Estimation of the Selected Treatment Mean in Two-Stage Drop-the-Losers Design

A common problem faced in clinical studies is that of estimating the effect of the most effective (e.g., the one having the largest mean) treatment among $k~(\geq2)$ available treatments. The most effective treatment is adjudged based on numerical values of some statistic corresponding to the $k$ treatments. A proper design for such problems is the so-called "Drop-the-Losers Design (DLD)". We consider two treatments whose effects are described by independent Gaussian distributions having different unknown means and a common known variance. To select the more effective treatment, the two treatments are independently administered to $n_1$ subjects each and the treatment corresponding to the larger sample mean is selected. To study the effect of the adjudged more effective treatment (i.e., estimating its mean), we consider the two-stage DLD in which $n_2$ subjects are further administered the adjudged more effective treatment in the second stage of the design. We obtain some admissibility and minimaxity results for estimating the mean effect of the adjudged more effective treatment. The maximum likelihood estimator is shown to be minimax and admissible. We show that the uniformly minimum variance conditionally unbiased estimator (UMVCUE) of the selected treatment mean is inadmissible and obtain an improved estimator. In this process, we also derive a sufficient condition for inadmissibility of an arbitrary location and permutation equivariant estimator and provide dominating estimators in cases where this sufficient condition is satisfied. The mean squared error and the bias performances of various competing estimators are compared via a simulation study. A real data example is also provided for illustration purposes

On Estimating the Selected Treatment Mean under a Two-Stage Adaptive Design

Adaptive designs are commonly used in clinical and drug development studies for optimum utilization of available resources. In this article, we consider the problem of estimating the effect of the selected (better) treatment using a two-stage adaptive design. Consider two treatments with their effectiveness characterized by two normal distributions having different unknown means and a common unknown variance. The treatment associated with the larger mean effect is labeled as the better treatment. In the first stage of the design, each of the two treatments is independently administered to different sets of $n_1$ subjects, and the treatment with the larger sample mean is chosen as the better treatment. In the second stage, the selected treatment is further administered to $n_2$ additional subjects. In this article, we deal with the problem of estimating the mean of the selected treatment using the above adaptive design. We extend the result of \cite{cohen1989two} by obtaining the uniformly minimum variance conditionally unbiased estimator (UMVCUE) of the mean effect of the selected treatment when multiple observations are available in the second stage. We show that the maximum likelihood estimator (a weighted sample average based on the first and the second stage data) is minimax and admissible for estimating the mean effect of the selected treatment. We also propose some plug-in estimators obtained by plugging in the pooled sample variance in place of the common variance $\sigma^2$, in some of the estimators proposed by \cite{misra2022estimation} for the situations where $\sigma^2$ is known. The performances of various estimators of the mean effect of the selected treatment are compared via a simulation study. For the illustration purpose, we also provide a real-data application

On Solving Fixed Charge Transportation Problems Having Interval Valued Parameters

In this article, we propose a new method for solving the interval fixed charge transportation problem (IFCTP), wherein the parameters (associated cost, fixed cost, supply, and demand) are represented by interval numbers. First, an equivalent bi-objective fixed charge transportation problem (FCTP) is derived from the given IFCTP, and then the equivalent crisp problem is solved using a fuzzy programming technique. To demonstrate the solution procedure, two existing numerical examples (Safi and Razmjoo {\cite{bakp1}}) are coded and solved in LINGO 19.0. We establish the effectiveness of our proposed method through a comparison of the results achieved with those of two pre-existing methods

Trends of Traffic-Related Injuries Treated Across a Jefferson Health Trauma Center

Every day in the city of Philadelphia, 5 children are involved in traffic-related incidents. Each year, over 100 people are killed in traffic accidents, and 250 more are seriously injured. Philadelphia has one of the highest rates of traffic-related deaths in the US. Fatal or serious crashes are more than twice as likely in low-income areas of the city and 30% more likely to occur in areas where most of the population are people of color. Before beginning to craft and implement policies to improve public safety, locations of incidents, ethnicities and home neighborhoods of victims, insurance types, and hospital care path are imperative to understand. This study serves as a pioneer to gather and statistically analyze data on traffic-related incidents. It will demonstrate that such a study is logistically possible and as more trauma units within the Jefferson enterprise are added, future data will become more robust and help to inform public health policy and hospital guidelines. In examining admissions to Jefferson’s Center City/Methodist trauma unit from 2007 to 2016, we analyzed 2,392 traffic-related incidences, and subsequent admissions, across the city. The mean age of the patient population studied in our sample was 44 years with an average Glasgow Coma Score of 13.42. The median length of stay (LOS) was 5 days, and a larger percentage of the patients examined in our study were male and Caucasian compared to the Philadelphia population. The most reported symptom was loss of consciousness, reported in 660 patients, and the most prescribed medication class was opiates, prescribed to 2,026 patients. A correlation was found between Injury Severity Score and LOS. This study helps to better understand the patients we serve and identify trends that we hope will contribute to ongoing efforts addressing traffic-related deaths at the Jefferson Enterprise

TRADITIONAL USES, PHYTOCHEMISTRY AND PHARMACOLOGICAL ACTIVITIES OF PAPAVER SOMNIFERUM WITH SPECIAL REFERENCE OF UNANI MEDICINE AN UPDATED REVIEW

Papaver somniferum commonly known as Khashkhash /Afyon, belongs to family Papaveraceae. It is one of those traditional plants, which have a long history of usage as medicine. The opium poppy (Papaver somniferum) produces some of the most widely used medicinal alkaloids like morphine, codeine, thebain and porphyroxine which are the most important component of this plant. Apart from these alkaloids, opium poppy produces approximately eighty alkaloids belonging to various tetrahydrobenzylisoquinolinederived classes. It has been known for over a century that morphinan alkaloids accumulate in the latex of opium poppy. According to Unani literature, it possesses most important theurapeutic values as modern literature and research studies also prove its therapeutical importance. It is used as analgesic, narcotic, sedative, stimulant as well as nutritive, etc. It is also useful in headache, cough, insomnia, cardiac asthma, and biliary colic. In this paper we have provide a review on habitate, pharmacological actions, phytochemical with special refrence to Unani Medicine. In this review, an attempt is made to explore the complete information of Papaver somniferum including its  phytochemistry and pharmacology. Key words: Khashkhash, Biliary colic, Alkaloid, phytochemistry

TRADITIONAL USES, PHYTOCHEMISTRY, AND PHARMACOLOGICAL ACTIVITIES OF AMLA WITH SPECIAL REFERENCE OF UNANI MEDICINE - AN UPDATED REVIEW

Emblica officinalis, commonly known as Amla belongs to family Euphorbiaceae, is widely used for medicinal purposes in Indian traditional system of medicine (Unani, Ayurveda, and Siddha). It is well known that all parts of Amla are useful in the treatment of various diseases. Various studies on Amla suggest that it has antiviral, antibacterial, and antifungal actions. It is one among those traditional plants, which have a long history of usage as a fruit and remedy. It is amazingly effective as natural antiaging drug. It is a very effectual plant in the treatment of acidity and peptic ulcer. According to Unani literature, it possesses nutritional as well as therapeutic values, and thus, it is one of the herbal nutraceuticals. Modern literature and research studies also prove its medicinal importance. Its fruit is used traditionally as an antioxidant, immunomodulator, antipyretic, analgesic, antitussive, anticancer, and gastroprotective. It is also useful in diarrhea, dysentery, diabetes, fever, headache, mouth ulcer, hair growth, scurvy, and constipation. Phytochemical studies on amla disclosed major chemical constituents including tannins, alkaloids, polyphenol, fatty acid, glycosides, phosphatides, vitamins, and minerals. Gallic acid, ellagic acid, phyllembein, and ascorbic acid are also found to be biologically effective. Various reports show the presence of catechol, β-carotene, flavonoids, pyrogallol, superoxide, and dismutase enzyme in Emblica fruit. In this review, an attempt is made to explore the complete information of E. officinalis including its phytochemistry and pharmacology.</jats:p

Understanding organizational factors affecting the quality of work life (qwl) of healthcare providers in tertiary care hospitals: A qualitative exploratory study

Introduction: Quality of work life (QWL) among healthcare providers (HCPs) plays a critical role in shaping the overall healthcare system\u27s effectiveness and the well-being of its workforce. This study aims to shed light on the perception of QWL among HCPs and organizational factors influencing their QWL in private-sector tertiary care hospitals in Karachi, Pakistan, and qualitatively compare the perceptions and experiences across different specialties and cadres. Method: The study adopted a qualitative exploratory design, employing in-depth interviews as the primary data collection method. A total of 42 healthcare providers from three private-sector tertiary care hospitals participated, representing the departments of internal medicine, general surgery, and obstetrics and gynecology. Results: The findings revealed that HCPs across tertiary care hospitals in Karachi perceived QWL to be a combination of a well-paying job, a good work-life balance, a comfortable and stress-free working environment and conditions, supportive leadership, and support from family. Organizational factors affecting the QWL were identified by the participants as fair monetary compensation, increased workload, lack of infrastructure that facilitates employee amenities, decision-making autonomy at the workplace, and feedback, recognition, and appreciation from the leadership, including rewards for performance and patient appreciation. Emotional and practical support from colleagues was also found to significantly influence the QWL of HCPs by mitigating workplace stress. One of the unique findings of the study was the identification of family expectations as a factor affecting QWL, as healthcare providers often struggle to meet families’ unrealistic demands for time and presence In view of these, initiatives to improve QWL, such as introducing confidential mental health services support facilities like safe transport, childcare, and breastfeeding rooms for women, and the need for personal development skills to cope with workplace challenges were also highlighted. Conclusion: Healthcare organizations are encouraged to inculcate a culture that prioritizes employee well-being and promotes a positive work culture by establishing wellness committees focused on improving QWL and mitigating burnout