Amal Almohisen

In the vast statistical literature, there are numerous probability distribution models that can model data from real-world phenomena. New probability models, nevertheless, are still required in order to represent data with various spread behaviors. It is a known fact that there is a great need for new models with limited support. In this study, a flexible probability model called the unit Maxwell-Boltzmann distribution, which can model data values in the unit interval, is derived by selecting the Maxwell-Boltzmann distribution as a base-line model. The important characteristics of the derived distribution in terms of statistics and mathematics are investigated in detail in this study. Furthermore, the inference problem for the mentioned distribution is addressed from the perspectives of maximum likelihood, method of moments, least squares, and maximum product space, and different estimators are obtained for the unknown parameter of the distribution. The derived distribution outperforms competitive models according to different fit tests and information criteria in the applications performed on four actual air pollutant concentration data sets, indicating that it is an effective model for modeling air pollutant concentration data.

Count data consists of both observed and unobserved events. The analysis of count data often encounters overdispersion, where traditional Poisson models may not be adequate. In this paper, we introduce a tractable one-parameter mixed Poisson distribution, which combines the Poisson distribution with the improved second-degree Lindley distribution. This distribution, called the Poisson-improved second-degree Lindley distribution, is capable of effectively modeling standard count data with overdispersion. However, if the frequency of the unobserved events is unknown, the proposed distribution cannot be directly used to describe the events. To address this limitation, we propose a modification by truncating the distribution to zero. This results in a tractable zero-truncated distribution that encompasses all types of dispersions. Due to the unknown frequency of unobserved events, the population size as a whole becomes unknown and requires estimation. To estimate the population size, we develop a Horvitz–Thompson-like estimator utilizing truncated distribution. Both the untruncated and truncated distributions exhibit desirable statistical properties. The estimators for both distributions, as well as the population size, are asymptotically unbiased and consistent. The current study demonstrates that both the truncated and untruncated distributions adequately explain the considered medical datasets, which are the number of dicentric chromosomes after being exposed to different doses of radiation and the number of positive Salmonella. Moreover, the proposed population size estimator yields reliable estimates.

Antimicrobial dispensing without a prescription has been identified as a significant contributor to the burgeoning crisis of antimicrobial resistance. To combat this, the Saudi Ministry of Health introduced a stringent antimicrobial restriction policy in mid-2018, mandating prescriptions for all antimicrobial drug dispensations at pharmacies. Therefore, this study aimed to assess the immediate impact of this policy on retail antimicrobial sales. To do so, we analyzed annual sales data from 2017 to 2019 sourced from the IQVIA-MIDAS^® database, which included a range of antimicrobials, such as antibiotics, antifungals, and other related agents. The analysis revealed a notable reduction in overall antimicrobial sales by 23.2%, decreasing from 818.9 million SAR in 2017 to 648.4 million SAR in 2019. While the Wilcoxon signed-rank test indicated a statistically significant median reduction in total antimicrobial sales post-policy implementation (p = 0.0397), it is important to acknowledge that the long-term effects and adherence to the policy require further investigation. Notably, sales of amoxicillin dropped by 70% in 2019 compared to 2017, contributing largely to the decline. Conversely, a continuous increase in sales of some antimicrobial drugs following the restriction policy was observed, led by amoxicillin/clavulanic acid. Our data support the implementation of antimicrobial restriction measures as an effective means of controlling excessive antimicrobial sales and dispensing without prescriptions.

In any longitudinal study, a dropout before the final timepoint can rarely be avoided. The chosen dropout model is commonly one of these types: Missing Completely at Random (MCAR), Missing at Random (MAR), Missing Not at Random (MNAR), and Shared Parameter (SP). In this paper we estimate the parameters of the longitudinal model for simulated data and real data using the Linear Mixed Effect (LME) method. We investigate the consequences of misspecifying the missingness mechanism by deriving the so-called least false values. These are the values the parameter estimates converge to, when the assumptions may be wrong. The knowledge of the least false values allows us to conduct a sensitivity analysis, which is illustrated. This method provides an alternative to a local misspecification sensitivity procedure, which has been developed for likelihood-based analysis. We compare the results obtained by the method proposed with the results found by using the local misspecification method. We apply the local misspecification and least false methods to estimate the bias and sensitivity of parameter estimates for a clinical trial example.