In this study we expectedly found differences in all studied parameters between representatives of the group III (patients on OAT) and the remaining donors and patients. No significant differences were revealed between normal healthy donors (group I) and patients of the group II, except for prothrombin F1+2 which was significantly higher in group II compared to healthy donors.

Further, for all the analyzed parameters but fibrinogen and APTT ratio the cut-off points discriminating between users and non-users of OAT lie far beyond the 25–75 percentile ranges estimated for group III by ROC curve analysis (Table ​(Table33).

Secondly, using a multiparametric discriminant function analysis we showed all the groups were significantly separated apart (Fig. ​(Fig.1)1) and the variables which mostly contributed to a significant discrimination of the groups, with a maintenance of a minimum tolerance of 0.5, were factor X (partial Wilk's lambda = 0.812, p « 0.0001), protein C (partial Wilk's lambda = 0.907, p < 0.0002), fibrinogen (partial Wilk's lambda = 0.922, p < 0.001) and prothrombin F1+2 (partial Wilk's lambda = 0.939, p < 0.003). The most precise a posteriori allocation of cases to the a priori assigned groups was found for the OAT patients (93%), whereas the least precise characterized the control healthy donors (41%).

Third, the associations between raw data of INR and each of the remaining tested variables were apparently hyperbolic and characterized by very significant Spearman's rank correlation coefficients (Fig. ​(Fig.22 inserts and legend). To cope with the requirements of data linearity for multivariate parametric analyses, we verified various mathematical transformations of raw data (logarithmic, semilogarithmic, reciprocal, square root). Based on the estimates of individual linear correlation coefficients and homogeneity of raw data distributions we chose the logarithmic transformation of raw data (X' = log(X) and Y' = log(Y)). Fig. ​Fig.22 (right panels) shows the linear partial associations between INR and other variables. Contrary to rank correlation, we observed significant linear associations of INR with all variables but the APTT ratio and fibrinogen (the latter not shown). Simple linear (Pearson's) correlation coefficients between all the analyzed variables are given in Table ​Table44.

In general, to reason on which of independent variables contributes mostly to the variability of INR, we employed the analysis of multiple regression. The residual analysis (including testing for normality, homoscedasticity, autocorrelation, linearity and outlying observations) was always employed as a routine prior to the appropriate multiple regression analysis performed on log-transformed data. In the standard classical model of multiple regression we included one dependent variable (INR) and all 7 independent variables: fibrinogen, APTT ratio, FII, FVII, FX, protein C and prothrombin F1+2. The significant regression coefficients were found only for five of these variables, whereas neither fibrinogen nor APTT ratio contributed significantly to the explaining of INR variability. Due to the low tolerance values for all of thus included significant variables (0.1–0.3), pointing to a considerable collinearity of all independent variables in such a model, we further employed the ridge model of a forward stepwise multiple regression with a lambda = 0.1. By the extension of such criteria we finally built up the regression function including five significant independent variables: FII, FVII, FX, protein C, prothrombin F1+2, altogether explaining over 92% of INR variability and each having a tolerance of at least 0.22 (Table ​(Table5).5). Then, we gradually eradicated from the model the independent variables with the lowest significance and F_remove values to finally approach a two-component model including only FII and FVII (overall R² = 0.903, tolerance = 0.378 for each, partial correlation coefficients: r_FII = -0.711, r_FVII = -0.659, p « 0.0001 for each).

Using the above algorithm we accomplished the following regression equations – for the complete five-component model:

[INR] = -0.136 * [FII] -0.211 * [FVII] -0.104 * [FX] -0.088 * [protein C] -0.048 * [prothrombin F1+2] + 1.133

and the other for the "eradicated" two-component model:

[INR] = -0.251 * [FII] -0.296 * [FVII] + 1.168,

where [INR] = log(INR), [FII] = log(FII activity), [FVII] = log(FVII activity), [FX] = log(FX activity), [protein C] = log(protein C activity), [prothrombin F1+2] = log(concentration of prothrombin fragment F1+2).

In summary, (i) three of the assayed clotting parameters (factors II, VII and X) appeared as very strong modulators of prothrombin time (INR), (ii) protein C and prothrombin fragments F1+2 had moderate influence, (iii) whereas both APTT ratio and fibrinogen had no significant impact on INR variability.

It should be emphasized that regardless of the complexity of the overall multiple regression model, comprising from 2 to 7 independent variables, the variability of INR was largely explained by the variabilities of the included independent variables (from 90.3% for the 2-component model up to 92.9% for the models including 5–7 variables). Further, the dominance of the complex multiple regression model (with 5 independent variables of significant contribution) over single variable models in explaining the total variability of INR was from 3.6% for FII and 5% for either FVII or FX to over 25% for F1+2. This clearly demonstrates that each of these most significant contributors (clotting factors II, VII or X) remained apparently sufficient in explaining the vast portion of an overall INR variability. Moreover, due to collinearity and low tolerance of independent variables included in the multiple regression model, one should rather consider such a ridge multiple regression model which compromises the minimal number of independent variables with the maximal overall determination coefficient. If so, there is no need to monitor a large variety of clotting-related parameters and rather to choose a few most discriminating variables. Our estimates show that such conditions are generally substantiated in the multiple regression model comprising FII and FVII that altogether explained over 90% of overall INR variability.

To verify such an assumption we made a comparison between a standard method (monitoring of INR) and other (alternate) methods (prediction of INR based on the monitoring of selected clotting factors and/or coagulation-related variables). We used the above mentioned regression equations (for the 2-component model or for the 5-component model) to calculate the predicted INR values and compared the latter with the experimental INR evaluated using a standard laboratory procedure [13]. Despite a very significant linear correlation between INR_experimental and INR_predicted (Fig. ​(Fig.3),3), we were further interested whether these two approaches may be interchangeably applied in diagnostic practice, i.e. whether these methods produce comparable data. The differences between INR_experimental and INR_predicted within the pairs of data exceeded the range of doubled SD_difference only in 4.5% and 3% of cases for the 2-component model and the 5-component model, respectively, which points to a very good compatibility between both methods used to monitor INR (Fig. ​(Fig.4).4). The mean difference between the methods enables to extrapolate the results obtained with a regression method (INR_predicted) to those predicted to be read with the other one (INR_experimental), provided the dispersion of differences lies in a narrow confidence limit around the mean difference in the sample (Fig. ​(Fig.4).4). Considering the dispersion of the differences recorded within the pairs of data (since the standard errors of lower or upper limit are respectively = 0.00666 for the 2-component model and = 0.00594 for the 5-component regression model, and assuming the normal distributions of the differences for the 2-component model 95% = -0.1112 ± 0.1081 (-0.1248; -0.0976) and 95% = 0.1051 ± 0.1081 (0.0915; 0.1187) and for the 5-component model 95% = -0.0987 ± 0.0965(-0.1105;-0.0863) and 95% = 0.0947 ± 0.0965 (0.0826; 0.1068)), we may conclude that the outcomes of the 'experimental' method of the monitoring of INR are likely to be by up to 10^0.1112 = 1.29 lower or by up to 10^0.1187 = 1.31 higher compared to the results obtained with the use of the regression method including 2 independent variables, and by up to 10^0.0987 = 1.26 lower or by up to 10^0.0947 = 1.24 higher compared to the results obtained with the use of the regression method including 5 independent variables. Overall, we conclude that it is fully justified to state that both methods of the estimation of INR as the hallmark of the overall plasma coagulation capacity (INR_experimental and INR_predicted) may be used interchangeably.

Finally, we employed the above mentioned multiple regression models to verify whether and how far the assigned relationships may be affected by (1) medication or co-medication and (2) co-morbid conditions. The first group of variables included (a) the use of OAT and its dosing, (b) the use of acetylsalicylic acid and dosing, (c) use of other drugs grouped into four classes: statins, steroids, thyroxin, (d) OAT as the excluded grouping variable. The second group of variables concerned the presence of other accompanying diseases and disorders, including venous thromboembolism, ischaemic heart disease, myocardial infarction, stroke, diabetes, hypertension, liver and intestinal tract diseases including ulceration, thyroid diseases, cancer, osteoporosis, uraemia and kidney diseases, mastopathy, gynaecological disorders, allergy, and rheumatoid diseases.

To perform this study, and for the purpose of the analysis, we have chosen selected clotting factors directly participating in subsequent steps of a coagulation pathway dependent on tissue factor and factor VII, previously referred to as extrinsic coagulation pathway. In addition, we picked up two other factors either directly or indirectly related to thrombin generation: protein C and prothrombin fragment F1+2 [17]. Whereas the former is crucial in haemostatic feedback mechanisms governing de novo thrombin generation [21], the latter is claimed to be less affected by various compounding variables than for example TAT, and therefore it appears to reflect coagulability more accurately [22]. To ensure that the estimated associations are representative as much as possible, we have deliberately enrolled into the study a large cohort of people representing not only healthy donors, but also those in whom co-morbid conditions and/or co-medication might be observed.

All the parameters selected to this study have already been proven to be affected by OAT [23]. The vitamin K-dependent coagulation factors VII and X, as well as inhibitor protein C have been reported to show a highly significant correlation with treatment intensity [4,17,24]. Therefore, by the inclusion of a heterogenous study population comprising both patients on OAT and healthy donors, as well as varying group of patients without OAT (of whom 20% were on aspirin), we deliberately broadened up the naturally existing variability of the studied parameters.

Overall, the prothrombin time (INR) was affected mostly by three of the assayed clotting factors: FII, FVII and FX. Protein C and prothrombin fragments F1+2 had moderate influence, whereas no significant impact on INR variability has been revealed for either APTT ratio or fibrinogen. As deduced from R² values, each of assayed parameters explained a very significant part of INR variability (from 10% in the case of fibrinogen up to nearly 90% in the case of factor II), when analyzed in the single variable regression models. Based on the values of partial correlation coefficients, only 5 parameters (mainly factors VII, II and X which explained up to 92–93% of INR variability) showed significant partial contributions to INR, whereas the effects of both fibrinogen or APTT ratio remained negligible. It clearly points that each of these insignificant parameters bears a large portion of a 'hidden' variability resulting probably from their associations with other plasma coagulation-derived variables and not necessarily with INR. It goes along with the results of Jerkeman et al., who found the strongest associations with PT in the case of factor X, protein C, factor VII, IX and protein S. Unfortunately, factor II was not covered by the scope of that study [17]. These results correspond also with those obtained recently by D'Angelo et al., who found FII monitoring to be a good alternative for INR monitoring, as the parameter reflecting more closely in vivo antithrombotic potential [4]. Similar type of agreement analysis has been reported by Kumar et al., however, the authors claimed only 50–77% proportion of variability of the INR explained by the activities of clotting factors II, VII, IX and X [23]. Our estimates only partly correspond to those reported by Weinstock et al., who investigated the group composed of 80 OAT patients on initial- and long-term warfarin therapy and 40 healthy volunteers, and, using a univariate analysis, they concluded that factor VII, and not prothrombin, may be the predominant factor monitored by INR [9]. On the other hand, Lind et al. pointed that plasma levels of the vitamin K-dependent coagulation factors are not equal in long-term OAT patients. Using a multivariate analysis they showed factor II levels to be the least significant of the three clotting factors (II, VII, X) measured in the determining of the international normalized ratio in plasma or whole blood [8], which opposes our present findings. Considering such a moderately consistent array of data, the question may be raised why not all studies in this area reached the same estimates concerning the contributions of factors II and VII to INR. We suggest that the conflicting results with other authors' findings may be due to different PT reagents for INR, since different PT reagents have different sensitivities to individual coagulation factors and inhibitors.

Another problem which needs to be addressed here is why FVII and FII activities, which were significantly lower in patients on OAT, did not contribute significantly to the discrimination of the three groups of subjects. To reasonably interpret such an inconsistence we have to remember that the inclusion of any variables into the model of discriminant function analysis is based on the compromise between the largest contribution of a given variable to the improvement of the model (given by the partial Wilk's lambda) and non-collinearity of included variables (given by tolerance). In our analysis, both FII and FVII were highly redundant parameters, collinear with other parameters and characterized by low tolerance values (below 0.240). On the other hand, both FII and FVII showed merely moderate contributions (partial lambda Wilks' values close to 1), compared to other analyzed variables. Therefore, despite their significant differences between groups, these two parameters were not included in the model as the best discriminating parameters.

It is worth emphasizing that the associations obtained by us were still valid in both healthy subjects and patients suffering from different diseases. Neither the use nor the intensity of OAT, nor the use of acetylsalicylic acid nor of any other medications biased significantly these associations. This finding appears especially worth mentioning, since it implies that the revealed association is a more generalized phenomenon, not merely attributed to either OAT patients on one hand, or to healthy individuals with undisturbed haemostasis on the other. In our opinion such a universality of the estimated relationship is challenging in looking forward to novel strategies of the monitoring of an overall haemostatic capacity in health or disease. On the other hand, however, we need to admit that our estimates apply predominantly to acenocoumarol since other anticoagulants have not been studied in our present approach.