Comparative evaluation of methods to determine intra‐individual reference ranges in nutrition support team (NST)‐related tests

Abstract Background The intra‐individual reference range is generally narrower than the commonly used reference range. Consequently, close monitoring of changes in the laboratory test results of individuals based on the inter‐individual reference range remains challenging. Methods We examined the determination of individual reference ranges using four indicators of nutritional conditions: transferrin (TRF), albumin (ALB), retinol‐binding protein (RBP), and transthyretin (TTR). The subjects comprised 20 healthy individuals and blood samples were collected and tested five times at 2‐week intervals. We used the measurement results for the four indicators and examined individual reference ranges using four methods, including calculation methods based on the reference change value and Bayesian inference. Results The resulting intra‐individual reference ranges were narrower than the currently used inter‐individual reference range for all measurements using four methods. Furthermore, the intra‐individual coefficient of variation [CV (intra)] was smaller than the inter‐individual coefficient of variation [CV (inter)] for TRF, RBP, and TTR for all 20 subjects. The means CV (intra) for the four indicators were also lower than the corresponding CV (inter). Conclusions The intra‐individual reference range can be used to validate the standard deviation and coefficient of variation for currently used indicators. Moreover, Bayesian methods are speculated to be the most versatile.

significant variations may be overlooked if using the inter-individual reference range alone. Also, observed variation, which may not be clinically significant, in the intra-individual reference range, could be outside the inter-individual reference range. [1][2][3][4][5][6][7][8] Consequently, close monitoring of variations in the clinical laboratory results of an individual is difficult and can lead to unnecessary secondary examinations if the values obtained exceed the general reference range. [1][2][3][4][5][6][7][8] For example, serum enzymes, such as γ-glutamyl transpeptidase and alkaline phosphatase, in addition to uric acid, total cholesterol, and albumin (ALB), have narrower intra-individual variations than inter-individual variations; thus, the reference range is consistent with inter-individual variations. Therefore, although there are significant changes in the values for an individual, such changes will not be detected as long as each is within the reference range, which is the reason for the low sensitivity of these reference ranges. 4,9 Both the intra-individual and inter-individual reference ranges can be used for evaluation, although there are differences in the mean value and standard deviation. If each individual subject is healthy, the measured values fall within the statistically established intra-individual reference range. [1][2][3][4][5][6][7][8] However, if the measured value is statistically abnormal, an alarm can be triggered sooner than determining it with the intra-individual reference range. This is because the intra-individual reference range is narrower than the inter-individual reference range. [1][2][3][4][5][6][7][8] Clinical physicians can use both the inter-individual and the intra-individual reference range to classify subjects who are undergoing a health examination/ patients who are visiting clinic as "healthy", "observation is required" or "close examination is required" and to make a comprehensive decision, in combination with their medical knowledge and experience, if active treatment is necessary for them by using the test results as important information.
Patients suffering from malnutrition tend to suffer for an extended period of time during which their condition typically worsens. 10,11 Nutritional state management is a factor associated with metabolic disorders and slow healing of wounds, resulting in prolonged hospital stays. 12 Therefore, objective nutritional evaluation (objective data assessment: ODA) is essential for patients requiring close monitoring of their nutritional state. This study examined the determination of individual reference ranges for four nutritional indicators: transferrin (TRF), ALB, retinol-binding protein (RBP), and transthyretin (TTR). 13,14 These indicators are also biomarkers with different half-lives. Each indicator can be determined using four methods. In Method (I), the standard deviations obtained from multiple measurements are considered as the standard deviation of the indicator, and the reference range is calculated as the mean ± 1.96 standard deviation measured for an individual. 1-8 Method (II) uses the reference change value (RCV), which is calculated from the mean and the coefficient of variation (CV) of measurements obtained from an individual over time, ie, the standard deviation (RCV) = RCV × mean ×1/100 is calculated and then used in the reference range = mean ±standard deviation (RCV). [15][16][17] In Method (III), assuming that the individual reference range has a normal distribution, we define the range that includes 95% of the healthy measurement results as μ ± 2σ, estimated as mean ± 2S, and consider mean X − Cn (Cn = t n−1 (0.025)√(n + 1)/n, t n−1 (0.025): the top 2.5% of 5 distributions for freedom n − 1) < mean X < mean X + Cn as the reference range. 18 Method (IV) is a reference range model in which variables are converted to present the measured values in a normal distribution. We first estimate inter-individual variations, intra-individual variations, and time effects in a mixed-effect model that uses measured values as the response variables, the individual as the random effects, and the point-in-time as fixed effects (or random effects). Next, the distributions of the measured values for an individual observed during medical examinations are estimated on the basis of Bayesian inference posterior distribution with inter-individual variations, intra-individual variations, and overall mean as prior distributions. [19][20][21][22][23] 2 | MATERIAL S AND ME THODS

| Subjects
Analysis of the individual reference ranges was conducted using data measured from 20 staff members of the SRL Diagnostics Pathology Laboratory (Tokyo, Japan). These volunteers [age: 45.2 ± 8.0 years (mean ± standard deviation)] presented no abnormal findings in inhouse examinations, during interviews with an industrial physician, and had normal chest X-rays. The volunteers comprised 11 men (age: 46.4 ± 8.1 years), of which two were in their 30s, five in their 40s, and four in their 50s, and nine women (age: 43.7 ± 8.0 years), of which three were in their 30s, three in their 40s, and three in their 50s. These subjects were healthy adults and their dietary and exercise habits were not regulated. 2 All laboratory results were anonymous but linkable.
This study was conducted with strict adherence to the ethical policy on medical research involving humans, with approval from the SRL ethics review committee (approval no. 12-06). All participants provided written informed consent prior to participating in the study.

| Statistical analysis
The four test indicators were measured five times for 20 subjects.
We obtained the mean, standard deviation, inter-individual coefficient of variation [CV (inter)], and intra-individual coefficient of variation [CV (intra)] of the measurements from each individual over time. Using the mean of five measurements obtained for each subject, we calculated the mean and standard deviation for all 20 subjects and then examined the difference among the means of the subjects with the overall mean using the F-test and t test.

| Method (I): This calculation method uses the mean ± 1.96 standard deviation based on multiple measurements and the standard deviation from each individual
We obtained the mean, standard deviation, and CV for each set of measurement four results as follows, 1st and 2nd data, from 1st to 3rd data, from 1st to 4th data, and from 1st to 5th data. We considered the standard deviation obtained for measurements from 1st to 5th as the standard deviation of the test indicators, and calculated the reference range for each individual as the mean ± 1.96 standard deviation. [1][2][3][4][5][6][7][8] We calculated the skewness and kurtosis obtained from each item and each measured value in advance, and confirmed the normal distribution.

| Method (III): This calculation method uses measurement results of past normal time under the normal distributional assumption
Assuming that the individual reference range has a normal distribution, we defined the range in which 95% of the measurement results from healthy subjects fall within μ ± 2σ and estimate the error as the mean ± 2S. The smaller the number of measurements, the larger the estimation error. We determined the range in which the present measurement result X can be determined to be within or beyond the reference range based on previous measurements from healthy individuals (X1, X2, …, Xn). The present measurement results X are samples from the normal distribution population N (μ, σ^2) (μ and σ are unknown), which is equivalent to previous measurement results from healthy subjects (X1, X2, …, Xn). This is a test of the null hypothesis, and the same concept as the t test for the difference between two groups can be applied.
The T-distribution becomes T = X-mean (n)/S^((1＋(1^n)). If the top 2.5% of the t-distribution with freedom n − 1 t(n − 1)(0.0025) is used, when |T|>t(n-I) (0.025), the null hypothesis is rejected with a significance level of 5%, and it can be assumed that the physiological state changed due to a certain factor. In other words, we can consider the range in which the present data have a 5% false-positive rate, and the null hypothesis cannot be rejected (mean X-Cn < X<X mean X + Cn), as the reference range. 18 In this study, Cn = t(n-1) (0.025) ^((n + 1)/n). Using the value of 3.041 when n = 5 as the significance level α = 0.05. 18

| Method (IV): This calculation method uses Bayesian inference
We assumed that the individual reference ranges obtained using  We assume that the mean μ0 and standard deviation σ0 of the test value X for data from a healthy subject have a normal distribution.
The test value of an individual i at time j, X ij , is expressed with the following equation: where μi is the mean of the test result X for individual i through the time j = 1, n, where t ij is the temporal variation of intra-individual test values and e ij are measurement errors.
Let us assume that t ij and e ij have the same dispersions τ 2 and σε 2 regardless of the time and subject, and τ and ε are independent.
The population mean μ0 and standard deviation σ0 are predicted ahead of time, and with this prior distribution, the mean for N observations, and assuming a dispersion of σ2, follows a normal distribution of N (μn, σn) using Bayesian interference. If there is no observation, the reference value for the test is the individual reference value.

| Analytical accuracy
We obtained acceptable accuracy for the four target indicators with the mean X-Rs-R method with two kinds of reference sera during the for RBP and TTR. We obtained the mean total variations for the total variations in each reference serum in monthly sets collected over a 2 month period.

| Determining the reference range by each statistical analysis method
We obtained the maximum, minimum, mean, and standard deviation for the four indicators measured in 20 subjects based on five measurements per subject. Figure 1 compares the results for each test indicator for the 20 subjects and the results of the five measurements for each subject. The data were statistically analyzed using the four methods described above and the following results were obtained: Method (I), mean ± 1.96 standard deviation; Method (II), mean ± standard deviation (RCV); and Method (III), mean ± 3.041 standard deviation (mean ± 2S) ( Table 2). The RCV obtained from the results of five measurements for each test indicator were as follows: TRF = 11.64%, ALB = 12.68%, RBP = 20.54%, and TTR = 15.89% (Table 2). We also performed a statistical analysis with Bayesian in-

| Comparison of inter-individual CV and intraindividual CV
Next, we compared CV (inter) and CV (intra) calculated using the five measurement results for the 20 subjects ( Figure 2). For TTF, RBP, and TTR, the CV (intra) was smaller than the CV (inter) for all 20 cases. For ALB, the CV (intra) was smaller than the CV (inter) in 18 of the 20 cases ( Figure 2). The mean CV (intra) of the 20 subjects was lower than CV (inter) for TRF, RBP, ALB, and TTR ( Figure 2).

| Temporal variations in reference range estimates
Using the five measurements from the 20 subjects for the four test The first measurement was determined by comparing mean X-Cn < mean X < mean X + Cn and the reference ranges reported in previous studies. 18,24,27 For reference ranges estimated using

Methods [(I)-(III)], the approximation tendency could be confirmed
from the third measurement. In contrast, the reference range obtained with Method (IV) was much wider than those obtained with Methods (I) and (II), whereas it was narrower than that obtained with Method (III) (Figure 3). Intra-individual reference ranges examined with the four methods in the present study were also narrower than inter-individual reference ranges currently being used after five measurements ( Figure 3).

| D ISCUSS I ON
The typical procedure to determine a reference range is as follows 25,28-31 :

Reference individuals are selected from healthy individuals. A
population of reference individuals selected for each sex and age group comprises at least 120 individuals.
2. Statistical analysis: mean ± 2 standard deviation (more accurately, 95% of the normal distribution is equivalent to mean ± 1.96 standard deviation, and mean ± 2 standard deviation is the range that includes 95.45% of the normal distribution).
3. The above selection conditions for reference individuals, measurement conditions, and statistical analysis must be clearly stated.
In other words, the reference range of test values is expressed as a 95% confidence interval of inter-individual variations, including   The concept of individual reference was proposed by Williams 41 in 1967, and a long-term evaluation of health conditions of individuals was considered to lead to the early discovery of chronic diseases. In many tests, variations caused by physiological factors were larger for inter-individual than for intra-individual assessments, which led to the acknowledgment of the importance of intra-individual variations. 42 In the current study, we examined individual reference ranges for Methods (I)-(III) and compared these with the commonly used reference range (inter-individual reference range).

TA B L E 3 Estimation of inter-individual variability and intra-individual variation using mixed effects model
We found that the individual reference ranges calculated using the three methods were narrower, closely capturing physiological vari-  Furthermore, when the individualized referential area is narrower than the collective one, changes and development of the diseases of the patients or subjects might be spotted earlier for appropriate treatments. On the other hand, when the individualized referential area is wider than the collective one, unnecessary treatments might be avoided.

| CON CLUS ION
In the present examination, TRF, RBP, and TTR had lower CV (intra) than CV (inter) in all 20 subjects, and the mean CV (intra) was lower than the mean CV (inter) for TRF, RBP, and TTR. In contrast, CV (intra) was higher than CV (inter) for ALB in two of the 20 cases although mean CV (intra) for ALB was lower than that of CV (inter), suggesting that there may be cases where the intra-individual reference value is not appropriately understood.
Nevertheless, the preferred method for determining the individual reference range should allow close observation of temporal changes in test indicators with large inter-individual differences.
Such methods will play an important role in the development of new biomarkers and in routine diagnosis. For nutrition support team (NST)-related test indicators in particular, the results F I G U R E 2 Comparison of inter-individual and intra-individual coefficient of variations. Coefficient of variation (CV) (inter) and CV (intra) were calculated for each measured indicator using five measurements from the 20 cases, along with the mean and standard deviation of CV (intra) for the 20 cases. On x-axis, CV (inter) means the coefficient variation of the average value by 20 subjects. The number 1 to 20 shows the coefficient variation of the measurement data of five measurements for each subject, and CV (intra) means the average data of the CV for each subject. On y-axis, the value shows the coefficient variation data obtained using the chosen method should closely reflect, for example, the postoperative nutritional state, allowing management of central venous nutrition and the reduction of complications (infections), thereby closely capturing the nutritional state of an individual. 14,19 Furthermore, such methods could be widely applied to test indicators such as those related to pre-and post-dialysis tests and glucose tolerance tests.

ACK N OWLED G M ENTS
The authors thank Mitsuharu Itabashi (SRL.Inc Tokyo, Japan) for actual testing, Hirokazu Nishijima (SRL.Inc Tokyo, Japan) for coordination of tests, Toshihito Furukawa (Biostatistical Research Co. Ltd. Tokyo, Japan) for advice about statistical analyses, and Yasushi Kasahara (Fujirebio Inc Tokyo, Japan) for advice about the paper preparation.

CO N FLI C T O F I NTE R E S T
There are no conflicts of interest to be disclosed.

AUTH O R S CO NTR I B UTI O N S
Each author has made an important scientific contribution to the study and the manuscript.