The escalating use of prescribed drugs has increasingly raised concerns about polypharmacy. This study aims to examine changes in rates of polypharmacy and potentially serious drug-drug interactions in a stable geographical population between 1995 and 2010. This is a repeated cross-sectional analysis of community-dispensed prescribing data for all 310,000 adults resident in the Tayside region of Scotland in 1995 and 2010. The number of drug classes dispensed and the number of potentially serious drug-drug interactions (DDIs) in the previous 84 days were calculated, and age-sex standardised rates in 1995 and 2010 compared. Patient characteristics associated with receipt of ≥10 drugs and with the presence of one or more DDIs were examined using multilevel logistic regression to account for clustering of patients within primary care practices. Between 1995 and 2010, the proportion of adults dispensed ≥5 drugs doubled to 20.8%, and the proportion dispensed ≥10 tripled to 5.8%. Receipt of ≥10 drugs was strongly associated with increasing age (20–29 years, 0.3%; ≥80 years, 24.0%; adjusted OR, 118.3; 95% CI, 99.5–140.7) but was also independently more common in people living in more deprived areas (adjusted OR most vs. least deprived quintile, 2.36; 95% CI, 2.22–2.51), and in people resident in a care home (adjusted OR, 2.88; 95% CI, 2.65–3.13). The proportion with potentially serious drug-drug interactions more than doubled to 13% of adults in 2010, and the number of drugs dispensed was the characteristic most strongly associated with this (10.9% if dispensed 2–4 drugs vs. 80.8% if dispensed ≥15 drugs; adjusted OR, 26.8; 95% CI 24.5–29.3). Drug regimens are increasingly complex and potentially harmful, and people with polypharmacy need regular review and prescribing optimisation. Research is needed to better understand the impact of multiple interacting drugs as used in real-world practice and to evaluate the effect of medicine optimisation interventions on quality of life and mortality.

We propose a new generalized family of distributions called the exponentiated generalized power series (EGPS) family of distributions and study its sub-model, the exponentiated generalized logarithmic (EGL) class of distributions, in detail. The structural properties of the new model (EGPS) and its sub-model (EGL) distribution including moments, order statistics, Rényi entropy, and maximum likelihood estimates are derived. We used the method of maximum likelihood to estimate the parameters of this new family of distributions. Simulation study was carried out to examine the bias and the mean square error of the maximum likelihood estimators for each of the model's parameters. Finally, we showed real life data examples to illustrate the models' applicability, flexibility and usefulness.

In this paper, we present the generalized flexible-G family for creating several continuous distributions. Our new technique features are that it adds only two extra shape parameters to any chosen continuous distribution and is not derived from any parent distribution that currently exists. Several special cases of this family are provided. The generalized flexible-G family offers significant improvements in flexibility, fit, and applicability across a wide range of fields. The family's model parameters are estimated using the maximum likelihood estimation method. A simulation study is conducted to assess the consistency of the maximum likelihood estimates. The generalized flexible log-logistic, a specific case of our novel family, is applied to both patient's analgesia and reliability data in order to illustrate the significance of the family. The generalized flexible log-logistic outperforms several competitive models provided in this paper. Furthermore, the generalized flexible log-logistic performs better than traditional distributions such as the BurrXII, Gumbel, and Weibull models.

A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

One of the most important applications of statistical models is in analyzing survival data. In this study, we developed the Gamma Type Two Half Logistic Topp-Leone-G model using the technique earlier proposed by Zografos and Balakrishnan. Different characteristics of the proposed distribution are obtained. In order to estimate the model parameters based on complete and censored data, the maximum likelihood estimation method is used. Through Monte Carlo simulation, the performance of the estimators is evaluated. The proposed distribution's potential significance and applicability are empirically demonstrated using actual datasets. We found that our new distribution is a very competitive model for describing both complete and censored observations in survival analysis. The work demonstrated that in certain cases, our new model performed better than other parametric models with the same number of parameters.