Fractional derivative multivariable grey model for nonstationary sequence and its application

Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.

Multivariate predictive model for asymptomatic spontaneous bacterial peritonitis in patients with liver cirrhosis

BACKGROUNDSpontaneous bacterial peritonitis (SBP) is a detrimental infection of the asciticfluid in liver cirrhosis patients, with high mortality and morbidity. Earlydiagnosis and timely antibiotic administration have successfully decreased themortality rate to 20%-25%. However, many patients cannot be diagnosed in theearly stages due to the absence of classical SBP symptoms. Early diagnosis ofasymptomatic SBP remains a great challenge in the clinic.AIMTo establish a multivariate predictive model for early diagnosis of asymptomaticSBP using positive microbial cultures from liver cirrhosis patients with ascites.METHODSA total of 98 asymptomatic SBP patients and 98 ascites liver cirrhosis patients withnegative microbial cultures were included in the case and control groups,respectively. Multiple linear stepwise regression analysis was performed toidentify potential indicators for asymptomatic SBP diagnosis. The diagnosticperformance of the model was estimated using the receiver operatingcharacteristic curve.RESULTSPatients in the case group were more likely to have advanced disease stages,cirrhosis related-complications, worsened hematology and ascites, and higher mortality. Based on multivariate analysis, the predictive model was as follows: y (P) = 0.018 + 0.312 × MELD (model of end-stage liver disease) + 0.263 × PMN(ascites polymorphonuclear) + 0.184 × N (blood neutrophil percentage) + 0.233 ×HCC (hepatocellular carcinoma) + 0.189 × renal dysfunction. The area under thecurve value of the established model was 0.872, revealing its high diagnosticpotential. The diagnostic sensitivity was 73.5% (72/98), the specificity was 86.7%(85/98), and the diagnostic efficacy was 80.1%.CONCLUSIONOur predictive model is based on the MELD score, polymorphonuclear cells,blood N, hepatocellular carcinoma, and renal dysfunction. This model mayimprove the early diagnosis of asymptomatic SBP.

Association of polymorphisms in C1orf106,IL1RN,and IL10 with post-induction infliximab trough level in Crohn’s disease patients

Background:Trough levels of the post-induction serum infliximab(IFX)are associated with short-term and long-term responses of Crohn’s disease patients to IFX,but the inter-individual differences are large.We aimed to elucidate whether single gene polymorphisms(SNPs)within FCGR3A,ATG16L1,C1orf106,OSM,OSMR,NF-jB1,IL1RN,and IL10 partially account for these differences and employed a multivariate regression model to predict patients’post-induction IFX levels.Methods:The retrospective study included 189 Crohn’s disease patients undergoing IFX therapy.Post-induction IFX levels were measured and 41 tag SNPs within eight genes were genotyped.Associations between SNPs and IFX levels were analysed.Then,a multivariate logistic-regression model was developed to predict whether the patients’IFX levels achieved the threshold of therapy(3 lg/mL).Results:Six SNPs(rs7587051,rs143063741,rs442905,rs59457695,rs3213448,and rs3021094)were significantly associated with the post-induction IFX trough level(P=0.015,P<0.001,P=0.046,P=0.022,P=0.011,P=0.013,respectively).A multivariate prediction model of the IFX level was established by baseline albumin(P=0.002),rs442905(P=0.025),rs59457695(P=0.049),rs3213448(P=0.056),and rs3021094(P=0.047).The area under the receiver operating characteristic curve(AUROC)of this prediction model in a representative training dataset was 0.758.This result was verified in a representative testing dataset,with an AUROC of 0.733.Conclusions:Polymorphisms in C1orf106,IL1RN,and IL10 play an important role in the variability of IFX post-induction levels,as indicated in this multivariate prediction model of IFX levels with fair performance.