A novel randomized scrambling technique for mean estimation of a finite population.

In recent decades, the randomized response technique has attracted researchers due to its usefulness in sensitive surveys. The randomized response procedure is used for the collection of responses on sensitive issues such as cheating in examination, income earned through illegal sources, expenditure on luxury items, and amount of tax paid, etc. This study introduces a new variant of quantitative randomized response models for use with sample surveys where the variable of interest is quantitative. The properties of a mean estimator based on the new technique have been studied. Further, the combined and separate evaluation metrics for efficiency and privacy level have also been derived and compared with those of the existing methods. Further, a simulation study has been conducted to prove the improvement in the degree of privacy protection and efficiency. The findings reveal that the suggested randomized response technique is not only more efficient than the existing techniques, but also improves the joint measure of efficiency and respondents' privacy, making it preferable over the existing techniques. A real-world example of a sample survey through the suggested model is also presented which illustrates its usefulness in practical surveys on sensitive issues.

An efficient estimator of population variance of a sensitive variable with a new randomized response technique.

In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.

A comparative study of randomized response techniques using separate and combined metrics of efficiency and privacy.

In social surveys, the randomized response technique can be considered a popular method for collecting reliable information on sensitive variables. Over the past few decades, it has been a common practice that survey researchers develop new randomized response techniques and show their improvement over previous models. In majority of the available research studies, the authors tend to report only those findings which are favorable to their proposed models. They often tend to hide the situations where their proposed randomized response models perform worse than the already available models. This approach results in biased comparisons between models which may influence the decision of practitioners about the choice of a randomized response technique for real-life problems. We conduct a neutral comparative study of four available quantitative randomized response techniques using separate and combined metrics of respondents' privacy level and model's efficiency. Our findings show that, depending on the particular situation at hand, some models may be better than the other models for a particular choice of values of parameters and constants. However, they become less efficient when a different set of parameter values are considered. The mathematical conditions for efficiency of different models have also been obtained.

An improved version of systematic sampling design for use with linear trend data.

In survey sampling, systematic sampling design has attracted survey researchers in recent years due to its simplicity of use. We introduce a modified variant of systematic sampling scheme which improves the efficiency of a recently developed diagonal systematic sampling method. The suggested modification is also found to be more efficient than the other popular sampling designs in circumstances where the units of the population under consideration exhibit an increasing or decreasing perfect or near-perfect linear trend. Moreover, it is observed that the conditions for efficiency are mathematically strong and practically always hold, hence making the suggested sampling design preferable over the available sampling designs.

Risk Factors of End Stage Renal Disease in Peshawar, Pakistan: Odds Ratio Analysis.

AIM: The basic aim of this study was to discover the association of End Stage Renal Disease (ESRD) with various risk factors. End Stage Renal Failure is the last stage of the chronic renal failure in which kidneys become completely fail to function. MATERIALS AND METHODS: The data were collected from the patients of renal diseases from three major hospitals in Peshawar, Pakistan. Odds ratio analysis was performed to examine the relationship of ESRD (a binary response variable) with various risk factors: Gender, Diabetic, Hypertension, Glomerulonephritis, Obstructive Nephropathy, Polycystic kidney disease, Myeloma, SLE Nephritis, Heredity, Hepatitis, Excess use of Drugs, heart problem and Anemia. RESULTS: Using odds ratio analysis, the authors found that the ESRD in diabetic patients was 11.04 times more than non-diabetic patients and the ESRD were 7.29 times less in non-hypertensive patients as compared to hypertensive patients. Similarly, glomerulonephritis patients had 3.115 times more risk of having ESRD than non-glomerulonephritis. Other risk factors may also, to some extent, were causes of ESRD but turned out insignificant due to stochastic sample. CONCLUSION: The authors concluded that there is a strong association between ESRD and three risk factors, namely diabetes, hypertension and glomerulonephritis.

Statistical Study of Risk Factors of End Stage Renal Failure in Peshawar, Pakistan.

BACKGROUND: End Stage Renal Failure (ESRD) is the last stage of the chronic renal failure in which kidneys become completely fail to function. AIM: The basic aim of this study was to discover the important risk factors of ESRD and to construct a model for prediction of the ESRD patients in various hospitals of Peshawar, Pakistan. MATERIAL AND METHODS: The data were collected from the patients of renal diseases from three major hospitals of Peshawar. Brown method was used to obtain initial model, then backward elimination logistic regression analysis was performed to find the significant variables (risk factors). The response variable (ESRD) in this study is binary; therefore, logistic regression analysis is used to identify the significant variables. A Statistical Package GLIM and SPSS were used for fitting the model and for finding the significant variables. RESULTS: The backward elimination procedure selects predictor variables diabetic, hypertension, glomerulonephritis and heredity, for males. Thus, these variables are the main causes of ESRD. For females, the predictor variables selected are hypertension & (Diabetic*Hypertension), which means that hypertension and hypertensive diabetic are significant causes of ESRD. CONCLUSION: Our main conclusion from this analysis is that diabetic, hypertension and glomerulonephritis are the significant risk factors of ESRD.