BIOS 9131 – Advanced Statistical Theory for Biostatistics I

This course provides an advanced study of theoretical statistics. Topics include: an introduction probability and sample space, conditional probability and Bayes Theorem, probability distribution of a random variable, discrete and continuous random variables, functions of random variables, moments and moment generating functions, order statistics and their distributions, discrete distributions, continuous distributions, bivariate and multivariate normal distribution, modes of convergence, limiting moment generating functions, and the central limit theorems. 3 hour

BIOS 9130—Research Seminar in Biostatistics

This course is designed to provide the student with the current best practices in biostatistical consulting. Topics include: Identifying and constructing appropriate questions to ask clients regarding their consultation request, an overview of appropriate statistical methods and SAS software procedures to use for specific study designs and statistical analysis of collected data, directing a consultation appointment without faculty lead, conducting exploratory data analyses, conducting effective analyses based on appropriate statistical methods, conducting needed simulation (including Monte Carlo methods and Bootstrap methods) and providing oral and written communication of statistical findings. 3 credit house

Daily Walking and Life Expectancy of Elderly People in the Iowa 65+ Rural Health Study

The purpose of this paper is to investigate the hypothesis that outdoor daily walking, as an exercise, has an effect on the rate of mortality among those elderly people in the Iowa 65+ Rural Health Study (RHS). RHS is a prospective longitudinal cohort study of 8 years follow-up from 1981 to 1989. It consists of a random sample of 3,673 individuals (1,420 men and 2,253 women) aged 65 or older living in Washington and Iowa counties of the State of Iowa. Our analysis was conducted only on those non-institutional individuals who could without any help walk across a small room; this reduced the total number of individuals in the study to 2,717. Moreover, a total of 923 individuals died during the period of the study. The life histories of those individuals were obtained and divided into two cohorts; one containing 1,134 who exercise daily by walking and the other containing 1,583 who do not exercise daily by walking. The interviewers asked participants about 17 medical conditions, from which 13 are included in our study. We found that daily walking exercise is related inversely to total mortality before and after adjusting for the other factors in particular for age group and health conditions. We observed that hazard ratio (HR) of death was the highest among those individuals having a history of cancer (HR = 2.971) and history of stroke (HR = 2.127). However, individuals with a history of stroke in the “daily walking group” have HR = 0.856 and their risk of death were reduced by 81% compared to those in no “daily walking group.

Double Median Ranked Set Sample: Comparing To Other Double Ranked Samples For Mean And Ratio Estimators

Double median ranked set sample (DMRSS) and its properties for estimating the population mean, when the underlying distribution is assumed to be symmetric about its mean, are introduced. Also, the performance of DMRSS with respect to other ranked set samples and double ranked set samples, for estimating the population mean and ratio, is considered. Real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The analysis and simulation indicate that using DMRSS for estimating the population mean is more efficient than using the other ranked samples and double ranked samples schemes except in case of uniform distribution. Also, using double sampling schemes substantially increase the relative efficiency of ratio estimators relative to their counterpart schemes of one stage samples. Moreover, DMRSS is superior to other double sampling schemes for ratio estimation

A Test of Symmetry Based on the Kernel Kullback-Leibler Information with Application to Base Deficit Data

The assumption of the symmetry of the underlying distribution is important to many statistical inference and modeling procedures. This paper provides a test of symmetry using kernel density estimation and the Kullback-Leibler information. Based on simulation studies, the new test procedure outperforms other tests of symmetry found in the literature, including the Runs Test of Symmetry. We illustrate our new procedure using real data

A More Efficient Nonparametric Test of Symmetry Based on Overlapping Coefficient

In this paper we provide a more efficient nonparametric test of symmetry based on the empirical overlap coefficient using kernel density estimation applied to an extreme order statistics, namely extreme ranked set sampling. Our simulation investigation reveals that our proposed test of symmetry is at least as powerful as currently available tests of symmetry. Intensive simulation is conducted to examine the power of the proposed test. An illustration is provided using cardiac output and body weight of neonates in a neonatal intensive care unit

Inference on Overlapping Coefficients in Two Exponential Populations

Three measures of overlap, namely Matusita’s measureρ , Morisita’s measure λ and Weitzman’s measure Δ are investigated in this article for two exponential populations with different means. It is well that the estimators of those measures of overlap are biased. The bias is of these estimators depends on the unknown overlap parameters. There are no closed-form, exact formulas, for those estimators variances or their exact sampling distributions. Monte Carlo evaluations are used to study the bias and precision of the proposed overlap measures. Bootstrap method and Taylor series approximation are used to construct confidence intervals for the overlap measures

Estimation Using Bivariate Extreme Ranked Set Sampling With Application To The Bivariate Normal Distribution

In this article, the procedure of bivariate extreme ranked set sampling (BVERSS) is introduced and investigated as a procedure of obtaining more accurate samples for estimating the parameters of bivariate populations. This procedure takes its strength from the advantages of bivariate ranked set sampling (BVRSS) over the usual ranked set sampling in dealing with two characteristics simultaneously, and the advantages of extreme ranked set sampling (ERSS) over usual RSS in reducing the ranking errors and hence in being more applicable. The BVERSS procedure will be applied to the case of the parameters of the bivariate normal distributions. Illustration using real data is also provided

On Matched Pairs Sign Test Using Bivariate Ranked Set Sampling: An Application to Environmental Issues

The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived. The Pitman asymptotic relative efficiency is used to compare the asymptotic performance of the matched pairs sign test using BVRSS versus using BVSRS. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using BVRSS for the matched pairs sign test is substantially more efficient than using BVSRS. Illustration using palm trees data from sultanate of Oman is provided. Key words: Bootstrap method, bivariate ranked set sample, power of the test, P-value of the test, Pitman\u27s relative efficiency, sign test

Correction of Verication Bias using Log-Linear Models for a Single Binaryscale Diagnostic Tests

In diagnostic medicine, the test that determines the true disease status without an error is referred to as the gold standard. Even when a gold standard exists, it is extremely difficult to verify each patient due to the issues of costeffectiveness and invasive nature of the procedures. In practice some of the patients with test results are not selected for verification of the disease status which results in verification bias for diagnostic tests. The ability of the diagnostic test to correctly identify the patients with and without the disease can be evaluated by measures such as sensitivity, specificity and predictive values. However, these measures can give biased estimates if we only consider the patients with test results who also underwent the gold standard procedure. The emphasis of this paper is to apply the log-linear model approach to compute the maximum likelihood estimates for sensitivity, specificity and predictive values. We also compare the estimates with Zhou’s results and apply this approach to analyze Hepatic Scintigraph data under the assumption of ignorable as well as non-ignorable missing data mechanisms. We demonstrated the efficiency of the estimators by using simulation studies