Search

Background Patients with membranous nephropathy (MN) and poor kidney function or active disease despite previous immunosuppression are underrepresented in clinical trials. It is unknown how effective rituximab is in this population. Methods This prospective, multi-centre, single-arm, real-world study of patients with active MN [urine protein-creatinine ratio (uPCR) >350 mg/mmol and serum albumin <30 g/L, or a fall in estimated glomerular filtration rate (eGFR) of at least 20% or more over at least 3 months] evaluated rituximab in those with contraindications to calcineurin inhibitors and cytotoxic therapy. The primary outcome was change in rate of eGFR decline before and after rituximab. Complete or partial remission were defined as uPCR <30 mg/mmol or uPCR <350 mg/mmol with a ≥50% fall from baseline, respectively. Results A total of 180 patients [median age 59 years, interquartile range (IQR) 48–68] received rituximab and were followed up for a median duration of 17 months. Seventy-seven percent had prior immunosuppression. Median eGFR and uPCR at baseline were 49.2 mL/min/1.73 m2 (IQR 34.4–80.6) and 766 mg/mmol (IQR 487–1057), respectively. The annual rate of decline of eGFR fell from 13.9 to 1.7 mL/min/1.73 m2/year following rituximab (Z score = 2.48, P < .0066). At 18 months 12% and 42% of patients were in complete or partial remission, respectively. Rituximab was well tolerated; patient survival was 95.6% at 2 years and in patients in whom eGFR was available, kidney survival was 93% at 2 years. Conclusion Rituximab significantly reduced the rate of eGFR decline in active MN including those who had received prior immunosuppression or with poor baseline kidney function. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new model derived from Pólya–Eggenberger urn model. This model is defined by considering a delay in collecting information. The mathematical formulation of this model is done through four parameters; the number of balls in the first structure (N0), the number of white balls in the first structure (W0), the number of rewarded balls of the color of the ball withdrawn (a), and the length of the delay (i). As the first attempt to deal with point estimation in this model, we consider at any time one of the parameters separately as unknown conditioned to knowing the other three parameters, and find its estimation. Accordingly, we introduce a sufficient estimator for this model, and found on it, obtain the maximum likelihood estimators for each of the four parameters. In addition, moment estimators for N0 and W0 are calculated. Also, for the other parameters, we obtain estimators based on the correlation coefficient of consecutive withdrawals. To evaluate the performance of the obtained estimators and compare their accuracy, we apply five simulations of the delayed Pólya urn model. The simulations have been done with the software Matlab R2015b. According to the simulation study, the estimators obtained from the method of moments are preferable to maximum likelihood estimators. [ABSTRACT FROM AUTHOR]

The epidemic of COVID-19 has been the most mathematically informative pandemic. The unprecedented information gives rise to some unprecedented models, problems, and discussions. One of these new matters is modeling the epicenters of a pandemic. The present paper is the first attempt to model the waiting time to introduce a new epicenter during a pandemic. This modeling is conducted in terms of time-to-event, the number of epicenters, and the normalized time. We model the waiting time data by an exponential distribution, therefore, the number of epicenters can be represented through a Poisson process. Then, the parameters are estimated by the method of moments and maximum likelihood method. All the simulations are the result of 10,000 runs conducted on MATLAB R2015b. It is expected to encounter 12 and 14 (with probability 95%, 3-24 and 7-23) epicenters from 15th May to 13th June and from June 14 to July 12, 2020, respectively. We forecast that the cumulative number of confirmed cases for coming epicenters is over 10,000 when they join the existing epicenters. The paper suggests that the time to epicenter is a suitable criterion to compare the spreading speed of an epidemic in different periods or even different epidemics. The study aims to model the time to the next epicenters during the pandemic COVID-19. The study introduces the time to epicenter as a criterion to study of spreading speed of an epidemic in different periods or compare different epidemics. The study deals with the number of cumulative confirmed cases at the time that a region become epicenter. The study proposes the Poisson process as the model to describe the number of epicenters. The study suggests that exponential distribution can model the time to event for the epicenters of COVID-19. [ABSTRACT FROM AUTHOR]

Pólya urn models are of the well-known probabilistic concepts and stochastic processes. The proportion of the colors is the question of the most interest in these models. Always, the structure (The number of all the balls in the urn and the proportion of the colors) of the urn at the beginning is given. Also, in the studies where the outcome of certain withdrawals is known, these withdrawals are connected to the first structure, and there is no gap between the known structure and the additional information about the color of the withdrawn balls. The existing gap between the first structure and any relevant information motivates this paper. In the present article, we consider the Pólya-Eggenberger urn model. We prove that an urn with an initial known structure after some unknown withdrawals – conditioned to meet an assumption – behaves like an urn with a known structure. By the results of the present paper, we overcome the complexity and ambiguity caused by the unknown withdrawals, and in spite of the lack of information concerning some withdrawals, we deal with the urn as a process that behaves like a completely determined structure. To illustrate the truth of the obtained results, we simulate several urns and survey the variation in the probabilities of the colors. [ABSTRACT FROM AUTHOR]

Objective: The UK is one of the epicenters of coronavirus disease (COVID-19) in the world. As of April 14, there have been 93 873 confirmed patients of COVID-19 in the UK and 12 107 deaths with confirmed infection. On April 14, it was reported that COVID-19 was the cause of more than half of the deaths in London. Methods: The present paper addresses the modeling and forecasting of the outbreak of COVID-19 in the UK. This modeling must be accomplished through a 2-part time series model to study the number of confirmed cases and deaths. The period we aimed at a forecast was 46 days from April 15 to May 30, 2020. All the computations and simulations were conducted on Matlab R2015b, and the average curves and confidence intervals were calculated based on 100 simulations of the fitted models. Results: According to the obtained model, we expect that the cumulative number of confirmed cases will reach 282 000 with an 80% confidence interval (242 000 to 316 500) on May 30, from 93 873 on April 14. In addition, it is expected that, over this period, the number of daily new confirmed cases will fall to the interval 1330 to 6450 with the probability of 0.80 by the point estimation around 3100. Regarding death, our model establishes that the real case fatality rate of the pandemic in the UK approaches 11% (80% confidence interval: 8%–15%). Accordingly, we forecast that the total death in the UK will rise to 35 000 (28 000–50 000 with the probability of 80%). Conclusions: The drawback of this study is the shortage of observations. Also, to conduct a more exact study, it is possible to take the number of the tests into account as an explanatory variable besides time. [ABSTRACT FROM AUTHOR]

In this paper, we define and study a stochastic SIR model on the class of regular rooted trees, in order to describe the spread of an epidemic on a closed population. A generalized geometric random variable is defined, which is essential for our study in this stochastic process. The main objective of this paper is to obtain the distribution of random variable X , the number of infected individuals at the stopping time that a diagnosis occurs. The analyses, simulations, and figures created with the software MATLAB certify the validity of the obtained results. [ABSTRACT FROM AUTHOR]