Abstract: The literature of count regression models covers a large scope of studies and applications that implemented simple and standard models for count response variables by using Poisson regression models, binomial regression models, negative binomial regression models, geometric regression models, or generalized Poisson regression models. These regression models have received considerable attention in various situations. Nevertheless in many fields, the distribution of the count response variable may display a feature of excess zeros for which the aforementioned regression models may fail to provide an adequate fit. To remedy this handicap, a class of distributions known as zero-inflated models is considered as the most appropriate approach for dealing properly with this issue of excess zeros. In addition to the zero-inflated problem, it happens quite often that the sample data sets under investigation are not completely observed. This refers to the missing data problem. In this study, our primary interest is in reviewing studies that considered simultaneously the missing data problem and the zero-inflated feature in modeling zero-inflated data. Moreover, we discuss their methodologies and results and some potential directions of the future research.

Abstract: One of the major issues in securing blood supply to patients worldwide is to provide blood of the best achievable quality, in the needed quantities. Central Blood Services (CBS’s) worldwide are daily faced with the problem how to satisfy demands for blood from various hospitals. These hospitals, in their turn, are faced with the problem how to satisfy demands for blood from their patients. To solve these problems in a cost-effective way is notoriously difficult, because (i) the amounts of available blood and of blood demand are random, (ii) blood can only be used during a limited amount of time, (iii) one must distinguish various blood components (red blood cells, plasma and platelets) with different associated costs and perishability and (iv) one must distinguish persons with different blood types (like AB+ and O−) with different capabilities to act as donor or as recipient. In this review paper we provide the subject background, describing the blood characteristics and the operation of CBS and hospital blood banks. In particular we describe blood demand, blood components and blood types. We depict blood screening procedures and their processing times and provide with some real data. Particularly we describe a stochastic approach to blood screening and inventory. An emphasis will be given to inventory management and blood allocation, stochastic imput-output of the inventory system and some cost functions involved.

Abstract: The research study was formulated based on promoting a healthy and conducive environment in other to assist student to get satisfied with the process of learning endeavor. The priority for any University is to create enabling healthy environment for conducive atmosphere for learning to take place in other to give and get the best from their student. This study covers a sample of 227 student from Near East University Cyprus, closed ended question was design to generate the response of student from the University, after then analysis was carry out via SPSS version 18.0. Statistical analysis perform with the SPSS were Descriptive Statistics, Chi-Square test, Independent Sample t-Test, One way Anova and correlation. Student information used in generating the responses were place of residence, gender, on-scholarship and not on scholarship student, continent background to mentioned but few.

Abstract: A prelude to interpret a pattern in the repeating incidences is to identify the underlying frequency distribution of the collected data. A case in point is the Poisson distribution which is often selected for medical count data such as gene mutations, medication error and number of ambulatory pickups in a day. A requirement for the Poisson distribution is that the variance ought to be equal to the mean. The variance signifies the volatility in the occurrences. An implication is that the volatility becomes more when the average incidence is higher. When this requirement of the functional equivalence of the Poisson mean and variance is breached, the data deviates from a Poisson distribution. How could a data analyst recognize and point out to the medical team the dilution level of the requirement in their data' For this purpose, a simple and easier geometrical approach is developed in this article and illustrated with several historical data sets in the literature.

Abstract: Alternative medicine it is a medicine that is not taught in traditional medicine. It is based on ancient historical foundations and different experiments in treatment without building it on the basis of scientific teacher. Alternative medicine is used in many peoples, especially non-developed peoples. Alternative medicine is used as primary medicine. The evidence of poor quality and knowledge about the awareness of using the natural drugs instead of using the chemical medication in the hospital. Little is known about the prevalence of natural medication in the Europe, especially in Cyprus. To determine the knowledge, community awareness, and to define the difference treatment practice between natural elements and chemical drugs. To identified the rate of the knowledge that students had and evaluate the results and measure it. Cross-sectional survey were performed by using SPSS and the Pearson Chi-Square test was done to determine the differences perform the questionnaire at near East University in Cyprus. We print our data as questionnaire paper and give it to 562 international students with different backgrounds. A total of 562 questionnaires were administered for this survey and the percentage respondents gender of students was 62.3% in males and 37,3% were females, also The Percentage of Respondents of students choose strongly disagree that were 47% and few of students shown 6.1% Percentage in strongly disagree. Furthermore, studentâ€™s percentage of that prefer use of natural elements that were 66.5% cheaper with strongly agree, 21.2% with agree, 2.8% with strongly disagree, and disagree that were 9.5%. Furthermore, students 38.0% Yoga with good scale, 35.2% Herbal with good scale and 34.6% Holy books with excellent scale. (Respectively, p

Abstract: A multiple testing procedure can be a single-step procedure such as Bonferroni's method or a stepwise procedure such as Hochberg's stepup method and Hommel's method. It can be an α-exhaustive or α-conservative approach. We develop a single α-exhaustive procedure that can improve power 2-5% over Hochberg's and Hommel's methods in common situations when the test statistics are mutually independent. The method can also be generalized to dependent test statistics. The idea behind our method is to construct the rejection rules using the product of marginal p-values and by controlling the upper bounds of the kth order terms so that α is controlled for any configuration of k null hypotheses. Such upper bounds or critical values are determined progressively from k = 1 towards k = K, the number of null hypotheses in the problem.

Abstract: In this article, entropy in the collected data about the Gaussian population mean is traced from its embryonic stage as new data are periodically collected. The traditional Shannon's entropy has shortcomings from the data analytics point of view and it creates a necessity to refine the Shannon's entropy. Its refined version is named Gaussian Nucleus Entropy in this article. Advantages of the refined version are pointed out. The Prior, likelihood, Posterior and predictive nucleus entropies are derived, interconnected and interpreted. The results are illustrated using data on cesarean births in thirteen countries in the period [1987, 2007]. The medical communities and families are alarmed, as the cesarean births are increasing not due to emergency or necessity basis but rather for monetary or convenience basis. Nucleus entropy based data analysis answers whether their alarm is baseless.

Abstract: We describe a Bayesian adaptive design for early phase cancer trials of a combination of three agents. This is an extension of an earlier work by the authors by allowing all three agents to vary during the trial and by assigning different drug combinations to cohorts of three patients. The primary objective is to estimate the Maximum Tolerated Dose (MTD) surface in the three-dimensional Cartesian space. A class of linear models on the logit of the probability of Dose Limiting Toxicity (DLT) are used to describe the relationship between doses of the three drugs and the probability of DLT. Trial design proceeds using conditional escalation with overdose control, where at each stage of the trial, we seek a dose of one agent using the current posterior distribution of the MTD of this agent given the current doses of the other two agents. The MTD surface is estimated at the end of the trial as a function of Bayes estimates of the model parameters. Operating characteristics are evaluated with respect to trial safety and percent of dose recommendation at dose combination neighborhoods around the true MTD surface.

Abstract: The main objective of this paper is to identify the independent predictors affecting the survival of HIV/AIDS infected patients on Antiretroviral Therapy (ART), an interval censored event time outcome. A total of 2052 HIV/AIDS patients, who were on ART at Ram ManoharLohia Hospital, New Delhi, India, during the period of April 2004 to December 2010, were included for analysis. Accelerated Failure Time Models (AFTM) viz., exponential, Weibull, lognormal and loglogistic for interval censored survival data, have been used to determine the significant predictors for HIV/AIDS infected patients. The best model is selected on the basis of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values. Out of 2052 HIV/AIDS patients 65.4% were males and 34.6% were females. A majority 93.7% of patients had CD4 cell counts below 350 cells/mm3 at the time of initiation of ART. The mean age of patients at diagnosis was 34.28±8.19 years. The prognostic factorsviz., age, sex, CD4 cell count, past smokers, baseline hemoglobin and baseline BMI are found to be statistically significant (p<0.000) for HIV/AIDS patients on ART. Hence, a special attention is needed for patients with low CD4 cell counts, low BMI and low hemoglobin. Lognormal AFT model is found to be the best model to identify the independent predictors for survival of HIV population.

Abstract: For a clinical trial design with paired data, it often involves missing observations. In such a case, the data from the trial become a mixture of paired and unpaired data. A commonly used approach for the analysis of the trial data is to ignore the incomplete pairs. Such a treatment of missing data is not statistically efficient. We propose a simple method that will allow us to use all data, including the incomplete pairs. The method is optimal in the sense that it minimizes the variance. We will show how to design classical and adaptive trials with the proposed method. The proposed method can also be used for meta-analysis, in which, some trials with paired data and some are not.

Abstract: Classifying objects/individuals is common problem of interest. Receiver Operating Characteristic (ROC) curve is one such tool which helps in classifying the objects/individuals into one of the two known groups or populations. The present work focuses on proposing a Hybrid version of the ROC model. Usually the test scores of the two populations namely normal and abnormal tend to follow some particular distribution, here in this study it is considered that the test scores of normal follow Half Normal and abnormal follow Rayleigh distributions respectively. The characteristics of the proposed ROC model along with measures such as AUC and KLD are derived and demonstrated using a real data set and simulation data sets.

Abstract: Non-inferiority of a diagnostic test to the standard is a common issue in medical research. For instance, we may be interested in determining if a new diagnostic test is noninferior to the standard reference test because the new test might be inexpensive to the extent that some small inferior margin in sensitivity or specificity may be acceptable. Noninferiority trials are also found to be useful in clinical trials, such as image studies, where the data are collected in pairs. Conventional noninferiority trials for paired binary data are designed with a fixed sample size and no interim analysis is allowed. Adaptive design which allows for interim modifications of the trial becomes very popular in recent years and are widely used in clinical trials because of its efficiency. However, to our knowledge there is no adaptive design method available for noninferiority trial with paired binary data. In this study, we developed an adaptive design method for non-inferiority trials with paired binary data, which can also be used for superiority trials when the noninferiority margin is set to zero. We included a trial example and provided the SAS program for the design simulations.

Abstract: Missing data is a common occurrence in longitudinal studies of health care research. Although many studies have shown the potential usefulness of current missing analyses, e.g., (1) Complete Case (CC) analysis; (2) imputation methods such as Last Observation Carried Forward (LOCF), multiple imputations, Expectation-Maximization algorithm approach; and (3) methods using all available data such as linear mixed model and generalized estimation equations approach, the CC analysis or LOCF imputation method have been popular due to their simplicity of execution regardless of some critical drawbacks. The proposed approach employs the generalized least squares method using all available data without deletion or imputations for missing outcomes, producing the best linear unbiased estimate. A simulation study was conducted to compare the proposed approach to commonly used missing analyses under each missing data mechanism and showed the validity of the proposed approach, especially with the first order autoregressive correlation structure. B-spline is applied to the proposed model to manage non-linear relationships between outcome and continuous covariate. Application to a cell therapy clinical trial is presented.

Abstract: Therapeutic potential of a new antidepressant drug isevaluated frequently based on multi-item psychometric scales. The total scoreof a psychometric scale is calculated based on the responses of multiple-items,in which each item is scored on a likert scale. Missing responses in some ofthe items are inevitable and hence it is a problem in calculating the totalscore of a scale. Different approaches can be used to handle the missing itemresponses in constructing the total scores of a psychometric scale. Oneapproach is that if a patient has missing responses in one or more items,his/her total score will be missing; another approach is that the missing itemresponse will be imputed before calculating the scale total score. For theimputation, different methods can be used. Each of the methods has somedrawbacks. This paper compares six methods, commonly used in imputing themissing item responses when there are missing responses at one or more items,but not missing more than 50% items of the scale. Simulation studies indicatethat substituting the mean of the completed items of a scale for a givenpatient is generally the most desirable method for imputing both the random andnon-random missing items in the psychometric scale construction.

Abstract: In a cancer prevention trial, an outcome such as cancer severity cannot be evaluated in individuals who do not develop cancer. In such a situation, the principal stratification approach has been applied. Under this approach, the Principal Strata Effect (PSE) has been considered, which is defined as the effect of treatment on the outcome among the subpopulation in which individuals would have developed cancer under either treatment arm. However, in this study, the author does not apply this approach to the situation. Instead, the author discusses the mediation analysis approach, in which Natural Direct and Indirect Effects (NDE and NIE) are considered. This approach has an advantage as it considers two possible mechanisms of treatment control of cancer severity: The first is that the treatment may prevent an individual from getting cancer, which could be regarded as control of cancer severity; the second is that even if the treatment does not prevent an individual from getting cancer, it may still impair the cancer severity. The former mechanism corresponds to the NIE and the latter corresponds to the NDE, although the PSE can consider only the latter mechanism. Methodologies proposed in the context of vaccine trials are applied to data from a randomized prostate cancer prevention trial.

Abstract: This article considers the analysis of Multiple Linear Regressions (MLRs) that are essential statistical method for the analysis of medical data in various fields of medical research like prognostic studies, epidemiological risk factor studies, experimental studies, diagnostic studies and observational studies. An approach is used in this article to select the â€œtrueâ€ regression model with different sample sizes. We used the simulation study to evaluate the approach in terms of its ability to identify the â€œtrueâ€ model with two options of distance measures: Ward's Minimum Variance Approach and the Single Linkage Approach. The comparison of the two options performed was in terms of their percentage of the number of times that they identify the â€œtrueâ€ model. The simulation results indicate that overall, the approach exhibited excellent performance, where the second option providing the best performance for the two sample sizes considered. The primary result of our article is that we recommend using the approach with the second option as a standard procedure to select the â€œtrueâ€ model.

Abstract: Menopause is not an illness but rather an important event as it changes the body physiology and mental cognition via hormonal changes. During data analysis of menopauses incidence data, new bivariate distribution is discovered. Their marginal, conditional distribution and statistical properties including the inter and partial correlations are explored and utilized to interpret menopauses data. A likelihood ratio hypothesis testing procedure is constructed to test the statistical significance of the sample estimate of the chance for menopause and estimate of the chance for operative menopause. The menopause data are analyzed and interpreted in the illustration. Research directions for future work are pointed out.

Abstract: Multi-state stochastic models are useful tools for studying complex dynamics such as chronic diseases. The purpose of this study is to determine factors associated with the progression between different stages of the disease and to model the progression of HIV/AIDS disease of an individual patient under ART follow-up using semi-Markov processes. A sample of 1456 patients has been taken from a hospital record at Amhara Referral Hospitals, Amhara Region, Ethiopia, who have been under ART follow up from June 2006 to August 2013. The states of disease progression adopted in the multi-state model were defined based on of the following CD4 cell counts: â‰¥500(SI); 200 to 499(SII);

Abstract: A primary data of 836 eligible women in the age group of 15-49 years is used to determine the causal effects of covariates on under-five mortality. The eight covariates viz., Number of family Members (NHM), Type of Toilet Facility (TTF), Total Children ever Born (TCB), Parity (PAR), Duration of Breastfeeding (DBF), use Contraceptive (CMT), DPT and Ideal Number of Girl (ING) are considered as covariates of the study. By applying Coxâ€™s regression analysis, six covariates viz., TTF, NHM, CMT, DBF, DPT and ING have substantially and significantly effect on under-five mortality. Further, a life table of under-five children under study is constructed using the estimate of survival function obtained from Coxâ€™s regression model.

Abstract: The Wald interval is easy to calculate; it is often used as the confidence interval for binomial proportions. However, when using this confidence interval, the actual coverage probability often falls under the nominal coverage probability in small cases. On the other hand, several confidence intervals where the actual cover age probability does not fall under the nominal coverage probability are suggested. In this study, we intro-duce five exact confidence intervals where the actual coverage probability does not fall under the nominal coverage probability and we calculate the expected length of the confidence intervals and compare/verify the accuracy of the coverage probabilities. Further, we examined the characteristics of these five exact confidence intervals at length. Coverage probability of Sterne was significantly closer to 0.95 than the other confidence intervals and stable. Its expected Length are not scattered in the width compared with the other methods. As a result, we found that the quality of the confidence interval based on the Sterne test is its availability for small samples.

Abstract: Biomass and extracellular polysaccharide of Ganoderma tsugae have various biological activity including anti-inflamatory activity, antioxidant activity and antitumor activity. However, the growth rate of G. tsugae in nature is very slow. Therefore, many studies have attempted to develop mass culture systems for G. tsugae using laboratory techniques. Many parameters of submerged fermentation for G. tsugae were studies to determine the optimization of process by combination of statistical techniques. Ten parameters from preliminary results and literature reviews (maltose, skim milk, KH2PO4+K2HPO4, MgSO4ï€-7H2O, CaCO3, vitamin B5+B6, olive oil, ethanol, pH and shaking speed) were screened by Packett Berman design. The significant parameters were determined the optimal ranges by path of steepest ascent method. The optimal condition of process was performed by response surface method. Maltose, skim milk and pH are significant parameters for G. tsugae cultivation. The conditions of 31.031 g L-1 maltose, 14.055 g L-1 skim milk and an initial pH of 7.12 resulted in the maximum extracellular polysaccharide content of 415 mg L-1 and the same fermentation broth at an initial pH of 6.46 exhibited the most biomass at 15.776 g L-1. Finally, the optimal condition was compared with un-optimal condition which result indicates that the combination of statistical techniques enhance the productions of biomass and extracellular polysaccharide (13X and 1.5X of the control, respectively). Therefore, these strategies are useful for improvement of submerged fermentation of G. tsugae which it can apply in pharmaceutical industry.

Abstract: The model is an abstraction of the reality. The selection of the usual inverse binomial as an underlying model for the number of patients waiting in months for heart and lung transplant is questionable because the data exhibit not the required balance between the dispersion and its functional equivalent in terms of the mean but rather an over or under dispersion. This phenomenon of over/under dispersion has been a challenge to find an appropriate underlying model for the data. This article offers an innovative approach with a new model to resolve the methodological breakdown. The new model is named Imbalanced Inverse Binomial Model (IIBM). A statistical methodology is devised based on IIBM to analyze the collected data. The methodology is illustrated with a real life data on the number of patients waiting in months for heart and lung transplants together. The results in the illustration do convince that the new approach is quite powerful and brings out a lot more information which would have been missed otherwise. In specific, the odds of receiving the organs are higher under an estimated imbalance in the data than under an ideal zero imbalance in all the states except Alabama. The odds are consistently higher under an estimated imbalance in the data than under an ideal zero imbalance across all the age groups waiting in months. Further research work is needed to identify and explain the factors which might have caused the imbalance between the observed dispersion in the data and its functionally equivalent amount according to the underlying inverse binomial model for the data. The contents of this article remains the foundation on which the future research work will be built.

Abstract: The rape victims are frightened to report with a fear of retaliation or humiliation. Consequently, the number of reported rapes is under-estimated. How should the number of unreported rapes be identified is discussed in this article. For this purpose, the Poisson distribution is modified and it is named Bumped-up Poisson distribution in this article. Related probability-informatics are derived to estimate the unreported rapes and proportion fearing to report. A hypothesis testing procedure is developed to assess the significance of an estimated proportion fearing. Our approach is tried with the reported rapes during the years 2007 and 2008 in a random sample of nations in all the continents. Proximities among the nations are identified in rape incidences.

Abstract: The amount of health benefits derived from breastfeeding is influenced by age of the child at initiation of the first breast milk, the duration and intensity of breastfeeding and age at which the child is introduced to supplementary foods and other liquids. In this study, the general trend of timing of breastfeeding initiation among nursing mothers in Nigeria between 1990 and 2003 is examined. The timing of initiation of the first breast milk to a child by her mother is measured in a three-level ordinal scale (immediately, within 24 h and days after birth) and the impacts of some socio-economic and maternal factors on this are determined. Results from this study revealed a significant improvement in the trend of early initiation of breast milk among Nigeria mothers between 1990 and 2003 (p

Abstract: The simulations on single vacancy defect transients for FCC structure were conducted to study the change in its final structure, especially the average atomic volume. The numerical code â€œALINEâ€ was employed for this purpose. The results obtained showed that when a single vacancy defect occurred in a perfect FCC-crystal structure, the average atomic volume was found to be suddenly increased and then gradually decreased down the value close to the initial value. This suggested that the FCC structure was able to expand and fill the volume originally occupied by the missing atom.