Improved exponential type variance estimators for population utilizing supplementary information.

This paper contributes to the existing literature on variance estimators by utilizing supplementary information. The variance estimation problem of a finite population is a significant matter as sometimes, it is tough to control the variation. For this purpose, an optimum family of exponential variance estimators is suggested under simple random sampling. Moreover, different specific members of the proposed estimators are identified by incorporating various known characteristics of the supplementary variable in the suggested generalized class of estimators. The derivations for the expressions of bias as well as mean square error (MSE) of the proposed estimators are conducted. The suggested family of estimators is studied in different situations by using sets of real data and simulation studies for their performance. To evaluate the efficiency of the suggested estimators, R software is used for the analysis. The study compares the performance of the proposed estimators against the traditional estimators. The theoretical and numerical comparisons show that the estimators suggested in the study are superior in efficiency as compared to the existing estimators.

Improved exponential type mean estimators for non-response case using two concomitant variables in simple random sampling.

This paper addresses new exponential estimators for population mean in case of non-response on both the study and the concomitant variables using simple random sampling. The expressions for theoretical bias and mean square error of new estimators are derived up to first-order approximation and comparisons are made with the existing estimators. The proposed estimators are observed more efficient as compared to the considered estimators in the literature. For instance, the classical [4] unbiased estimator, the estimator of [9], and other existing estimators under the explained conditions. The theoretical results are supported numerically by using real-life data sets, under the criteria of bias, mean square error, percent relative efficiency and mathematical conditions. It is also clear from the numerical results that the suggested exponential estimators performed better than the estimators in the literature.

Methods for Improving the Variance Estimator of the Kaplan-Meier Survival Function, When There Is No, Moderate and Heavy Censoring-Applied in Oncological Datasets.

In case of heavy and even moderate censoring, a common problem with the Greenwood and Peto variance estimators of the Kaplan-Meier survival function is that they can underestimate the true variance in the left and right tails of the survival distribution. Here, we introduce a variance estimator for the Kaplan-Meier survival function by assigning weight greater than zero to the censored observation. On the basis of this weight, a modification of the Kaplan-Meier survival function and its variance is proposed. An advantage of this approach is that it gives non-parametric estimates at each point whether the event occurred or not. The performance of the variance of this new method is compared with the Greenwood, Peto, regular, and adjusted hybrid variance estimators. Several combinations of these methods with the new method are examined and compared on three datasets, such as leukemia clinical trial data, thalassaemia data as well as cancer data. Thalassaemia is an inherited blood disease, very common in Pakistan, where our data are derived from.

Regression analysis of hydro-meteorological variables for climate change prediction: A case study of Chitral Basin, Hindukush region.

In the present study, hydro-meteorological variables of Chitral Basin in Hindukush region of Pakistan were studied to predict the changes in climatic components such as temperature, precipitation, humidity and river flow based on observed data from 1990 to 2019. Uncertainties in climate change projection were studied using various statistical methods, such as trend variability analysis via stationarity test and validation of regression assumptions prior to fitting of regression estimates. Also, multiple regression models were estimated for each hydro-meteorological variables for the given 30 years of observed data. Results demonstrated that temperature and, precipitation were inversely related with one another. It was observed from the regression model that temperature is decreases by 0.309 °C on the average increases in precipitation by one unit. Temperature also decreases for the increase in humidity by average 0.086 °C. Since, precipitation is negatively related with temperature, thus for increases in temperature the annual precipitation decreases by 0.278 mm annually. Humidity on the other hand, increases by 0.207% by increasing in precipitation and the temperature that causes humidity to decrease by 0.99%. Thus, it demonstrated that the flow in Chitral river increases due to precipitation by 0.306 m3/s for the change in precipitation by one unit. Findings from the present study negated the general perceptions that flow in the Chitral river has increased due to recession of glaciers with increase in the intensity of temperature.

Statistical errors in medical research - a review of common pitfalls.

BACKGROUND: Standards in the use of statistics in medical research are generally low. A growing body of literature points to persistent statistical errors, flaws and deficiencies in most medical journals. METHODS: In this paper we present a comprehensive review of common statistical pitfalls which can occur at different stages in the scientific research process, ranging from planning a study, through conducting statistical data analysis and documenting statistical methods applied, to the presentation of study data and interpretation of study results. RESULTS: 47 potential statistical errors and shortcomings, differentiated for the distinct phases of medical research are presented and discussed. CONCLUSIONS: Statisticians should be involved early in study design, as mistakes at this point can have major repercussions, negatively affecting all subsequent stages of medical research. Consideration of issues discussed in this paper, when planning, conducting and preparing medical research manuscripts, should help further enhance statistical quality in medical journals.

Statistical analysis of the different factors affecting the diarrhea.

Diarrhea is a worldwide problem facing both developing countries and developed countries, especially in pediatric population. Because of shortage of health facilities and lack of good food in developing countries, it is known fact that developing countries are facing this death taking problem more. The main purpose of this study was to examine the various factors which affect the recovery time of diarrhea. A multiple linear regression was applied to analyze the data and to select a model. The response variable for the study was the recovery time of diarrhea. The results of the analysis show that the Zinc is the main factor which affect the recovery time in Peshawar.