The European Biological Variation Study (EuBIVAS): Biological Variation Data for Coagulation Markers Estimated by a Bayesian Model.

BACKGROUND
For biological variation (BV) data to be safely used, data must be reliable and relevant to the population in which they are applied. We used samples from the European Biological Variation Study (EuBIVAS) to determine BV of coagulation markers by a Bayesian model robust to extreme observations and used the derived within-participant BV estimates [CVP(i)] to assess the applicability of the BV estimates in clinical practice.


METHOD
Plasma samples were drawn from 92 healthy individuals for 10 consecutive weeks at 6 European laboratories and analyzed in duplicate for activated partial thromboplastin time (APTT), prothrombin time (PT), fibrinogen, D-dimer, antithrombin (AT), protein C, protein S free, and factor VIII (FVIII). A Bayesian model with Student t likelihoods for samples and replicates was applied to derive CVP(i) and predicted BV estimates with 95% credibility intervals.


RESULTS
For all markers except D-dimer, CVP(i) were homogeneously distributed in the overall study population or in subgroups. Mean within-subject estimates (CVI) were <5% for APTT, PT, AT, and protein S free, <10% for protein C and FVIII, and <12% for fibrinogen. For APTT, protein C, and protein S free, estimates were significantly lower in men than in women ≤50 years.


CONCLUSION
For most coagulation markers, a common CVI estimate for men and women is applicable, whereas for APTT, protein C, and protein S free, sex-specific reference change values should be applied. The use of a Bayesian model to deliver individual CVP(i) allows for improved interpretation and application of the data.


Introduction
Coagulation markers play a central role in a variety of clinical settings, such as evaluation of a patient presenting with suspected thromboembolism or increased bleeding tendency, monitoring anticoagulant therapies, evaluation of liver function, and as risk assessment markers. To ensure correct interpretation of coagulation markers in these and other contexts, data on biological variation (BV) are necessary. BV data are used to set analytical quality specifications (APS), to assess changes in a measurement series within an individual by the reference change value (RCV) (1), to examine the use of population-based reference intervals (2), and to derive personalized reference intervals (3). However, for these applications, BV estimates must be reliable and representative for the populations to which they are applied. BV components include the within-subject BV (CV I ), which describes the natural fluctuation of the concentration around a set point within an individual, usually reported as an average (mean) CV I estimate for the study population, and the between-subject BV (CV G ), which describes the variation between the set points of different individuals (4).
BV studies are usually undertaken as prospective experimental studies in healthy volunteers, but different statistical approaches are applied to deliver the BV estimates. The most frequently used method is that detailed by Fraser and Harris, in which duplicate analysis of samples is followed by analysis of variance (ANOVA) (5) or CV-ANOVA (6). However, these approaches depend on laborious data analysis including assessment of outliers at 3 levels, and variance homogeneity of both the analytical variation (CV A ) component and the CV I to provide generalizable results. Furthermore, data normality is assumed to construct confidence intervals (CI) (6). As shown by systematic reviews, these criteria are fulfilled by only a small number of BV studies (7). To overcome these issues, we recently explored a Bayesian approach for estimating BV (8). Our work has shown that a Bayesian model applying an adaptive Student t distribution is robust to extreme observations and does not require variance homogeneity to provide relevant results (8). Furthermore, in the Bayesian analysis, each individual's personal CV I , termed the within-participant CV I [CV P(i) ], can be estimated (8). The distribution of the individual CV P(i) can be used to assess whether data are homogeneous, and, as such, if a central CV I estimate is representative for the study population, if subgroup analysis is required or if the data are too heterogeneous for an average CV I estimate to be of value. In this way, the Bayesian approach provides an opportunity to evaluate whether the derived BV data are fit for purpose. The aims of our study were to deliver BV estimates for the following coagulation markers; activated partial thromboplastin time (APTT), prothrombin time (PT), fibrinogen, D-dimer, antithrombin (AT), protein C, protein S free, and factor VIII (FVIII) derived from the European Biological Variation Study (EuBIVAS) population (9), and to use the distribution of the CV P(i) to assess the applicability of using mean CV I estimates in clinical practice.

STUDY POPULATION AND SAMPLE COLLECTION
The EuBIVAS is a multicenter study involving 6 laboratories situated in Italy, Norway, Spain, the Netherlands, and Turkey (9). For this study on coagulation markers, 92 healthy participants; 39 men (21-59 years), 43 women (21-49 years), and 10 women (55-69 years) ( Table 1 in the online Data Supplement) were included, after assessment of eligibility based on clinical information and laboratory analyses, as previously detailed (9). For each individual, fasting blood samples were drawn for 10 consecutive weeks (April to June 2015). The EuBIVAS protocol was approved by the Institutional Ethical Review Board of San Raffaele Hospital in agreement with the World Medical Association Declaration of Helsinki and by the Ethical Board/Regional Ethics Committee as relevant for each involved center. All participants signed informed consent.

PREANALYTICAL AND ANALYTICAL PHASE
The same protocol was applied by all sites (9). Sample materials for coagulation analyses were collected in BD Vacutainer V R sodium citrate tubes (3.2%). Samples were centrifuged at 3000g for 10 minutes at room temperature within 1 hour of sampling. Platelet-poor plasma was removed without disturbing the sedimented cells and aliquoted in Nalgene cryovials, which were frozen rapidly at À80 C by immersion in a bowl with methanol and dry ice. All samples from each laboratory were sent collectively, frozen on dry ice, to San Raffaele Hospital, where they were stored at À80 C until analysis in 2017. The frozen samples were rapidly thawed in a 37 C water bath for 5 minutes and thoroughly mixed prior to being analyzed in duplicate in the same analytical run on an ACL Top 750 CTS (Instrumentation Laboratory S.p.A., a Werfen company). Only 3 results were below the limit of detection, all of which were D-dimer (< 21 ng/mL). The following single results outside clinical decision limits were excluded; D-dimer of 951 (week 9) and 3730 ng/mL (week 10) in a woman 26 years of age and AT of 74.9% (week 8) in a man 31 years of age. Single lot reagents, calibrators, and internal quality controls were used during the study period (online Supplemental Table 2), and no systematic changes in the concentrations of controls were detected (online Supplemental Table 3).

DATA ANALYSIS
Before calculating the BV measures, data were adjusted to counteract the effect of a trend in the results, by multiplying data at each time point by the factor "overall median"/"time point median", providing a constant median over the sampling period. Trend adjustment was applied to the overall study population and separately to the following 4 subgroups; men, all women, and women below and above 50 years, before analysis. To deliver the BV estimates, a Bayesian model, previously described in detail (8), was applied. In this model, Student t distributions, instead of normal distributions as in classical ANOVA, are assumed for the analytical and withinsubject effects to make the model more robust to extreme observations (8). In addition, previous information (priors) (10) is included in the model, to deliver more precise estimates when analyzing with Bayesian updating. In our model, we applied the following prior distributions and hyperparameters for the priors, as detailed in (8). N truncated indicates that only the positive part of the normal distribution is used in the estimation routine and SDs are defined as positive where l and r refer to the mean and SD, respectively. To estimate these priors, which were included in the analysis of the overall group as well as subgroups, previously published data from Kristoffersen (11) and de Maat (12) were used (online Supplemental Table 4). Inference in the model results in posterior distributions, obtained computationally, which provide estimates of the mean fl[CV P(i) ]g and SD fr[CV P(i) ]g of the CV P(i) , and CV G and CV A with corresponding SDs. Based on the estimated parameters, randomly generated CV P(i) were thereafter used to deliver the predicted distributions fd[CV P(i) ]g, from which the 20th [dCV P(i)_ 20], 50th [dCV P(i) _50], and 80th [dCV P(i) _80] percentiles and the SD were calculated. In the following, when the term CV I is used, it refers to the estimated measure, i.e., the l[CV P(i) ]. The credible interval is defined as the central portion of the posterior distribution that contains 95% of the values. A lack of overlap between the 95% credible intervals of the l[CV P(i) ] was used to indicate differences between subgroups. As an indicator of the degree of heterogeneity, the estimated Harris-Brown heterogeneity ratio; 100%fr[CV P(i) ]/l[CV P(i) ]g was calculated (13). For a homogeneous population with an average of S samples from each individual, this ratio should be below 100%/sqrt(2S) (13), i.e., for our study below 22.4% as 10 samples were included. In addition, we calculated the predicted Harris-Brown ratio by using the dCV P(i) _50 and SD from the d[CV P(i) ]. The posterior distribution of the parameters in the model were also used to calculate individual CV P(i) with 95% credible intervals for all study participants. For selected measurands, we performed a regression analysis with the response being the CV P(i) and the predictor being the study participants' homeostatic set point. 3) running on a Manjaro Gnu/Linux box. Stan is a probabilistic programming language for implementation of Bayesian inference (14). The main codes are available at https://gitlab.com/thoror/bayesian_bv_pa per (8).

Results
The CV P(i) for the study participants, with different symbols indicating men, women below and above 50 years, are displayed for all measurands in Figs. 1-4. CV P(i) appeared homogeneously distributed for all study participants for PT (Fig. 1), fibrinogen (Fig. 2), and AT and FVIII (Fig. 4), in line with the estimated Harris-Brown heterogeneity ratios being <22.4% (Table 1). For APTT (Fig. 1) and protein C (Fig. 3), the Harris-Brown ratio also indicated homogeneous data, but CV I estimates were lower in men than in women below 50 years (Table 1, Fig. 5). For protein S free (Fig. 3), the Harris-Brown ratio was above the cutoff for the overall group, but below in females, with differences in subgroup estimates observed between men and women 50 years (Table 1, Fig. 5). For D-dimer, the CV I estimate was lower in women >50 years compared to below, but the Harris-Brown heterogeneity ratios were high for both subgroups (Table 1, Fig. 2). No differences in CV P(i) were observed for participants from the different sites (online Supplemental Table 1), smokers (n ¼ 20), or females using oral contraceptives (n ¼ 4). The study participants' individual CV P(i) appeared related to the homeostatic set point for fibrinogen (b ¼ 0.012; P ¼ 0.005) and protein S free (b ¼ À0.047; P < 0.0001) (online Supplemental Fig. 1). Based on visual inspection, there was no clear relationship between the individual CV P(i) for each study participant for the different coagulation markers, with the exception of fibrinogen and protein S free (online Supplemental Fig. 2).

Discussion
Many studies have reported BV estimates for commonly analyzed measurands such as coagulation markers. However, the methodological quality and power of these studies vary, with potential impact on the applicability of these estimates in clinical practice. We used samples from the highly powered EuBIVAS study to deliver BV estimates by a Bayesian method. The Bayesian approach offers several advantages compared to classical frequentist methods. These include not needing to fulfill formal requirements related to outlying data and variance homogeneity. Furthermore, our Bayesian model provides the study participants' CV P(i) which, among other applications, allow us to assess the distribution of the data used as basis for the BV estimates (Figs. 1-4). BV components are typically reported in the form of a mean estimate, and it is therefore essential that this is representative for the population from which it has been derived, for the estimates to be safely used.

APPLICABILITY OF COAGULATION MARKER BV ESTIMATES
In our study, we report both the estimated l[CV P(i) ] and the 50th percentile of the predicted distribution; the [dCV P(i) _50] ( Table 1). The predicted values take into account that extreme values may occur more often than the posterior distribution suggests and are thus associated with larger SD. Typically, the estimated and predicted point estimates are similar, but larger differences may be evident when the number of included participants is small. In our study, the largest difference was observed for FVIII in women above 1264 Clinical Chemistry 67:9 (2021) dCV P(i) _50 was 10.8%. To appraise the homogeneity of the data, the predicted and the estimated Harris-Brown heterogeneity ratios can be used (Table 1) (8). The estimated Harris-Brown heterogeneity ratio, calculated based on the estimated measures, reflects the actual Fig. 2. Individual within-participant BV estimate [CV P(i) ] with 95% credibility intervals for fibrinogen and D-dimer. The participants are sorted by their CV P(i) , with women <50 years shown as triangles, women >50 years as squares, and men as filled circles.

Biological Variation of Coagulation Markers
Clinical Chemistry 67:9 (2021) 1265 study data, and is therefore used to assess the distribution of the BV estimates in our study. This ratio is below the cutoff of 22.4% for APTT, PT, fibrinogen, AT, protein C, and FVIII for the overall study population (Table 1). This indicates that these data are homogenous, as also illustrated in Figs. 1-4, and that using a Fig. 3. Individual within-participant BV estimate [CV P(i) ] with 95% credibility intervals for protein C and protein S free. The participants are sorted by their CV P(i) , with women <50 years shown as triangles, women >50 years as squares, and men as filled circles.
1266 Clinical Chemistry 67:9 (2021) common CV I estimate is appropriate. For APTT and protein C, the CV I estimates derived for men are lower than those for women 50 years (Table 1) as illustrated in Fig. 1 for APTT; where CV P(i) for men and women below 50 years are clearly separated, and for protein C in Fig. 3. This indicates that applying different CV I Fig. 4. Individual within-participant BV estimate [CV P(i) ] with 95% credibility intervals (Crl) for antithrombin (AT) and factor VIII (FVIII). The participants are sorted by their CV P(i) , with women <50 years shown as triangles, women >50 years as squares, and men as filled circles.

Biological Variation of Coagulation Markers
Clinical Chemistry 67:9 (2021) 1267 estimates for women and men may be relevant for these markers, depending on the purpose for which the data are being used. For protein S free, the Harris-Brown heterogeneity ratio was below the cutoff only in women 50 years, and differences in estimates were observed between subgroups (Table 1, Fig. 5). Thus, in this setting, applying subgroup estimates appears most appropriate, despite the somewhat heterogeneous data in men and women >50 years (Fig. 3). Generally, providing robust estimates for women >50 years is challenging due to the small number of participants in this group. This is particularly evident for FVIII (Fig. 4), where the broad individual 95% credibility intervals for these individuals reflect both the variation in the individual CV P(i) as well as the small number of participants. For D-dimer, the Harris-Brown heterogeneity ratios were high in the overall study population and in the subgroups, as illustrated in Fig. 2. Thus, the data are so heterogeneously distributed that to apply an average CV I estimate for this measurand would generally not be recommended. The high amount of "noise" in the D-dimer data may be related to low concentrations of D-dimer in healthy individuals, with most study participants having concentrations around 200-300 ng/mL, associated with high CV A estimates (Table 1).
In studies where classical methods such as ANOVA are applied to deliver BV estimates, outlying results have to be excluded to fulfill outlier and variance homogeneity criteria, but how much data must be excluded depends on the heterogeneity of the data (8). For some measurands, outlying results may make up a substantial amount of the data (15), which reduces the generalizability of the resulting BV estimates. In our study, we only excluded 3, clearly pathological, results from the data set. The low estimated degrees of freedom for the analytical component in our study indicate extreme observations in the data set between replicates (online Supplemental Table 5), but these were not necessary to exclude.
In a setting with homogeneous data, the classical frequentist and the Bayes approach will provide similar results (8). A disadvantage with applying a Bayesian model is that it requires more specialized knowledge and that running the analysis may be a relatively timeconsuming process and require a high amount of data processing power. Choosing appropriate prior distributions may also be challenging. In our model, we applied priors based on the most recent publications reporting data on most of our markers (online Supplemental  Table 4) (11,12). For APTT, the lCV P(i) was clearly lower than the chosen prior. In our analysis, the priors were given low weight, with a SD of 10%. Thus, these priors had little influence on the results, and rerunning the analysis with a lower prior for APTT, based on (11), did not change the results for APTT (data not shown).
For most measurands in our study, the CV P(i) was not related to the concentration of the homeostatic set point (online Supplemental Fig. 1). This is an important finding with clinical implications, indicating that a common CV I estimate is relevant for participants with different homeostatic set points, which is particularly important when calculating personalized reference intervals (3). Individual l[CV P(i) ] of fibrinogen and protein S free appeared related to the homoeostatic set point and to each other (online Supplemental Figs. 1 and 2). The concentrations of these markers may be influenced by acute phase (16,17). A previous EuBIVAS publication found transient increases in C-reactive protein in some participants (15), possibly caused by subclinical acute phase episodes. It is thus possible that this may have influenced also the results of fibrinogen and protein S free in these participants. However, a similar pattern is not seen for factor VIII, also an acute phase protein, suggesting that our observation may be coincidental.
The samples in our study were stored at À80 C for 2 years before analysis, but data indicate that most coagulations markers are stable for up to at least 24 months at À74 C (18). Furthermore, all the samples from the same participant were thawed simultaneously and analyzed in one run. Only 1 manufacturer's reagent was used, but it is unlikely that this will affect BV estimates, as long as the same measurand is targeted (19).

MARKERS
Previous studies on coagulation markers have described different approaches regarding the statistical analysis of the data. Some have followed the protocol of Fraser (5), excluding outlying data points and assessing variance homogeneity (11,(20)(21)(22), whereas others have not (12). These studies also differed with regard to study design, with de Maat (12) and Kristoffersen (11) applying monthly samplings, and Falay (20) and our study applying weekly samplings. The CV I estimates reported in these studies are quite similar, except for APTT, where de Maat (12) reported a higher CV I estimate than other studies. This discrepancy could be explained by the lack of outlier exclusion in the de Maat study. Our CV I estimates for protein C, protein S free, and FVIII were also lower than those reported from the other studies. This may be related to our study design or differences in data analysis. We also found small, but significantly lower CV I estimates in men than women 50 years for APTT, protein C, and protein S free. Differences between sexes have previously not been reported. Previous studies, including 20-40 participants, may not have been sufficiently powered to assess sex differences. This is of particular relevance for coagulation markers where hormonal factors play a central role, and where the higher CV I estimates in fertile women may be related to the variation of hormones during the menstrual cycle (23).

APPLICATION OF BV DATA FOR COAGULATION MARKERS
The coagulation markers assessed in our study have different clinical applications. These include diagnosis for inherited thrombophilia, hemophilia, and venous thromboembolism, for evaluation of liver function, and as part of diagnostic algorithms such as for, e.g., disseminated intravascular coagulation (DIC). The clinical context in which these markers are used must be taken into account when considering the applicability of the BV data. For most of the markers, data were homogenous for the overall population. Thus, setting APS based on these estimates, for the purpose of general diagnosis and monitoring, appears appropriate. Our finding that the CV P(i) was not dependent on the homeostatic set point (online Supplemental Fig. 1), also indicates that these APS may be relevant for patients with different measurand concentrations, but further studies are required to confirm this. For heterogeneous data, different percentiles of the dCV P(i) may be used to set APS. D-dimer displayed high heterogeneity, but is usually applied as a rule-out test in patients with low pretest probability for venous thromboembolism (24), and, thus, a clinical outcome model is recommended for setting APS (25).
All the markers included in the study showed marked individuality (Table 1). In this setting, the RCV provides a measure, with a given probability, for assessing whether a difference in consecutive results can be expected given the CV I and CV A for a participant in steady state conditions. For RCV calculation, laboratories' own long-term CV A estimates must be included. For markers with differences in CV I between subgroups such as for APTT and protein C, different RCVs should be applied for women and men. For protein S free, different CV I estimates were found between men, and women 50 years and >50 years. Data for the women 50 years were homogeneous, but not for men or women >50 years (Table 1). When data are heterogeneous, instead of using a mean CV I estimate, different percentiles of the predicted distribution of the CV P(i) may be used for RCV calculation, depending on the clinical purpose. Thus, in a clinical situation where it is important to identify a change, e.g., for a rule-in approach for further diagnostic work-up, the dCV P(i) _20 can be used to deliver a RCV, which increases the sensitivity. For a rule-out approach, the dCV P(i) _80 will deliver a RCV aimed at increasing specificity. Regarding D-dimer, data were so heterogeneous that applying an average CV I estimate in RCVs to be used as part of, e.g., DIC assessment should be avoided. Furthermore, the BV estimates for D-dimer are based on low concentrations found in healthy individuals, often close to the limit of detection, and may thus not be appropriate for monitoring of patients.

Conclusions
In this study, we deliver updated BV estimates for commonly requested coagulation markers by the use of a Bayesian method, based on samples from the large-scale, highly powered EuBIVAS. Our Bayesian model, which is robust to extreme observations and includes prior information, is of particular value when assessing relatively heterogeneous data. Our results indicate that for most coagulation markers, a common CV I estimate is applicable, whereas for others, such as APTT, protein C, and protein S free, sex-specific RCVs should be applied. Furthermore, our study illustrates that D-dimer data are so heterogeneous that the use of a mean CV I estimate is not recommended for, e.g., RCV calculations. The use of a Bayesian model to deliver BV estimates with individual CV P(i) allows for improved interpretation and application of the data.

Supplemental Material
Supplemental material is available at Clinical Chemistry online.