Clinical Application of Condence Interval for Monitoring Changes in Tumor Markers to Determine the Responsiveness to Cancer Treatment

Background: Tumor markers are used to monitor disease progression and determine the responsiveness to cancer treatment. However, there are no standardized criteria for monitoring serial tumor marker measurements. Herein, we have developed our own monitoring system for interpreting changes in tumor markers using overlapping 95% condence intervals (CIs) to determine whether the changes are signicant. Methods: Two-year data, including 117,289 results for 11 tumor markers in our laboratory, were analyzed. The distributions of absolutely delta% and cut-off values for certain percentiles were calculated. CI ranges for each tumor marker were set based on biological variation, and data were analyzed for each patient assessed at health check-ups and clinics, individually and overall. Results: Most tumor markers had low indices of individuality, with between inter-individual variability. The 95th percentile cut-offs for each tumor marker were much higher in the health check-up group than in the clinic group. In decreasing order, the percentages of results with no overlap in 95% CIs were thyroglobulin antigen, 14.9%; protein induced by vitamin K absence-II (PIVKA), 11.9%; prostate-specic antigen, 9.8%; and cancer antigen 72-4, 8.7%. After correction using the reference interval, the percentages decreased to less than 5%, except for PIVKA (10.9%). Conclusions: We suggest that our own monitoring system can serve as a criterion for delta check and auto-verication of tumor markers. Further studies are required to validate and demonstrate this concept in real clinical situations using actual clinical data reecting disease progression in cancer patients and responsiveness to cancer treatment. RI: Reference interval; RCV: Reference change value; CI: Condence interval; LIS: Laboratory Alpha-fetoprotein; HCG: Beta-human chorionic gonadotropin; CA15-3: Cancer antigen 15-3; CA19-9: Cancer antigen 19-9; CA72-4: Cancer antigen 72-4; CA125: Cancer antigen 125; CEA: Carcinoembryonic antigen; PIVKA: Protein induced by vitamin K absence-II; PSA: Prostate-specic antigen; SCC: Squamous cell carcinoma antigen; TG: Thyroglobulin antigen; IRB: Institutional review board; CV A : Analytical coecient of variation obtained from the internal quality control program; CV I : Within-subject variation; CV G : Between-subject variation;


Background
In recent decades, there have been many improvements in laboratory medicine. However, it is di cult to determine the signi cance of changes between two consecutive laboratory results. Obviously, many laboratory results have variability in many aspects, including pre-analytical, analytical, and post-analytical factors [1][2][3][4][5][6]. Thus, clinicians, as well as laboratory physicians, should be aware of the potential risk of false interpretation.
Together with these confounding factors, biological variation is an important factor to consider when interpreting the changes in serial laboratory measurements. The term "biological variation" represents the physiological and metabolic properties according to the diverse status of healthy or non-healthy individuals and re ects uctuations in serial measurements [7][8][9].
Comparing the changes in serial laboratory results is important for assessing the clinical status of a patient and responsiveness to therapy as well as predicting the point when additional interventions are necessary [6][7][8][9][10][11]. Conventional reference intervals (RIs) may also provide information about these points, but they are often of limited value [2,[11][12][13]. For analytes with a large RI, two consecutive results may be within the RI even if they differ signi cantly. In addition, when one of two consecutive results is outside the RI and another is inside, the clinical decision can be mistaken [11]. For these reasons, monitoring changes in serial laboratory results can be more helpful than conventional RIs in actual clinical situations [10]. Moreover, the decision limit should be set based on the individual properties of an analyte, factors associated with pre-and post-analysis, medical need, and clinical decision point [6].
For tumor markers, monitoring changes also plays an important role in patient management. The increasing interest in tumor markers as a less-invasive diagnostic tool for determining malignancy has encouraged their clinical use along with other diagnostic tools [2,13]. Ideal tumor markers should re ect early detection, a differential diagnosis, response to therapy, prognosis, and progression or recurrence of malignancy and provide accurate and reliable results [9]. However, the changes in tumor marker values can show wide uctuations over time and can be di cult to access. The analytical uncertainty and unreliability of tumor marker values determined by different methods are also obstacles for access [1,2]. Moreover, there are no uniform or standardized criteria for determining the clinical signi cance of a difference between two consecutive marker results [3,14].
Hence, it is di cult to set decision limits for interpreting the clinical signi cance of changes in tumor markers.
In clinical chemistry, biological variation is an important concept for explaining the variability of serial laboratory results. Biological variation includes analytical variation and within-and between-subject variation, thus, re ecting the variation of each analyte [10,12]. Moreover, numerous studies have examined the biological variations in tumor markers [1-3, 9, 13, 14]. One widely used evaluation tool based on biological variation is the reference change value (RCV), which has been used to interpret changes in serial laboratory results [8,10,11,15] and as a criterion for delta check and auto-veri cation [4,[16][17][18]. However, RCV is a onesided comparison method and still has limitations for analytes with a large intra-individual variation [11,18].
When comparing two independent values, the con dence interval (CI) assigns a statistical signi cance for each value [19,20].
The CI indicates a range of values that is likely to contain the parameter of interest with a speci ed probability, most often 95%. In two-sided comparison, the CIs for two certain values may overlap if they are not signi cantly different. In our previous study, we introduced the concept of CI into the interpretation of our clinical chemistry results [21].
To be best of our knowledge, there is no decision limit yet for conducting a delta check of tumor markers. Furthermore, there is no study regarding the association of overlapping CIs and laboratory results. In this study, we aimed to (i) apply overlapping CIs to Tumor markers were measured using the following automated analyzers: the ADVIA Centaur ® XP immunoassay system (Siemens Healthineers, Erlangen, Germany) for CA19-9, CA125, CEA, and PSA; the Cobas ® e 601 module (Roche Diagnostics, Basel, Switzerland) for CA15-3, CA72-4, HCG, SCC, and TG; and the uTASwako i30 (Wako Diagnostics, Osaka, Japan) for AFP and PIVKA. This study was approved by the institutional review board (IRB) of Wonju Severance Christian Hospital (IRB no. CR319041) and the requirement for informed consent was waived.

Data analysis
To calculate the changes in two consecutive tumor marker test results, pairs of test results were collected from each patient. The statistical methods are described in detail in our previous publication [21]. In brief, the following statistical processes were used.
(i) The absolute values of the percent difference between two consecutive test results were calculated using the formula, Absolute delta% = Current result -Previous result /Previous result × 100 (%). (ii) The distributions of absolute delta% were assessed to determine the median, interquartile range, and some speci ed percentile values (i.e., 90th, 95th, and 97.5th ). (iii) Overlapping CIs were used to monitor changes in serial tumor marker values, and CI ranges based on biological variation were calculated using the formula, where Z test indicates the Z score at which the degree of overlapping CIs at a given probability can reject a null hypothesis, CV A is the analytical coe cient of variation obtained from the internal quality control program of our laboratory, and CV I is the withinsubject variation from the Westgard database of biological variation with the desired speci cations of biological variation [22].
We also calculated the index of individuality, which is the ratio of CV I to between-subject variation (CV G ). Serial changes are known to be more important for an analyte with a low index (< 0.6), but conventional RI is diagnostically valuable for an analyte with a high index (> 1.4) [23,24].
As mentioned in our previous study, the chance of non-overlapping 95% CIs is not at a type I error probability of α = 0.05, which instead corresponds to that of 83.4% CIs [21], but at α = 0.0056. In other words, the chance of non-overlapping 83.4% CIs corresponds to that exceeding RCV 95% . In this study, we used the Z test values of 1.39, 1.65, and 1.98 at CIs of 83.4%, 90%, and 95%, respectively.
All statistical analyses were performed using SPSS version 25.0 (IBM Corp., Armonk, NY, USA) and the add-in Analyse-it version 5.11 (Analyse-it Software Ltd., Leeds, UK) in Microsoft Excel 2016 (Microsoft Corp, Redmond, WA, USA).

Development of a monitoring system
We developed a monitoring system using overlapping CIs for interpreting serial tumor marker values. The detailed processes are described in our previous study [21], and Fig. 1 is an example of our new system. If the 95% CIs of the previous and current test values do not overlap, then the two results are signi cantly different from each other. However, even in this case, if both values are within the RI, they have low clinical signi cance. Therefore, we conducted further analysis after correction using the RI. In other words, we proceeded with further analysis only if at least one previous or current test result deviated from the RI, and clinical signi cance was determined according to whether their CIs do not overlap.
Furthermore, through an administration menu of our system, we input our own CV A values obtained annually from our one-year internal quality control data. CV I is a xed value for each tumor marker, but it can also be changed if the Westgard database is changed.

Results
In total, 117,289 tumor marker results were analyzed over the study period, and 65,112 (55.5%) results were paired. Table 1 shows the test numbers for each tumor marker. We further analyzed the results by dividing them into health check-up and clinic (including both in-and out-patient) groups. AFP, CA125, CEA, and PSA, which are routinely tested tumor markers in our hospital, all showed higher percentages of paired results in the clinic group than in the health check-up group (p < 0.05 for all).  CV A is the analytical coe cient of variation obtained from the internal quality control program of our clinical chemistry laboratory; CV I and CV G are the within-and between-subject variation from the Westgard database with the desired speci cations of biological variation, respectively. Index of individuality is equal to CV I divided by CV G .
*For CA72-4 and PIVKA, CV I was determined by our laboratory because there were no references of allowable limits for these items. †For HCG, CV I was derived from the allowable limits of performance for biochemistry from the Royal College of Pathologists of Australasia.
CI, con dence interval. See Table 1 for other abbreviations. Table 3 shows the statistical characteristics for the absolute value of each delta% in each tumor marker. All tumor markers showed non-normality (non-parametric), which was con rmed by the Kolmogorov-Smirnov test (p < 0.05 for all). Of all tumor markers analyzed, CA15-3 (48.2%) and CEA (65.4%) showed the lowest 95th percentile cut-off value. However, CA19-9 (135.8%), SCC (185.3%), CA72-4 (188.7%), PSA (413.0%), TG (422.0%), and PIVKA (589.6%) showed high 95th percentile cut-off values of more than 100%. The 95th percentile cut-offs for all tumor markers were much higher in the health check-up group than in the clinic group. Many tumor markers showed right-skewed patterns in the histogram, but for some tumor markers (CA72-4, HCG, PIVKA, PSA, SCC, and TG), a higher proportion (absolute delta > 100%) was noted. The absolute delta% distributions for each tumor marker are illustrated in Supplementary Fig. 1. CEA, CA125, AFP, HCG, and SCC, respectively. After correction using the RI, the percentages decreased to less than 5%, except for PIVKA (10.9%). For the 95th percentile cut-offs, the percentages of non-overlapping 95% CIs were much higher in the health checkup group than in the clinic group for all analytes (p < 0.05).     Table 1 for other abbreviations.

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A tumor marker is a substance produced by a tumor or elevated by the presence of a tumor. The tumor marker concentration may be in uenced by treatment or surgery, and these markers allow for differentiating patients with malignancy from healthy individuals [26]. Tumor markers have been increasingly used in clinical applications. Changes in serial tumor marker values should re ect the clinical status and response to cancer treatment, as well as provide relevant information for treatment decisions [2]. However, previous studies of tumor markers have only focused on the detection, differentiation, and prognosis of cancer and responsiveness to therapy. There is little to no consensus regarding the interpretation of tumor marker results. Additionally, few studies have been conducted on the biological variation of tumor markers [1-3, 9, 13, 14]. The major obstacle in interpreting serial tumor marker values is the development of tools that can overcome existing limitations by considering random errors, analytical factors, and biologic variations [1,2,13,14].
In our previous study, we introduced our new monitoring system using overlapping 95% CIs in serial clinical chemistry test results.
Thereafter, in this study, we attempted to utilize our system to monitor serial tumor marker values, including CV A and CV I .
Furthermore, we have applied overlapping 95% CIs to monitor changes in two consecutive tumor marker results in our previous publication concerning clinical chemistry items [21]. The coe cients of variation, CV A , CV I , and CV G , for some tumor markers have been added to the Westgard database [22,25]. Here, we have applied overlapping CIs and CI ranges based on the biological variation for each tumor marker. Biological variation is important when considering tumor markers, especially for interpreting two consecutive results to assess cancer progression or responses to therapy [1,3,14].
In our study, the indices of individuality were low (< 0.6) in most tumor markers, except for SCC, indicating that many markers uctuate in the same individual. Therefore, when interpreting two consecutive tumor marker results, a monitoring tool is more valuable than RI or a speci ed cut-off value [23,24]. Considering each CV I , the application of overlapping CIs as a two-sided comparison of two consecutive tumor marker results can be clinically meaningful for monitoring changes.
We have integrated this concept into our LIS system for monitoring our routine tumor marker tests. After application in our laboratory, we collected the data from our LIS server and analyzed the statistical characteristics. We compared the percentages of test results with non-overlapping CIs before and after correction using the RI. As mentioned in the introduction, in the case of tumor markers with a large RI range, if both values are within the RI, it may not be clinically meaningful even if they show a signi cant difference [11]. This is essential for tumor markers because their cut-off values are important for diagnosing the presence of malignancy. However, since the signi cance of the RI may vary for each tumor marker, it is necessary to apply it according to the characteristics of each tumor marker or the clinical situation of each laboratory, such as in the case of clinical chemistry [21].
Our study has some limitations. First, we collected only tumor marker results from patients to gain an exemption for informed consent from the IRB. Therefore, we did not consider clinical information, such as whether a patient had a tumor or received a treatment. Instead, we estimate that most patients in the health check-up group are cancer free. Further prospective study is needed to compare the relationship between our system and the real clinical course of cancer patients and healthy individuals.
Second, we did not consider the time variable in our new system. Although the time difference is considered in delta checks for some routine clinical chemistry parameters, thus far, there are no tumor markers with a time-dependent role. Furthermore, the application of delta checks for tumor markers is not yet available for most clinical laboratories.

Conclusions
In conclusion, we have applied overlapping CIs to interpret changes in two consecutive tumor marker results. We suggest that this

Funding
None applicable.

Availability of data and materials
The dataset used and analyzed during the current study is available from the corresponding author on reasonable request.

Ethics approval and consent to participate
This study was approved by the institutional review board (IRB) of Wonju Severance Christian Hospital (IRB no. CR319041) and the requirement for informed consent was waived.

Figure 1
An example of our monitoring system for changes in two consecutive tumor marker results using overlapping 95% con dence intervals. (A) Initial result, (B) and (C) follow-up result of the patient. "HL/D/P/I" indicates the reference range (high, low), delta, panic ag, and serum index, respectively, showing a bias of more than ±10% for hemolysis, icterus, or lipemia. "95% CI" indicates the 95% con dence interval for the current result, and "95% CI_O" indicates whether the CIs of current and previous results overlap with each other. An arrow at "HL/D/P/I" indicates whether the test value has increased or decreased relative to the reference interval; a hyphen at "95% CI_O" indicates that the CIs of the current result have not changed signi cantly relative to the CIs of the previous result (B), and an arrow at "95% CI_O" indicates whether the CIs of the current result have increased or decreased signi cantly relative to the CIs of the previous result (C). See Table 1 for abbreviations.

Supplementary Files
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