An improved model of partition curve based on accumulation normal distribution function

Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

THE SUPERIORITIES OF BAYES LINEAR UNBIASED ESTIMATION IN PARTITIONED LINEAR MODEL

In this article, the Bayes linear unbiased estimation （BALUE） of parameters is derived for the partitioned linear model. The superiorities of the BALUE over ordinary least square estimator （LSE） are studied in terms of the Bayes mean square error matrix （BMSEM） criterion and Pitman closeness （PC） criterion.

A Study of the Equivalence of the BLUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models

Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.

Cost-Effectiveness Analysis of Atezolizumab plus Pemetrexed and Platinum in First-Line Treatment of Non-Squamous Non-Small Cell Lung Cancer in China

Objective: To evaluate the cost-effectiveness of atezolizumab plus pemetrexed and platinum-based (APP) in the first-line treatment of non-squamous non- small cell lung cancer (NSCLC). Methods: A partitioned survival model (PSM) was constructed based on the IMpower132 clinical trial. Total cost, quality- adjusted life years (QALY), and incremental cost-effectiveness ratio (ICER) were the main outputs of the model. Deterministic sensitivity analysis and probabilistic sensitivity analysis were adopted to test the uncertainty of the parameters. Results: The results of the base-case analysis illustrated that compared with PP, the incremental cost of APP was CNY 591040.94, the incremental utility was 0.46 QALY, and the ICER was CNY 1291414.83/QALY. Deterministic sensitivity analysis results illustrated that atezolizumab and other parameters have a greater impact on ICER. Probabilistic sensitivity analysis results show that no matter how each parameter changes, under the willingness to pay threshold of 3-times Chinese per capita GDP, the probability of APP has cost-effectiveness is 0. Conclusion: From the perspective of the Chinese health system, APP is not cost-effective for first-line treatment of non-squamous non-small cell lung cancer without sensitizing EGFR or ALK genetic alterations.

Cost-Utility Analysis of Nivolumab plus Chemotherapy in the First-Line Treatment of Upper Gastrointestinal Adenocarcinoma

Objective: To evaluate the cost-utility of nivolumab plus chemotherapy compared with chemotherapy alone as the first-line treatment for advanced gastric, gastro-oesophageal junction, and esophageal adenocarcinoma in China. Methods: Based on CheckMate649, a partitioned survival model was carried out with a circulation cycle of 6 weeks to simulate the patient’s lifetime. Sensitivity analysis were adopted to verify the robustness of the results. Results: The results of the base-case analysis showed that both the total cost and utility of the nivolumab group were higher, and the ICUR value was CNY 267498.67/QALY, more than 3 times the GDP per capita of China in 2020. The results of deterministic sensitivity analysis indicated that the three most influential factors were the utility value of PFS state, the cost of nivolumab and the discount rate. The results of probabilistic sensitivity analysis were consistent with those of base-case analysis, proving that the results were robust. The scenario analysis illustrated that economical price of nivolumab was CNY 3652.71. Conclusions: Under the willing-to-pay threshold of three times the GDP per capita of China in 2020, compared with chemotherapy alone, nivolumab plus chemotherapy is not a cost-effective option in China.

Source apportionment and suitability evaluation of seasonal VOCs contaminants in the soil around a typical refining-chemical integration park in China

Accurate source apportionment of volatile organic compounds(VOCs)in soil nearby petrochemical industries prevailing globally,is critical for preventing pollution.However,in the process,seasonal effect on contamination pathways and accumulation of soil VOCs is often neglected.Herein,Yanshan Refining-Chemical Integration Park,including a carpet,refining,synthetic rubber,and two synthetic resin zones,was selected for traceability.Season variations resulted in a gradual decrease of 31 VOCs in soil from winter to summer.A method of dry deposition resistance model coupling partitioning coefficient model was created,revealing that dry deposition by gas phase was the primary pathway for VOCs to enter soil in winter and spring,with 100 times higher fux than by particle phase.Source profiles for five zones were built by gas sampling with distinct substance indicators screened,which were used for positive matrix factorization factors determination.Contributions of the five zones were 14.9%,20.8%,13.6%,22.1%,and 28.6%in winter and 33.4%,12.5%,10.7%,24.9%,and 18.5%in spring,respectively.The variation in the soil sorption capacity of VOCs causes inter-seasonal differences in contribution.The better correlation between dry deposition capacity and soil storage of VOCs made root mean square and mean absolute errors decrease averagely by 8.8%and 5.5%in winter compared to spring.This study provides new perspectives and methods for the source apportionment of soil VOCs contamination in industrial sites.