The present work is a retrospective study based on clinical data of two cohorts of preterm infants with gestational age 23–30 WG born in four German hospitals with the highest level of care according to the German regulations. The study was approved by the ethic committee of School of Medicine Klinikum rechts der Isar, Technical University of Munich (Ref. 364/15), and Ethic Committee of University Hospital Essen, University Duisburg-Essen (Ref. 16-7284-BO).

The derivation cohort used for construction of IVH risk scores included 254 preterm infants born between 2006 and 2016. The prediction accuracy of the developed risk scores was validated on more recent population of 63 preterm infants (validation cohort) born between 2017 and 2019.

In all four settings, occurrence of IVH was diagnosed by cranial ultrasound performed routinely on day 1, 3, 7, 14 of life and more frequently (up to daily) in case of suspected hemorrhage. The severity of IVH was divided into four grades according to Papile classification (25). In the study, groups of patients with and without IVH diagnosis are referred to as the affected and control groups.

In both cohorts, the following clinical data were collected:

The six pregnancy pathologies and eight birth parameters were recorded shortly after birth, further 10 infant diagnoses were recorded during postnatal care. In addition, eight routinely measured clinical parameters were systematically recorded during 7 days before and 3 days after IVH diagnose, or 10 days after birth for preterm infants without IVH diagnosis.

In the present study we calculate CBF from the 6 medical parameters, namely WG, BW, MAP, pCO₂, pO₂ and Ht using the hierarchical cerebral vascular model that was initially proposed for adult brain (26) and then adjusted to the peculiarities of the immature brain (19, 27). In the model, the cerebral vascular system is represented by 19 serially connected levels, each containing parallel connected vessels of a certain size. At each level, the number of vessels and their length and diameter are scaled according to the patient’s gestational age and the brain weight estimated from the birth weight (28). At the capillary level, an additional area is added as a parallel circuit with the number of vessels corresponding to the relative volume of the germinal matrix at a given gestational age (29). Furthermore, the effect of Ht on blood viscosity is included in the calculation of vascular resistance (30, 31) and autoregulation activity of the brain vessels (vasoconstriction and vasodilation) is accounted by increasing and decreasing of vessel’s diameter according to the measured values of MAP, pCO₂ and pO₂ (19, 24, 27).

The calculated CBF value was included in the statistical analyses as an independent parameter. In addition, the mean value of CBF for the group of infants without IVH was calculated for each WG. The obtained CBF_mean value was used as a reference value of the optimal CBF at each WG and the CBF-CBF_mean value was included as a further predictive variable in the statistical analyses.

To build a risk score, multivariable stepwise logistic regression analysis was applied (1, 13). In our study, IVH diagnosis plays a role of response variable y, which has a binary type. The predictive variables (predictors) x_j are medical characteristics, which have either continuous or binary type. The selection of potential variables for scoring system started with the analysis of parameters related to IVH. To detect IVH risk factors, a univariate analysis was performed using two-sided Wilcoxon’s rank-sum test for continuous and Fisher’s exact test for categorical parameters (32). A 5% significance level, which corresponds to p-value = 0.05, was taken as the threshold value for including each parameter as a candidate variable in the multivariate prediction model.

The parameters found to be associated with IVH were then ranked in respect to the response variable according to the p-values of chi-square test with null hypothesis that predictor and response variable are independent. The p-value <0.05 means that the predictor and response variable are significantly associated with each other. Predictors with larger values −log(p) were ranked higher and the value −log(0.05) = 3 was taken as the threshold for including them into the score model.

Incorporation of independent predictors into risk scores was performed using a generalized linear regression with logit link function as follows:

In order to prevent overfitting, we implemented stepwise predictors selection. We started with a single variable model (N = 1) using the highest ranked predictor and added lower ranking predictors after running the chi-squared test with the null hypothesis that deviance of old and new regression models are equal. A p-value <0.05 rejects the null hypothesis and means that new predictor significantly improves the fitting model and should be included in the score. Only predictors with statistically significant coefficients b_j were included in the model, and only models that were statistically significantly different from the constant model were used further for construction of risk scores.

The coefficients b_j obtained by the linear regression analyses were then integrated in a risk score as follows:

Here x_j (t) is the value of the predictor j averaged over all measurements up to time t. For early IVH prediction, as long as the measured clinical parameters are not available, only the parameters of groups I–III were considered in the regression model. For the prediction of IVH on the second day, the clinical parameters were averaged over the first day of life (measurements of preterms with IVH on the first day are then excluded), and for the later prediction of IVH, parameters were averaged over all days before IVH.

To evaluate the effectiveness of the risk scores constructed, the receiver operating characteristic (ROC) method for classification between the control and affected groups was applied (33, 34). For each patient from control and affected groups score value was calculated, then true positive rate (TPR) and false positive rate (FPR) (Table 1) were computed for different threshold values. The ROC curves were constructed by plotting TPR against FPR, and the area under the ROC curve (AUC) was estimated (35). The later provides a quantitative measure of predictive power of the score: perfect predictor has AUC = 1, which corresponds to TPR = 1 and FPR = 0, and predictor with AUC = 0.5 is equivalent to random choice. The threshold for optimal performance was chosen at the point on the ROC curve with the smallest distance to the upper left corner of the unit square (36) and used further for the normalization of the regression coefficient b₀, so that the threshold for IVH risk was equal to 0 for all risk scores. The validation of the resulting IVH risk scores was performed by calculating the TPR and FPR using independent data from the validation cohort.

Statistical analyses was carried out using standard library of MATLAB2024a. Observations with missing values were not used in analyses, medical parameters that were measured less often than others were extended until the next regular measurement. For calculation of CBF, missing parameter values were replaced with the latest measured value.

Basic clinical characteristics of the derivation and validation cohorts are presented in Table 2. Here, continuous variables are expressed as mean and standard deviation, while binary variables are presented as the number of cases and percentages.

To create a risk score, the data from the derivation cohort of 254 patients (136 with and 118 without diagnosis of IVH) was used. During data collection, the affected and control groups were matched according to gestational age and birth weight. Thus, these parameters had statistically equal (p-value >0.05) mean values (Table 3) and, therefore, were not used in this study as predictor variables for risk assessment.

The statistical comparison of pregnancy pathologies, birth parameters and infant diagnoses in the affected and control groups of the derivation cohort is presented in Table 4. The table is sorted according to the p-value: the most significant parameters, i.e., those with the smallest p-value, are at the top. Seven parameters (EPH-gestosis/pre-eclampsia, PPROM, cardiopulmonary adaptation disorder, IUGR, IVF, RDS and FFTS) demonstrated inverse relationship with the development of IVH, i.e., the percentage of preterm infants with these diagnoses in the affected group was lower than in the control group. This can be explained by the effects of the medical treatment provided, which is out of scope of this study. Therefore, these parameters were not considered as predictor variables in the following risk assessment. Another seven parameters (sepsis, delivery mode, erythrocyte transfusion, chorioamnionitis, thrombocytopenia, NEC and multiple birth) had no significant association with IVH (i.e., p-value >0.5). Significant association with IVH (i.e., p-value <0.5) was revealed for the following 8 parameters: Apgar at 1 min, Apgar at 5 min, Apgar at 10 min, FIP/SIP, cholestasis, acidosis, male sex and pulmonary hemorrhage. The parameters found to be associated with IVH were further used as predictive variables in the logistic regression analyses.

We started the construction of risk scores with the ranking of the predictive variables (Figure 1), which were then included stepwise in the multivariable regression analyses according to their significance. For different clinical situations, several scores were designed (Table 5). The performance of the resulting scores was evaluated using the ROC analysis. We determined the optimal threshold from the ROC curve for patients with all grades of IVH and then calculated the TPR and FPR for patients with all (I–IV) and severe (III–IV) grades of IVH (the example of ROC curve with optimal threshold and corresponding scatter plot is shown in Figure 2).

For the initial prediction of IVH risk, we constructed the score S1 based only on pregnancy pathologies, birth parameters and infant diagnoses, which are usually known before measured parameters are available (Figure 1 left). Although eight parameters were significantly associated with IVH, two of them, namely Apgar at 1 min and Apgar at 5 min, were absent in the score due to their high correlation with Apgar at 10 min (Pearson correlation 0.61 and 0.77, respectively). The score S1 demonstrated only moderate performance (AUC = 0.74) and included several statistically insignificant coefficients, suggesting that this group of medical parameters was insufficient for effective IVH prediction.

The improvement of IVH prediction can be achieved by including routinely measured parameters in the regression model. In the first day of life, the availability of measurements is usually limited. To determine risk scores for first and second days of life, we averaged routinely measured parameters over the first day (patients with IVH on the first day are excluded from consideration at this stage). Thus, only pH and leukocyte count demonstrated significant association with IVH (Figure 1 middle). Two other parameters, CBF-CBF_min and pCO₂, were close to the limit of significance. It is important to note, that mathematically calculated parameter CBF-CBF_min had stronger association with IVH than each of the parameters used for its calculation (Figure 1 middle). The integration of the significant measured parameters averaged over the first day of life (Figure 1 middle) in the regression procedure resulted in the risk models with 4 and 3 parameters (score S2 and S3 in Table 5), which both had only significant regression coefficients and much better performance in ROC analyses than S1 (Table 5).

To construct a risk score for prediction of IVH when the values of all measured parameters are already available, we averaged them for all days before IVH and added averaged values to the regression analysis according to their significance (Figure 1 right). In this case, the calculated CBF was ranked fourth among statistically significant parameters and had a stronger association with IVH than pCO₂, pO₂, and Ht, which are used for its calculation. Inclusion of the measured parameters averaged over all days before IVH improved the resulting risk scores (scores S4 and S5 in Table 5). Further improvement in risk score was achieved by adding the calculated CBF to the regression model (scores S6 and S7 in Table 5). The performance of the risk score S7 is illustrated on the Figure 2 (left: ROC curve with optimal threshold value; middle: scatter plot of score values of individual patient).

In order to demonstrate the advantage of including the calculated CBF in the risk model, we constructed a risk score without CBF but with all clinical parameters used in the mathematical model to calculate CBF. The performance of the resulting risk score (S = pH + Leukocytes + pO₂ + pCO₂ + MAD + Ht, not in Table 5) with AUC = 0.88 appeared to be worse than AUC = 0.94 of the risk score S7 which includes CBF. This result indicates that the mathematical model for CBF calculation provides complementary information that improves the prediction of IVH risk.

Clinical characteristics of the validation cohort of 63 preterm infants are presented in Table 2. For each patient in the validation cohort, score values with coefficients presented in Table 5 were calculated (Figure 2 right) and used to determine FPR for control group and TPR for all and severe grades of IVH (Table 6). The best performance was achieved by the scores, which included routinely measured parameters and calculated CBF (scores S5, S6 and S7). For this scores, correct identification of patients with IVH (TPR) in the validation cohort remained at the same level as in the derivation cohort. False identification of healthy patients to be at risk of IVH (FPR) in validation cohort was higher than in the derivation cohort. However, increase of FPR was smaller for risk scores with fewer parameters, which were derived only from measured parameters (scores S5 and S7 in Table 6). The overestimation demonstrated by the scores with medical diagnoses can be explained by the fact that all medical diagnoses are in fact already characterized by the measured parameters. The moderate FPR value reflected the fact that the control group did not consist of absolute healthy individuals. All patients without IVH who had high score values (Figure 2 right), had also elevated CRP level (greater than 10 mg/L) indicating an inflammation. In this case, although they did not have IVH, they could not be regarded as healthy patients either.