The typical procedure to determine a reference range is as follows [25–29]:

(1) 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 measurement errors. Medical examination data are repeatedly measured for each individual, and as new information is added to the data longitudinally (inter-individually), distributions can be analytically divided into inter-individual variations and other errors, i.e., intra-individual variations. The most natural interpretation of inter-individual variations is a variable model in which individuals have normal distribution around the inter-individual mean [15–18]. In contrast, a previous study on triglyceride determined the reference range for an individual using between 25 to 7,055 cases and found Cvi values ranging from 2.3–31.9% for the shortest measurement interval of several times a day to once every 2.5 months [30]. Earlier studies on high-density lipoprotein (HDL) cholesterol showed that a population ranging from 25 to 1,058 cases provided Cvi values of 4.8–10.0% [1, 2, 22–24, 31, 32]. The RCV for ALB was reported to be 14.5% [33], similar to the RCV value of 12.7% obtained in this study.

Three factors can cause variations in measured values: disease, physiology, and measurement technique [1, 2, 23, 24, 34]. Physiological variations may include the age, sex (including pregnancy and menstrual period), and dietary factors (such as meals, drinking, smoking, and stress) of an individual, inter-individual variations affected by genetic factors, and intra-individual variations such as the condition of the individual prior to the examination (such as position, long- or short-term exercise), and conditions associated with blood sampling, such as the time of day [35]. In contrast, in terms of the limit of permissible errors for measurement methods, Tonks [36] divided ¼ of the reference range by the median of the reference range as the reference to evaluate the performance of the control survey for serological components; as a result, the maximum was set at 10%. Kitamura [9] and Cotlove et al. [37] focused on a component with intra-individual variations much narrower than the range of variations for the population by studying the physiological variations in an individual. They proposed the limit of permissible error (CV%) = ½ × (standard deviation for physiological intra-individual variations)/(mean of reference range) × 100. CV is expressed as CV% = standard deviation × 100/mean (%), which leads to total CV (CVt: total) = measured CV (CVa: analysis) + pre-measurement CV (CVp: pre-analysis) + inter-individual CV (Cvi: individual), which are indicators of intra-individual and inter-individual variations [38].

The concept of individual reference was proposed by Williams [39] 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 [40]. 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). We found that the individual reference ranges calculated using the three methods were narrower, closely capturing physiological variations in each individual. Furthermore, we examined Method (IV) as a new model to calculate reference ranges. Method (IV) is a mixed model of inter-individual reference range and intra-individual reference range, which allows calculation of a reference range for each individual while using the inter-individual reference range routinely used in clinical settings. Consequently, Method (IV) would be easily accepted in routine clinical settings.

The present study examined 20 cases and we obtained good results in determining the individual reference range. Currently, the commonly used inter-individual reference range is the mean ± 1.96 standard deviation of the reference individual. With Method (III), initially proposed by Tango [21], we found that the range of upper and lower limits is wider for indicators where CV (inter) > CV (intra) and CV (inter) < CV (intra) of the 20 subjects are similar. The present study demonstrated that a small number of measurements leads to a high estimation error when setting the individual reference range, and that calculating standard deviation from the RCV using the method proposed by Fraser [41] [Method (II)] is useful. In contrast, using Fraser’s method, the RCV must be obtained for each item ahead of time. The method proposed by Tango [21] is more versatile and the RCV converges after three measurements. Therefore, evaluating these methods with health examination and clinical data from actual subjects may provide information more useful in clinical settings. Nevertheless, these evaluations have taken the evaluation of the first measurement and the total fluctuation into consideration and thus, in terms of applicability, it is difficult to apply on new patients and experiment subjects.

On the other hand, since Bayesian inference can estimate individual referential area from the second measurement of new patients and subjects, its medical information is, all in all, more efficient and appropriate than the ones from conventional ways. In other words, clinical physicians might judge within daily criteria (among individuals) by using the initial values and install Bayesian inference in the system for the second time onward. By using the initial values then the measured ones since the second time onward, an integrated individual criteria area can be estimated without choosing smaller items. This Bayesian inference is a mixed model of the collective criteria area among individuals (in the initial check) and individualized criteria area (the second time onward). In the initial check, no subject has previous values so the normal criteria area in daily check is used. Then, a shift to Bayesian inference from the second time can increase the applicability. Hence, if we could install and utilize LIS (Laboratory information System) in the medical check systems in hospitals, useful information could be attained without placing extra burden on clinical physicians. 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. Moreover, when the individualized referential area is wider than the collective one, unnecessary treatments might be avoided.