Thyroid Function Tests in N onthyroidal Illness: Correction by Mathematical Method

This Article


Article Information:

Group: 2003
Subgroup: Volume 1, Issue 1, Winter
Date: March 2003
Type: Original Article
Start Page: 6
End Page: 13


  • R Kassayan
  • Endocrine Research Unit, Tehran University of Medical Sciences and Health Services, Tehran, I.R. Iran
  • Manouchehr Nakhjavani
  • Endocrine Research Unit, Tehran University of Medical Sciences and Health Services, Tehran, I.R. Iran
  • M Eghtesad
  • Endocrine Research Unit, Tehran University of Medical Sciences and Health Services, Tehran, I.R. Iran
  • L. Gouhari Hosseini
  • Endocrine Research Unit, Tehran University of Medical Sciences and Health Services, Tehran, I.R. Iran


      Affiliation: Endocrine Research Unit, Tehran University of Medical Sciences and Health Services
      City, Province: Tehran,
      Country: I.R. Iran
      Tel: -
      Fax: -


Diagnostic confusion results when subnormal free T4 values are reported in nonthyroidal illness (NTI) when a variety of free thyroxine index or analogue techniques are used to estimate free thyroxine levels. We tried to correct the changes in free thyroxine assessments by a mathematical method in nonthyroidal illness (NTI). Serum albumin was used to correct the measured hormone concentration by mathematical formulas.
Materials and Methods: The study included 56 patients with acute and chronic systemic illnesses and control groups. Total T4 (1T4), total T3 (TT3), free T4 and free T3 by analogue method (FT4A and FT3A), free T4 by back titration (FT4B), TSH-IRMA, reverse T3, T3 Resin Uptake (T3RU), TBG, albumin and total serum proteins (TSP) were measured. Free T4 index (FT4I) and T4[fBG ratio (T4TBGR) were calculated. Mathematical correction for each hormone was done through equations based on patient's original hormone level and albumin concentration. As an example, the formula for correction of FT4A was: expected FT4A = (patient's FT4A) - X (patient's albumin) + Y;
X = 1.11 x [(mean FT4A in normal subjects) "7- (mean albumin in normal subjects)]; Y = 1.11 x (mean FT4A in normal subjects).
Results: The decrease in albumin and TSP resulted in a decrease in 1T4 and 1T3, FT4A and FT3A in NTI, but it had no significant effect on FT4B. Mathematical correction resulted in an increase in sensitivity of FT4A from 55.4 to 96.4%, FT4B from 94.6 to 100%, T4TBGR from 80.4 to 98.2%, and FT41 from 69.6 to 100%, in differentiating NTI from hypothyroidism. The specificity of tests remained unchanged. The corrections did not affect normal, hypothyroid, and hyperthyroid controls.
Conclusions: Mathematical correction increased sensitivity of tests, which assess free T4 directly or indirectly, in differentiating NTI from hypothyroidism. NTI has been reported as the most common cause of errors reported in thyroid function tests so mathematical correction could significantly increase overall accuracy of free T4 assessments.

Keywords: Nonthyroidal illness;NTI;Sick euthyroid syndrome;SES;Free T4;Free thyroxine index;Albumin;Mathematical correction Introduction

Manuscript Body:


Nonthyroidal illness (NTI) is frequently accompanied by alterations in circulating thyroid hormone concentrations, despite patients remaining clinically euthyroid.' Although some NTI patients may indeed be hypothyroid.t routine assessment of thyroid function in acutely hospitalized patients has been questioned, because of low specificity and poor positive predictive value." We studied the effect of decrease in serum protein concentrations on thyroid function tests. Some previous studies demonstrated a correlation between low serum T3 and serum albumin in NTI patients.Y We tried to correct the effect of decreased serum albumin concentration on free T4 assessments by a mathematical method in order to improve their accuracy. The required variables for such correction are concentration of serum albumin and the measured hormone. Then.a computer program could be used to apply our mathematical formulas to the measurements and produce a corrected result.
Materials and Methods
The study included 56 patients with acute or chronic systemic illnesses hospitalized at a university general hospital (Table 1). The control groups included thirty healthy adults, ten hypothyroid and nine hyperthyroid patients. The inclusion criteria for NTI were absence of clinical evidence of thyroid disease, and negative history for known medications effective on thyroid axis regulation. Diagnoses in the patients admitted to the study included a wide variety of nonthyroidal illnesses such as gastrointestinal, liver, cardiovascular, pulmonary and cerebral disease, renal insufficiency, diabetes mellitus and cancer.

Table 1. Primary illness in 57 patients with nonthyroidal illness

Primary illness

NO of patients



Gastrointestinal disease


Renal disease


Uncontrolled diabetes mellitus


Respiratory disease


Cardiovascular disease


Cerebrovascular disease



Malignant diseases, including adenocarcinomas and lymphomas, were the most frequent. The age of patients ranged between 12 and 82 years. The patients had no evidence of thyroid disease during their hospital stay. FT4B and TSH in combination at admission time and follow up were used to rule out thyroid disease.
The hormonal measurements included Coat-A-Count DPC RIA total T4 (TT4), total T3 (TT3), and T3 resin uptake (T3RU), GammaCoat Clinical Assay RIA free T4 by analogue method (FT4A), GammaCoat Clinical Assays RIA free T4 by back titration (FT4B), and also free T3 by analogue method (FT3A), Coat-A-Count DPC IRMA TSH, and reverse T3by RIA (Serono Diagnostica).
The measurements of serum proteins included total serum proteins (TSP) by refractometry method and albumin by quantitative agarose gel electrophoresis (REP, stained by Panceau REP). Thyroxine binding globulin (TBG) was measured by Gammadab (Clinical Assays, RIA). The standard calculations included: free T4 index (FT4I) and T4/TBG ratio (T4TBGR). We tried to correct the effect of alterations in serum albumin concentrations on total and free thyroxine assessments by novel mathematical calculations. The following equations were used for calculation of expected free T4 assays (eFT4A and eFT4B) and expected free T 4 indirect assessments (eT4TBGR and eFT41) independent of albumin concentration changes: eFT4A = FT4A - 0.36 Albumin + 1.48
eFT4B = FT4B - 0.16 Albumin + 0.66
eT4TBGR = (T4/TBG) -0.61 Albumin+2.5
eFT41 = T4 (T3RU) -0.66 Albumin+2.71

Mathematical Basis of Calculations:

The mathematical basis for calculations of the expected values was based on the following equation:
Equation I: Expected Hormone Level = A x (Hormone level) + B x (Albumin) + C. A, B, and C are three unknown variables. For calculation of these factors we need three equations. We used three "clear assumptions for making these equations:
The first assumption is that in an assumed normal case with hormone level equal to "mean normal hormone level of normal control group (NH)" and albumin equal to "mean normal albumin of normal control group (NA)", the expected hormone level should be equal to "expected h0D110ne level of normal control group". The second assumption is that in another assumed case with hormone level equal to "zero", and albumin equal to "mean normal albumin of normal control group", the expected hormone level should be zero. The third assumption is that in a case with hormone level equal to "mean hormone level of low albumin group (LH)" and albumin equal to "mean serum albumin of low albumin group (LA)", expected hormone level should be equal to "expected hormone level in low albumin group(EH)".
First equation: NH =A x (NH) + B x (NA) + C
Second equation: 0 = A x (0) + B x (NA) + C
Third equation: EH = A x (LH) + B x (lA) + C
In the third equation we put the value of mean hormone level in normal control group (NH) instead of expected hormone level in low albumin group (EH) in case of free T4 assessments. The assumption was that the actual free T4 level should be normal in NTI. Solving the above three linear equations in three unknowns, it ensues:
B = - (NH -LH) -0- (NA -LA) and C = NA x [(NH - LH) -0- (NA - LA)}.
By calculating A, Band C from the above equation based on normal and NTI groups data and placing them in Formula 1, the expected values for free T4 (eFT4A, eFT4B, eT4TBGR, eFT41) are found.


The frequency of normal T3 and normal T4 in patients was 16%, low T3 and normal T4 or "low T3 state" was 37.5%, and low T3 and low T4 or "low T3-T4 state" was 46.5%. The results of free hormone assessments and new mathematically corrected indices are presented in Table 2.

Table 2. The results of free T4 assessments before and after mathematical correction by serum albumin and their" sensitivity and specificity in differentiating NTI from hypothyroidism


Normal controls






FT4A (ng/dL)











o 78±0.38













FT4B (ng/dL)





































8. 88±1.75




































FT4A was below the normal range in 44.6%, FT4B in 5.4%, TI4 in 46.4%, FT41 in 30.4%, and T4TBGR in 19.6% of NT I cases. In 2 out of3 patients with decreased FT4B the values were borderline low (0.81, and 0.87 ng/dL). In the third patient it was 0.69 ng/dL. The sensitivity and specificity offree T 4 assessments in differentiating NTI from hypothyroidism, before and after mathematical correction are demonstrated in Table 2. We also used TSP instead of albumin and got equivalent results. Mathematical corrections had no significant effect on normal controls, hyperthyroid and hypothyroid patients.
Mean and standard deviation of serum albumin was 4.11 ±O. 47 g/L in normal controls, and 2.58±0.75 g/L in NTI. Albumin was below the normal in 78.6%, TSP in 80.4%, and TBG in 14.3% of NT I. Albumin and TSP decreased significantly in NTI in comparison to control groups (pReverse T3 had a significant increase in NTI compared to normal controls (pTT3 was below the normal in 84% and FT3A in 58.9% ofNTI. Thyroid function in nonthyroidal illness 9 TSH was in the normal range in 94.6% of NTI patients and varied from 4.97 to 8.6 mUlL in three patients (5.4%). The lowest TSH value in NTl was 0.39 mUlL.

Table 3, The correlation among serum proteins and thyroid hormone assays in normal control group.

























* Numbers represent r (Correlation coefficient)

Table 4. The correlation among serum proteins and thyroid hormone assays in NTL

























* Numbers represent r (Correlation coefficient)

TSH in the present study did not change significantly in NTI, but its deviation from the mean value was greater than to the healthy controls (mean±SD was 2.08±1.95 in NTI versus 1.85±0.59 in healthy controls).


Nonthyroidal illness is probably a more common cause of abnormalities in the serum concentration of thyroid hormones than intrinsic thyroid disease. The prevalence of one or more abnormalities of thyroid function tests in patients with acute medical illnesses has been reported from 40% to 70%6.7 Although thyroid function test alterations occur in nonthyroidal illnesses.i" the result of in vitro estimation of free T4 does not always correlate with the transfer of T4 to tissues.'? Some mechanisms are involved in incompletely understood these Abnormalities. 13
Measurement of free thyroxine by analogue techniques or free thyroxine index result in subnormal free T4 levels because of technical lim itations.!" Thyroid hormone binding proteins, primarily albumin, affect free T4 measurements in analogue methods.!5-25 In these methods binding of T4 analogue to albumin is responsible for the erroneous results, falsely low, when the albumin concentration is markedly decreased. Hence in complicated clinical situations such as severe NTl, decrease in serum albumin concentration results in less binding of tracer by albumin and thus produces artifactually lowered free T4 measurements. Figure 1 demonstrates the correlation between serum albumin and FT4A and FT4B. These problems have not yet been solved despite attempts to improve the RIA system by adding blockers that chemically inhibit the analogue-albumin binding26,27 In the present study the adverse effects of decrease in serum albumin concentration on free T4 assess- ments were corrected by a mathematical method.

Fig. 1. Correlation between mean serum albumin and FT4 1-stell and 2- step in three groups of patients with NTI

Among the four free T4 assessments the FT4A had lowest accuracy. Its sensitivity in differentiating NTI from hypothyroidism rose from 55.4% to 96.4% after correction. Values obtained by FT4B are comparable to those determined with the direct methods2~,29 FT4B had the least correlation with fluctuations of serum proteins in this study. In three patients with low FT4B, TSH values were normal. Its sensitivity was 94.6% and increased to 100% after correction. Total T4 had significant correlation with albumin in NTl. Sensitivity ofT4([BG ratio (T4TBGR) and free thyroxine index (FTl) increased from 80.4% and 69.6% to 98.2% and 100% after correction, respectively. Thc specificity of all four tests remained unchanged. Free T3 by ultra filtration remains within normal range in NTI even in the severely ill, low T3- low T4 group30,3! It decreases with increasing severity of underlying disease in NTe2 The results of FT3A and TT3 were below the normal range in 58.9% and 83.9% of NTI, respectively. Cytokines have been implicated in the pathogenesis of low T3 syndrome during illness32,33 There is a strong negative relationship between serum T3 and serum interlukin-6 (IL-6) in NTI32 TGF- betal could playa role in the pathogenesis of some modifications of thyroid function observed in patients with nonthyroidal '4 illnesses.'
Albumin, TSP and TBG had no significant correlation with thyroid function tests in the normal control group. The exception was TSP with FT4A (r=-0.47, pTSH usually remains unchanged in NTI36 The causes of transient alterations in serum TSH values in some NTl are multifactorial, however low TSH values are most frequently found in patients who have received phar- macological doses of glucocorticoids or dopamine."
Each laboratory should use its own mean free hormone level and albumin concentration in a normal population as a reference for mathematical correction. The following are simplified formulas for calculating expected hormone values:
eFT4A = (patient's FT4A) - X (patient's
albumin) + Y,     where: X = 1.11 [(mean FT4A in normal subjects) -;- (mean albumin in normal subjects)], and Y = 1.11 (mean FT4A in normal subjects)
eFT4B = (patient's FT4B) - X (patient's     albumin) + Y.     where: X = 041 [(mean FT4B in normal subjects) -i- (mean albumin in normal subjects)] Y = 041 (mean FT4B in normal subjects)
eT4TBGR = [tpatient's T4) -7- (patient's TBG)]-X(patient's a lb u m i n t+Y, where:
X = 0.69 [(mean T4TBGR in normal subjects) -i- (mean albumin in normal subjects)] Y = 0.69 (mean T4TBGR in normal subjects)
eFf41 = (patient's T4) (patient's T3RU) - X     (patient's albumin) + Y.     where: X = 1.06 [(mean FT4I in normal subjects) -i- (mean albumin in normal subjects)] Y = 1.06 (mean FT4I in normal subjects)
Our mathematical correction increased sensitivity of tests, which assess free T4 directly or indirectly, in differentiating NTI from hypothyroidism. Its improved accuracy is comparable to the method of combining total T4 and T3RU to produce more accurate free T4 index (FfI). We suggest mathematical correction as a practical way to improve the results of thyroid function tests in NTI. This method is an example of application of mathematics in medicine.

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