The aim of the study was to identify the most effective serum tumor markers for early diagnosis of hepatocellular carcinoma based on the combination of diagnostic characteristics and correlations. Materials and Methods. There were observed 55 patients with chronic hepatitis C in the stage of liver cirrhosis with a verified diagnosis of hepatocellular carcinoma. The control group consisted of 55 patients with chronic hepatitis C at the stage of liver cirrhosis without hepatocellular carcinoma, comparable to the experimental group in terms of basic clinical profile. The following tumor markers were estimated in both groups: alpha-fetoprotein (AFP), alpha-fetoprotein-L3 (AFP-L3), annexin A2 (ANXA2), heparin-binding growth factor Midkine (MDK), glypican-3 (GPC3), des-gamma-carboxyprothrombin (DCP, PIVKA-II), dickkopf-related protein 1 (DKK-1), osteopontin (OPN), and Golgi protein 73 (GP73). There were also evaluated such indices as diagnostic sensitivity, specificity, positive predictive value, negative predictive value, likelihood ratio of a positive test, the possible correlation between alpha-fetoprotein and other tumor markers. The area under the ROC curve (AUC) was calculated at the 95% confidence interval. Results. The greatest sensitivity was revealed when using heparin-binding growth factor, annexin A2, osteopontin. Alpha-fetoprotein, alpha-fetoprotein-L3, glypican-3, des-gamma-carboxyprothrombin, dickkopf-related protein 1 had the best specificity. AUC>0.75 was found in annexin A2, heparin-binding growth factor, glypican-3, des-gamma-carboxyprothrombin, osteopontin, Golgi protein 73. The likelihood ratio of a positive test result was the highest for glypican-3. A significant correlation was found between alpha-fetoprotein and alphafetoprotein-L3, annexin A2, des-gamma-carboxyprothrombin. Conclusion. According to the aggregate indicators of diagnostic efficiency, heparin-binding growth factor, glypican-3, and osteopontin are the most promising tumor markers of those studied. When they are used, integral AUC values are above the average, the level of these tumor markers in the blood of patients with hepatocellular cancer does not correlate with alpha-fetoprotein. They are applicable for diagnosing liver cancer in AFP-negative patients. The combined use of AFP + GPC3, AFP + OPN has already shown their advantages. However, the efficacy of the combination of AFP + MDK, GPC3 + OPN has not been determined yet; therefore, significance of the combined use of these tumor markers in the diagnosis of liver cancer should be investigated in the near future.

Randomized smoothing is currently considered the state-of-the-art method to obtain certifiably robust classifiers. Despite its remarkable performance, the method is associated with various serious problems such as "certified accuracy waterfalls", certification vs. accuracy trade-off, or even fairness issues. Input-dependent smoothing approaches have been proposed to overcome these flaws. However, we demonstrate that these methods lack formal guarantees and so the resulting certificates are not justified. We show that the input-dependent smoothing, in general, suffers from the curse of dimensionality, forcing the variance function to have low semi-elasticity. On the other hand, we provide a theoretical and practical framework that enables the usage of input-dependent smoothing even in the presence of the curse of dimensionality, under strict restrictions. We present one concrete design of the smoothing variance and test it on CIFAR10 and MNIST. Our design solves some of the problems of classical smoothing and is formally underlined, yet further improvement of the design is still necessary.

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Liver cirrhosis in the outcome of hepatitis C is the leading cause of hepatocellular carcinoma (HCC) in the world. Early diagnosis and timely treatment of HCC are important for reducing mortality and increasing life expectancy of patients with hepatocellular carcinoma. To assess the risk of HCC, the definition of alpha-fetoprotein (AFP) in the blood is most widely used, but low sensitivity limits its diagnostic value. In 2012, a new HCC biomarker - osteopontin (OPN), which is a secreted phosphoprotein that has a high affinity for integrins was proposed. The level of acute renal failure begins to rise in the early stages of malignancy, before the period of HCC detection by imaging methods, and has significantly better sensitivity than AFP. The purpose of this study is to evaluate the diagnostic efficacy of the combined determination of alpha-fetoprotein and osteopontin in prospective monitoring of patients with chronic hepatitis C in the advanced phase of liver fibrosis. Monitoring of 588 patients with hepatitis C was carried out from February 2013 to February 2019. HCC was detected in 55 of them (2.6% per year). The combination of 2 biomarkers showed better diagnostic efficacy than alpha-fetoprotein and osteopontin separately: AUC 0.85 (95% CI 0.80-0.90) versus AUC 0.63 (95% CI 0.57-0, 70) and AUC 0.82 (95% CI 0.77-0.88), respectively. This combination showed a sensitivity of 85.5% and made it possible to diagnose HCC with a prognostic level of a positive result of 72.3% at 19,4±0,8 weeks before the diagnosis was confirmed by instrumental imaging methods (ultrasound, MRI, CT). In the combined variant, ARF made the greatest contribution to the increase in diagnostic efficacy (AUC). At an early and very early stage of HCC development, isolated HCC elevations were found in only 5.4% of patients. Conclusion: the combined use of alpha-fetoprotein and osteopontin as a diagnostic panel can be recommended for monitoring patients with liver cirrhosis in the outcome of hepatitis C and predicting HCC at an early stage of development.

Background. It is known, that genetic factors and the absence of minimal residual disease (MRD) are strongly affecting prognosis of chronic lymphocytic leukemia (CLL). Aim. To determine the influence of genetic abnormalities (GA) on achieving MRD-negative remissions in patients with CLL. Methods. Twenty-four adult pts (median age 57 years, range 35-67; male 14, female 10) with newly diagnosed CLL were included. The CLL was diagnosed according to the standard basic examination (complete blood count with differential, multicolor flow cytometry (MFC) of blood and bone marrow (BM), lymph node and BM immunohistochemistry (IHC), computered tomography). Cytogenetic studies were performed on blood samples using standard GTG-method. Interphase FISH analyses were performed according to the manufacturer's protocol using DNA probes: LSI 13(RB1)13q14, LSI ATM (11q22), CEP12, LSI TP53 (17p13.1) (Abbott). Immunophenotype (IFT) of CLL cells assessed with combinations: CD3/CD19, CD19/CD5, CD19/CD11c, CD19/CD20, CD19/CD22, CD19/CD23, CD19/CD25, CD19/CD38, CD19/CD43, CD19/CD81, CD19/HLA-DR, and CD19/CD5/CD23. We have used NCI revised guidelines (Hallek M, et al., 2008) for treatment initiation and assessment of response after completion of primary therapy with rituximab-based regimens (FCR or RB). All patients treated subsequently with rituximab maintenance. MRD was detected by MFC. Results. The frequency of GA in CLL was 50.0% (12/24): 15.0% (3/20) - by conventional karyotyping, 47.8% (11/23) - by FISH analyses and 9.5% (2/21) - using both methods. Stratification of patients into prognostic groups based on identified GA. Favorable prognosis (Group 1) - patients with del(13q) (n = 5); neutral prognosis (Group 2) - normal karyotype (n = 12) or trisomy of chromosome 12 (n = 3); unfavorable prognosis (Group 3) - del(11q) (n = 3) or the complex karyotype (n = 1). Statistically significant differences in the frequency of achieving MRD-negative remissions between FCR (5/11) vs. RB (5/13) were not detected (p<0.05). Complete remissions (CR) were reached in 37.5% (9/24) pts, partial remissions (PR) - 62.5% (15/24). The MRD-negative remissions were reached in 10 patients: in Group 1 - 2/5 (40%; CR - 1), in Group 2 - 5/15 (33.3%, CR - 6), in Group 3 - 75.0% (3/4; CR - 2). Statistically significant differences in PFS were detected between MRD-negative vs. MRD-positive groups (p=0.03). Median PFS in MRD-negative has not been reached. Median PFS MRD-positive was 33.1 month. Conclusions. Further researches aimed at examining the relationship between the presence or absence of MRD and genetic prognostic groups, will help to understand the most important factors affecting the overall and progression-free survival. Disclosures No relevant conflicts of interest to declare.