Support theorem for stochastic variational inequalities

We prove a support theorem of the type of Stroock-Varadhan for solutions of stochastic variational inequalities

Statistical considerations of noninferiority, bioequivalence and equivalence testing in biosimilars studies

In recent years, the development of follow-on biological products (biosimilars) has received increasing attention. The dissertation covers statistical methods related to three topics of Non-inferiority (NI), Bioequivalence (BE) and Equivalence in demonstrating biosimilarity. For NI, one of the key requirements is constancy assumption, that is, the effect of reference treatment is the same in current NI trials as in historical superiority trials. However if a covariate interacts with the treatment arms, then changes in distribution of this covariate will result in violation of constancy assumption. We propose a modified covariate-adjustment fixed margin method, and recommend it based on its performance characteristics in comparison with other methods. Topic two is related to BE inference for log-normal distributed data. Two drugs are bioequivalent if the difference of a pharmacokinetics (PK) parameter of two products falls within prespecified margins. In the presence of unspecified variances, existing methods like two one-sided tests and Bayesian analysis in BE setting limit our knowledge on the extent that inference of BE is affected by the variability of the PK parameter. We propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components: F-statistic function for variances and t-statistic function for difference of PK parameter. The advantage of the proposed method over existing methods is it helps identify range of variances where BE is more likely to be achieved. In the third topic, we extend the proposed likelihood method for Equivalence inference, where data is often normal distributed. In this part, we demonstrate an additional advantage of the proposed method over current analysis methods such as likelihood ratio test and Bayesian analysis in Equivalence setting. The proposed likelihood method produces results that are same or comparable to current analysis methods in general case when model parameters are independent. However it yields better results in special cases when model parameters are dependent, for example the ratio of variances is directly proportional to the ratio of means. Our research results suggest the proposed likelihood method serves a better alternative than the current analysis methods to address BE/Equivalence inference

Large Deviations for Multi-valued Stochastic Differential Equations

We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.Comment: 12 page

Effect of zinc acetate concentration on optimization of photocatalytic activity of p-Co3O4/n-ZnO heterostructures

In this work, p-Co3O4/n-ZnO heterostructures were fabricated on Ni substrate by hydrothermal-decomposition method using cobaltous nitrate hexahydrate (Co(NO3)(2)center dot 6H(2)O) and zinc acetate dihydrate (Zn(CH3COO)(2)center dot 2H(2)O) as precursors with zinc acetate concentration varying from 5.0 to 55.0 mM. Structure and morphology of the developed samples were characterized by X-ray diffraction (XRD), Raman spectroscopy, and scanning electron microscopy (SEM). Effect of zinc acetate concentration on the photocatalytic activity of p-Co3O4/n-ZnO heterostructures was investigated by degradation of methyl orange (MO) under the UV light irradiation. The fabricated p-Co3O4/n-ZnO heterostructures exhibited higher photocatalytic activity than pure Co3O4 particles. In order to obtain the maximum photocatalytic activity, zinc acetate concentration was optimized. Specifically, at 35 mM of zinc acetate, the p-Co3O4/n-ZnO showed the highest photocatalytic activity with the degradation efficiency of MO reaching 89.38% after 72 h irradiation. The improvement of photocatalytic performance of p-Co3O4/n-ZnO heterostructures is due to the increased concentration of photo-generated holes on Co3O4 surface and the higher surface-to-volume ratio in the hierarchical structure formed by nano-lamellas

The Effects of Cardiometabolic Factors on the Association Between Serum Uric Acid and Chronic Kidney Disease in Chinese Middle-Aged and Older Population: A Mediation Analysis

IntroductionTo explore whether dyslipidemia, hyperglycemia or hypertension has mediating effect on the association between serum uric acid (SUA) and the development of chronic kidney disease (CKD).MethodsWe conducted a mediation analysis to explore the potential mediating effects of systolic blood pressure (SBP), diastolic blood pressure (DBP), blood glucose, triglyceride (TG), total cholesterol (TC), high-density lipoprotein cholesterol (HDL-C) and low-density lipoprotein cholesterol (LDL-C) on the association between SUA and estimated glomerular filtration rate (eGFR). The data were obtained from China Health and Retirement Longitudinal Study (CHARLS), covering 5,762 individuals.ResultsSUA had a negative dose-response total effect on eGFR (β -3.11, 95% CI -3.40 to -2.82, P-value<0.001). The linear regression between SUA and seven potential mediators indicated that blood glucose (β 0.80, 95% CI 0.18 to 1.42, P-value=0.012), TG (β 10.01, 95% CI 8.22 to 11.79, P-value<0.001), TC (β 2.64, 95% CI 1.83 to 3.45, P-value<0.001), HDL-C (β -0.27, 95% CI -0.52 to -0.02, P-value=0.034) and LDL-C (β 1.15, 95% CI 0.49 to 1.80, P-value=0.001) all had significant dose-response association with SUA, but SBP and DBP showed no significant association with SUA. In terms of the association between potential mediators and eGFR, only TG (β 0.003, 95% CI -0.001 to 0.01, P-value=0.117) and HDL-C (β 0.01, 95% CI -0.02 to 0.04, P-value=0.444) did not have significant linear association with eGFR. The linear regression showed that SUA was directly associated with eGFR (P-value<0.001).ConclusionsThis study supported that the association between SUA and the risk of CKD was not mediated by hypertension, hyperglycemia or dyslipidemia