIHARA ET AL. AJ.C.P. April 986 VT^ VM(T 4 )/8 0.64VS(T 4 )/3 ff VM( )/ VS( )/45 VTW VM( U)/29.6 T,U' = 0.37VS( U)/3.9 wherefiguresin the square root represent a midpoint or a half width of each normal range adopted in our laboratory. The equations in (5) reduce to the following: T 4 = 2.7(VT^ -.02VM(T 4 ) )/VSfT^j = 2.7 X TJ = 2.55(V " -.0lVM( ) )/VS( ) = 2.55 X TJ U' = 5.34 (VfjU VM( U) )/VS( U) = 5.34 X U* J (5) (5') When the equations in (5') are put into the equations in (2) and are standardized in the same way as shown above, we obtain Z, = 4.53 X TJ X TJ + 6. X U* +0.8 Z 2 =.57 X TJ +.62 X TJ X U* Z 3 = X TJ X TJ X U* This conversion only gives a rough adjustment of the central position and spread of the distribution of each score in a given institution to that in our laboratory. Thus, the "standardized" scores obtained by the formulae (6) have to be re-standardized by normals of the institution. The linearity of each score may be lost unless our and the other institution have similar distributions of T 4,, and U, both in normal adults and the patient population, i.e., the distribution patterns were all normal in our normals and all square-root normals in our patient population. The discriminatory power of the scores, however, will not be much affected by such nonlinearity, as long as each institute uses its own re-standardized scores. (6) Downloaded from on 29 June 208