There is mounting evidence linking traumatic brain injury (TBI) to neurodegeneration. Clusterin (apolipoprotein J or ApoJ) is a complement inhibitor that appears to have a neuroprotective effect in response to tissue damage and has been reported to be upregulated in Alzheimer's disease. Here we investigated the time course and cellular expression pattern of clusterin in human TBI. Tissue from 32 patients with TBI of varying survival times (from under 30 min to 10 months) was examined using immunohistochemistry for clusterin alongside other markers of neurodegeneration and neuroinflammation. TBI cases were compared to ischemic brain damage, Alzheimer's disease and controls. Double immunofluorescence was carried out in order to examine cellular expression. Clusterin was initially expressed in an axonal location less than 30 min following TBI and increased in intensity and the frequency of deposits with increasing survival time up to 24 h, after which it appeared to reduce in intensity but was still evident several weeks after injury. Clusterin was first evident in astrocytes after 45 min, being increasingly seen up to 48 h but remaining intense in TBI cases with long survival times. Our results suggest clusterin plays a role in modulating the inflammatory response of acute and chronic TBI and that it is a useful marker for TBI, particularly in cases with short survival times. Its prominent accumulation in astrocytes, alongside a mounting inflammatory response and activation of microglial cells supports a potential role in the neurodegenerative changes that occur as a result of TBI.

Background: COVID-19 is currently on full flow in Pakistan. Given the health facilities in the country, there are serious threats in the upcoming months which could be very testing for all the stakeholders. Therefore, there is a need to analyze and forecast the trends of COVID-19 in Pakistan. Methods: We have analyzed and forecasted the patterns of this pandemic in the country, for next 30 days, using Bayesian structural time series models. The causal impacts of lifting lockdown have also been investigated using intervention analysis under Bayesian structural time series models. The forecasting accuracy of the proposed models has been compared with frequently used autoregressive integrated moving average models. The validity of the proposed model has been investigated using similar datasets from neighboring countries including Iran and India. Results: We observed the improved forecasting accuracy of Bayesian structural time series models as compared to frequently used autoregressive integrated moving average models. As far as the forecasts are concerned, on August 10, 2020, the country is expected to have 333,308 positive cases with 95% prediction interval [275,034–391,077]. Similarly, the number of deaths in the country is expected to reach 7,187 [5,978–8,390] and recoveries may grow to 279,602 [208,420–295,740]. The lifting of lockdown has caused an absolute increase of 98,768 confirmed cases with 95% interval [85,544–111,018], during the post-lockdown period. The positive aspect of the forecasts is that the number of active cases is expected to decrease to 63,706 [18,614–95,337], on August 10, 2020. This is the time for the concerned authorities to further restrict the active cases so that the recession of the outbreak continues in the next month.

Burning velocity of different chemicals is estimated using a model from mixed population considering inverted Kumaraswamy (IKum) distribution for component parts. Two estimation techniques maximum likelihood estimation (MLE) and Bayesian analysis are applied for estimation purposes. BEs of a mixture model are obtained using gamma, inverse beta prior, and uniform prior distribution with two loss functions. Hyperparameters are determined through the empirical Bayesian method. An extensive simulation study is also a part of the study which is used to foresee the characteristics of the presented model. Application of the IKum mixture model is presented through a real dataset. We observed from the results that Linex loss performed better than squared error loss as it resulted in lower risks. And similarly gamma prior is preferred over other priors.

Cancer is among the major public health problems as well as a burden for Pakistan. About 148,000 new patients are diagnosed with cancer each year, and almost 100,000 patients die due to this fatal disease. Lung, breast, liver, cervical, blood/bone marrow, and oral cancers are the most common cancers in Pakistan. Perhaps smoking, physical inactivity, infections, exposure to toxins, and unhealthy diet are the main factors responsible for the spread of cancer. We preferred a novel four-component mixture model under Bayesian estimation to estimate the average number of incidences and death of both genders in different age groups. For this purpose, we considered 28 different kinds of cancers diagnosed in recent years. Data of registered patients all over Pakistan in the year 2012 were taken from GLOBOCAN. All the patients were divided into 4 age groups and also split based on genders to be applied to the proposed mixture model. Bayesian analysis is performed on the data using a four-component exponential mixture model. Estimators for mixture model parameters are derived under Bayesian procedures using three different priors and two loss functions. Simulation study and graphical representation for the estimates are also presented. It is noted from analysis of real data that the Bayes estimates under LINEX loss assuming Jeffreys’ prior is more efficient for the no. of incidences in male and female. As far as no. of deaths are concerned again, LINEX loss assuming Jeffreys’ prior gives better results for the male population, but for the female population, the best loss function is SELF assuming Jeffreys’ prior.

In this article, Maximum likelihood estimation (MLE) and Bayesian estimation for Rayleigh distribution using progressive type-II censoring in the presence of outliers is considered. Inverse Gamma prior and Jeffreys prior are used for Bayesian estimation. Squared error loss function (SELF), precautionary loss function (PLF) and K-loss function (KLF) are used for obtaining the expressions of Bayes estimators and posterior risks. Credible intervals are also derived. A simulation study is presented to discuss the behavior of Bayes estimators. Applicability of the undertaken study is highlighted using three real data sets.