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Composite Reference Interval for Thyroid-Stimulating Hormone and Free Thyroxine, Comparison with Common Cutoff Values, and Reconsideration of Subclinical Thyroid Disease H. Alec Ross,1,2* Martin den Heijer,2 Ad R.M.M. Hermus,2 and Fred C.G.J. Sweep1 BACKGROUND: Examination of the 2-dimensional prob- ability distribution of thyroid-stimulating hormone (TSH) and free thyroxine (FT4) shows that the widths of the TSH and FT4 reference intervals derived from this bivariate distribution are mutually interdepen- dent, an aspect commonly ignored when interpreting thyroid testing results with separate reference intervals for TSH and FT4. We desired to establish and critically evaluate a composite reference interval for TSH and FT4 to allow bivariate classification of biochemical thy- roid conditions. METHODS: FT4 and TSH results of 871 healthy individ- uals [361 women and 510 men, 18–40 years old, with- out history of thyroid-related disease or medication, negative for anti–thyroid peroxidase (anti-TPO) anti- body] were transformed to standard normal variables by logarithmic transformation with correction for skewness and subsequent normalization. We estab- lished a 95% reference interval of the distance of each FT4/TSH pair of values to the center of the 2-dimensional probability distribution. RESULTS: The bivariate 95% reference interval is en- closed by a circular profile with radius 2.45 SD. By con- trast, conventional reference intervals comprise a square with the boundaries of�1.96 and�1.96 SD for both FT4 and TSH that enclose only 90% of all data. Compared with the�1.96 SD square, the bivariate ref- erence interval classified 4% fewer of 3651 healthy in- dividuals older than 40 years and 14% fewer of 712 anti-TPO–positive healthy individuals as subclinically hypothyroid. CONCLUSIONS: Conventional application of separate cutoff values for FT4 and TSH leads to overestimation of the incidence of subclinical thyroid disease. Ap plication of a composite overall reference interval is recommended. © 2009 American Association for Clinical Chemistry Subclinical thyroid disease is defined as the combina- tion of normal free thyroxine (FT4) 3 with either sub- normal or increased thyroid-stimulating hormone (TSH). It is common practice to apply the cutoff values corresponding to the 95% reference intervals (either parametrically or nonparametrically established) for FT4 and TSH established in a healthy reference popu- lation to decide how a particular FT4/TSH combina- tion should be biochemically classified (1–3). In a TSH vs FT4 diagram, this corresponds to division of the area into 9 rectangular sections. In such a graphical presen- tation (e.g., Fig. 1A), it is obvious that these limits do not follow uniform probability densities. Moreover, a 95% reference interval obviously should enclose 95% of the reference population, but the central section in which all FT4 and TSH values fall within their corre- sponding �1.96 SD limits encloses only 95% of 95%, i.e., 90.25% of all data points. The remaining 9.75% is distributed as follows: 0.25% for the combinations low/ low, high/low, low/high, and high/high FT4 and TSH and 9.5% for the combinations normal/low, normal/ high, low/normal, and high/normal. Thus, 4.75% of the reference populationwould be classified as subclin- ically hyper- or hypothyroid. Herein we propose a method to obtain a bivariate 95% reference interval for transformed and normal- ized FT4 and TSH values. The reference interval is based on combining these values in a function express- ing the distance from the center of the 2-dimensional distribution. We assume a uniform probability density and set the cutoff limit so that about 5% of the refer- 1 Department of Chemical Endocrinology and 2 Department of Endocrinology, Radboud University Nijmegen Medical Centre, Nijmegen, the Netherlands. * Address correspondence to this author at: 479 ACE, Department of Chemical Endocrinology, Radboud University Nijmegen Medical Centre, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands. Fax �31-24-3541484; e-mail a.ross@ace.umcn.nl. Received January 28, 2009; accepted August 4, 2009. Previously published online at DOI: 10.1373/clinchem.2009.124560 3 Nonstandard abbreviations: FT4, free thyroxine; TSH, thyroid-stimulating hor- mone; TPO, thyroid peroxidase. Clinical Chemistry 55:11 000–000 (2009) Endocrinology and Metabolism 1 http://www.clinchem.org/cgi/doi/10.1373/clinchem.2009.124560The latest version is at Papers in Press. Published August 27, 2009 as doi:10.1373/clinchem.2009.124560 Copyright (C) 2009 by The American Association for Clinical Chemistry ence population will exceed this bivariate reference limit. Because the reference population must be suit- able to identify cases of subclinical thyroid conditions, no signs of thyroid autonomy or failure should be con- spicuous. Within a population harboring some degree of thyroid autonomy, a negative correlation between FT4 andTSH is expected due to negative feedback; con- versely, in a group of individuals in which pituitary failure occurs, a positive correlation is anticipated. Therefore, if neither organ displays autonomy or fails by itself, no correlation should be observed between TSH and FT4. Basal TSH and FT4 concentrations de- pend on the partially genetically determined pituitary- thyroid set point (4 ) that appears to result in entirely random combinations of FT4 and TSH values among individuals. When this is the case, a bivariate reference limit is easy to calculate. To investigate the effect of this approach on the definition of subclinical hyper- and hypothyroidism, we estimated the frequencies of these conditions by composite, bivariate, and conventional univariate ap- proaches in a euthyroid older (compared to the refer- ence group) age group without anti-TPO antibodies, and in an anti-TPO–positive group. Study Participants andMethods The individuals included in this study originated from the Nijmegen Biomedical study (5 ). Serum TSH was measured by immunoluminometric assay in an Archi- tect random access assay system (Abbott Diagnostics). The functional detection limit (i.e., the concentration at which the interassay CV is 20%) was 0.007mU/L. At higher concentrations, interassay CVs were as follows: 3.3% at 0.250 mU/L, 3.6% at 1.72 mU/L, and 3.0% at 9.86 mU/L. Serum FT4 was estimated by a lumines- cence enzyme immunoassay in a Vitros ECI random access assay system (Ortho Clinical Diagnostics). This assay uses a labeled anti-T4 antibody in a medium that is essentially free of other extraneous T4-binding pro- teins. Serum samples may be diluted up to 8 times without significant effect on measurement results. In- terassay CVs were as follows: 3.8% at 10.1 pmol/L, 4.5% at 15.8 pmol/L, and 4.6% at 28.7 pmol/L. The total population consisted of 6434 individuals age 18 years and older. After exclusion of all those with self-reported thyroid disease and/or thyroid surgery, those on thyromimetics and thyrostatics and on other medication known to affect thyroid function or thy- roid function parameters, pregnant women and women on oral contraceptives, a group of 5235 healthy individuals remained. Individuals with increased anti- TPO antibodies (n � 712) (aTPO� group) were ex- cluded, and of the remaining 4523, TSH and FT4 concentrations were logarithmically transformed in- cluding a correction for skewness. Based on the mean and SD of the transformed values, 14 outliers were eliminated (see “Appendix” for transformation and outlier algorithms). In addition, 16 individuals with 0 1 2 3 4 5 6 0 5 10 15 20 25 FT 4 (pmol/L) T S H ( m U /L ) I II III IV V VI VII VIII –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 FT 4 (normalized) T S H ( n o rm a li ze d ) III III IV VI VII VIII V A B Fig. 1. (A) TSH and FT4 values as measured directly in the reference group, with reference limits obtained by reversal of the transformation and normalization, with conven- tional 1.96 SD limits (dotted lines) and composite limits (solid lines). Sections outside the curved reference zone correspond to thyroid conditions outlined in the text. (B) Normalized, transformed TSH and FT4 values for the reference group which formed the basis of the composite reference limits. 2 Clinical Chemistry 55:11 (2009) TSH below the functional sensitivity limit of 0.007 mIU/L were removed. Because we had observed a ten- dency toward lower TSH and higher FT4 concentra- tions with age (5 ), the reference groupwas restricted to people 40 years old and younger (n� 871). The distri- bution of transformed FT4 and TSH values in this ref- erence group was not found to differ from a normal gaussian distribution. From these data, we made a 2-dimensional diagram of transformed TSH plotted against transformed FT4. A reference limit was repre- sented by a circular profile centered at (0,0), which en- closes a specified fraction of all data points. The re- maining 3622 individuals were supplemented with results for the previously removed 13 of 14 outliers and for 16 values with TSH below the functional detection limit, all �40 years old, to form the older anti-TPO negative (�40, aTPO–) group (n� 3651). The squared normalized distance,D2, of each data point to the center of the distribution for this reference population equals the sum of the squared normalized TSH and FT4 values and is given by the following formula: D2 � ��log(TSH� 0.303� � 0.243 /0.171]2 � ��log(FT4 � 11.2� � 1.39 /0.0324] 2. With the assumption that TSH and FT4 are uncorre- lated, D2 is mathematically identical to the Mahalono- bis distancemeasure traditionally used formultivariate reference regions (6 ) and follows a �2 distributionwith 2 degrees of freedom so that P0.95 is at 5.99. For the distanceD, the critical value is 5.99 or 2.45. The con- stants 0.303 and 11.2 are corrections for skewness, 0.243 and 1.39 are the means of the transformed TSH and FT4 values, and 0.171 and 0.0324 are the corre- sponding SDs (see “Appendix”). Because all outliers except one were�40 years old, outlier removal had no effect on the parameters of the reference group. The area outside the composite reference interval may be subdivided into 8 sections (Fig. 1A and B), i.e., the number of combinations of low, normal, and high TSHandFT4with the combination normal/normal ex- cluded. The 4 corner sections I, III, VI, and VIII repre- sent the zones in which both TSH and FT4 exceed the same absolute limit of 1.73 (2.45/ 2) SD (or conven- tionally, �1.96 SD). Section I represents overt hypo- thyroidism with high TSH and low FT4, whereas sec- tion VIII represents overt hyperthyroidism with high FT4 and low TSH. Sections II and VII represent sub- clinical hypo- and hyperthyroidism, respectively. Using the z-test for population proportions, we compared observed frequencies in the sections statisti- cally to each other and expected values (7 ); P values �0.05 were considered significant. For P values�0.25, the predicate “not different” was assigned. Distribu- tions were tested for normality by Kolmogorov– Smirnov test (SPSS v. 16; SPSS Inc.). Results The distribution of transformed FT4 and TSH values in the reference group was not found by Kolmogorov– Smirnov testing to differ from a normal gaussian dis- tribution. The separate 95% univariate reference inter- vals obtained after reversal of the transformation were 0.51–3.48mIU/L for TSH and 9.8–16.9 pmol/L for FT4 (Fig. 1A). The circumference of the bivariate 95% ref- erence region is given by [1], with the value 5.99 as- signed toD2 (distanceD� 2.45). For each FT4 value, a pair of TSH values was obtained, representing the TSH reference interval corresponding to that particular FT4 value. Thus, for an FT4 value of 13.1 pmol/L, the lower and upper limits for TSH are 0.36 and 4.28 mU/L, re- spectively. Conversely, if TSH is 1.45, the range for FT4 is 9.0–18.0 pmol/L. Furthermore, if FT4 is 9 pmol/L, the reference interval for TSH would be restricted to a single value of 1.45 mU/L. When using the separate univariate reference in- tervals for TSH and FT4, 10.8% (n� 94) of data points in the reference group fall outside the area in which both criteria are met; by contrast, with the bivariate composite approach, 5.2% (n � 45) fall outside the constructed combined reference region. Both numbers fall close to the expected values of 9.75% and 5% (z-test for population proportions). The same holds after fur- ther subdivision into subclinical hypo- and hyperthy- roidism (see Table 1): separate limits give 2.4% and 2.8% (expected 2.4% for both), and the bivariate com- posite limit yields 1.2% and 0.8% (expected 1.1% for both). Fig. 2A and B shows the data from the group of healthy older (�40 years) individuals and healthy in- dividuals with positive anti-TPO superimposed on the reference grid. Table 1 presents the observed frequencies of sub- clinical hypo- and hyperthyroidism as assessed by the composite and conventional methods. In many in- stances, the differences between observed frequencies were significantly greater than expected from inclusion of a larger percentage of normal values (2.4% vs 1.1%) alone. This observation was particularly apparent in the frequency of subclinical hypothyroidism in the anti-TPO positive group. The estimate of subclinical hypothyroidism according to the conventional ap- proach was almost 24%, whereas the composite ap- proach indicated only 10%. In the elderly anti-TPO– negative group, the observed frequency of subclinical hypothyroidism was slightly higher than in the refer- ence group if the composite limits were used (1.5% vs 1.2%), but the difference was somewhat more pro- Composite Reference Interval for TSH and FT4 Clinical Chemistry 55:11 (2009) 3 nounced (3.3% vs 2.4%) when applying separate lim- its. For subclinical hyperthyroidism, the composite ap- proach gave frequencies for the elderly anti-TPO– negative and anti-TPO–positive groups that were higher than expected (3.4% and 2.8% vs 0.8%) on the basis of the reference group, but not significantly dif- ferent from each other. For the conventional method, frequencies for the elderly anti-TPO–negative and anti-TPO–positive groups were 7.3% and 5.1%, re- spectively, vs 2.8%, of which the former is significantly higher than the latter. Discussion Plots of TSH vs FT4 values from larger data sets show that the shape of the density distribution of points is egg-like (Fig. 1A) rather than rectangular.Whereas FT4 approximates a normal distribution, the distribution of TSH is skewed, but approximates a normal distri- bution after log transformation. Fine-tuning of the transformation by correcting for residual skewness, ap- plying log transformation for FT4 as well with subse- quent normalization, results in a circular-shaped 2-dimensional diagram for healthy individuals without any thyroid medication or sign of disease. This is a re- flection that, if the negative feedback system is at equi- librium, TSH and FT4 combine randomly among indi- viduals. A negative correlation will be observed if there is a tendency of thyroid autonomy within the data set, in the form of either thyroid hyperactivity or failure. Conversely, a trend toward pituitary auton- omy would lead to a positive correlation. If TSH and FT4 do correlate, the density distribution will tend toward an elliptic shape with Y � X and Y � �X as main axes. A trivariate (TSH, FT4 index, FT3 index) probability density distribution was presented by Kagedal et al. (8 ) for 3885 women 39–60 years of age. In this group, negative correlations were ob- served between logTSH and both FT4 and FT3 indi- ces and a positive correlation between FT4 and FT3 indices. This resulted in an ellipsoidal frequency dis- tribution and reference limit. We also observed a negative correlation between FT4 and logTSH for individuals �40 years old, which was the reason to exclude those from the reference group since our aim was to obtain a reference group that is suitable for detecting subclinical thyroid disease. Although the univariate probability density distributions of FT4 and TSH are mutually independent, the bivari- ate density distribution depends on both FT4 and TSH, and therefore the reference limits derived from the bivariate distribution for each parameter are mutually dependent. So the derived reference limits for FT4 are further apart if TSH values tend toward their average, than with TSH values toward the ex- tremes, and vice versa. Classification of thyroid conditions on the basis of a logTSH/FT4 diagram has been shown before (2 ). Al- though the authors indicated in their graph that the normal reference region was elliptical (and would be circular after normalization) rather than rectangular, this aspect was not further explored. The squared distance of each data point to the cen- ter of the distribution equals the sum of squared nor- malized TSH and FT4 values. As a consequence of nor- malization, TSH and FT4 each have a mean of 0 with variance 1. Thus, each squared transformed and nor- malized TSH and FT4 value is an estimate of this vari- ance. Therefore, the sum of squared TSH and FT4 will be �2 distributed with 2 degrees of freedom. The 95% reference interval corresponds to a �2 value of 5.99, so it encloses a circle with a radius of 2.45, which is the square root of 5.99. Indeed, 94.8% of all data from the reference group fall within this region; in contrast, 89.2% fall within the separately applied limits, mean- ing that 5% of healthy individuals would be inappro- priately classified as abnormal with the latter approach. Conversely, with the composite approach, the number Table 1. Observed and expected incidence rates in subclinical hyper- and hypothyroid ranges. Composite Conventional n Subclinical hypothyroid Subclinical hyperthyroid Subclinical hypothyroid Subclinical hyperthyroid Expected incidence 0.0108 0.0108 0.0238 0.0238 Observed incidence Reference 0.0115 0.00804 0.0241 0.0276 871 �40, aTPO� 0.0153a,b 0.0337a 0.0331a,b 0.0731a,b 3651 aTPO� 0.101a,b 0.0281a 0.237a,b 0.0506a,b 712 a Significant difference (z-test for population proportions) with reference and expected. b Significant difference between aTPO� and �40, aTPO�. 4 Clinical Chemistry 55:11 (2009) of healthy individuals not requiring further investiga- tion increases by 5%. Subdivision of the area outside the reference inter- val (see Fig. 1B) into sections corresponding to various thyroid conditions is intuitive when using conven- tional separate 95% limits at �1.96 SD. With the cir- cular reference area it is somewhat less obvious. The dividing lines must intersect at�1.73 SD, by which the corner sections will correspond to regions where not only TSH and FT4 combined fall outside the reference interval, but also separately exceed the same limit. This limit is defined by the 4 points on the circle where the absolute values of normalized TSH and FT4 are equal. This is at 2.45/ 2� 1.73 SD. For the reference population, the difference be- tween conventional and bivariate composite classifica- tions is almost exclusively located in the sections cor- responding to the 4 possible combinations normal/ abnormal, 2 of which represent subclinical hyper- and hypothyroidism. Plotting the data from the healthy anti-TPO–neg- ative participants older than 40 in the grid (Fig. 2A and B), it appears that the data are shifted downward and to the right with respect to the reference group. This is a corollary of observationswemade earlier (5 ). Interpre- tation of this shift depends on whether the composite reference limits or conventional reference limits are used. Table 1 shows that there was a slight but signifi- cant increase in frequency of subclinical hypothyroid- ism compared to the reference group, but the differ- ence tended to bemore pronouncedwith conventional classification. This was also true when considering the data fr