Demographic and clinical characteristics of the studied subjects, as well as the use of the drugs of known influence on the coagulation status (acetylsalicylic acid, statins, steroids, thyroxin), are presented in Table . All patients in group III received acenocoumarol (synthetic derivate of 3-(α-acetonylbenzyl)-4-hydroxycoumarin, vitamin K antagonist that impairs the synthesis of active plasma coagulation factors: II, VII, IX, X; Acenocoumarol®,Polfa-Warszawa, Poland) as a standard medication (Me = 18 mg/6 days, 25–75%QR = 12–24 mg/6 days). Indications for OAT in patients representing group III are listed in Table .
Demographic and clinical characteristics of the studied subjects
Indications for OAT in patients representing group III (with more than one indication for a patient possible)
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 ).
Laboratory parameters values
Secondly, using a multiparametric discriminant function analysis we showed all the groups were significantly separated apart (Fig. ) 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%).
Figure 1 Classification of donors and patients according to the multivariate discriminant function analysis including studied coagulation parameters. Dispersion ellipses (95%CI) are drawn based on the coordinates of two orthogonal discriminant functions (roots) (more ...)
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. 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. (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 .
Figure 2 Relationships between INR and plasma clotting factors, protein C and F1+2 prothrombin fragments in normal donors and patients on OAT. Cases representing patients on OAT are marked as open circles (○), those representing healthy donors or patients (more ...)
Simple linear correlation coefficients between investigated coagulation parameters
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 ). Then, we gradually eradicated from the model the independent variables with the lowest significance and Fremove 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: rFII = -0.711, rFVII = -0.659, p « 0.0001 for each).
Summary of a ridge multiple regression model for clotting parameters explaining the variability of INR as a dependent variable
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 INRexperimental
(Fig. ), 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 INRexperimental
within the pairs of data exceeded the range of doubled SDdifference
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. ). The mean difference between the methods enables to extrapolate the results obtained with a regression method (INRpredicted
) to those predicted to be read with the other one (INRexperimental
), provided the dispersion of differences lies in a narrow confidence limit around the mean difference in the sample (Fig. ). 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 100.1112
= 1.29 lower or by up to 100.1187
= 1.31 higher compared to the results obtained with the use of the regression method including 2 independent variables, and by up to 100.0987
= 1.26 lower or by up to 100.0947
= 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 (INRexperimental
) may be used interchangeably.
Linear regression as a measure of association between the values of INRexperimental and INRpredicted for (a) two-component model and (b) five-component model of multiple regression.
Figure 4 Scatter plot of the differences between pairs of data collected with the use of either 'experimental' or 'statistical' method as a measure of agreement between the compared methods for (a) the two-component model and (b) the five-component model of multiple (more ...)
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.
Neither the use of OAT, nor acetylsalicylic acid nor any other medications affected significantly the variability of the observed experimental INR. Also, we did not observe the statistically significant impact of any accompanying disorders and diseases on INRexperimental.