Haresh Rochani

On kernel density estimation based on different stratified sampling with optimal allocation

ABSTRACT Kernel density estimation is probably the most widely used non parametric statistical method for estimating probability densities. In this paper, we investigate the performance of kernel density estimator based on stratified simple and ranked set sampling. Some asymptotic properties of kernel estimator are established under both sampling schemes. Simulation studies are designed to examine the performance of the proposed estimators under varying distributional assumptions. These findings are also illustrated with the help of a dataset on bilirubin levels in babies in a neonatal intensive care unit.

A Simpler Approach for Mediation Analysis for Dichotomous Mediators in Logistic Regression

ABSTRACT Mediation is a hypothesized causal chain among three variables. Mediation analysis for continuous response variables is well developed in the literature, and it can be shown that the indirect effect is equal to the total effect minus the direct effect. However, mediation analysis for categorical responses is still not fully developed. The purpose of this article is to propose a simpler method of analysing the mediation effect among three variables when the dependent and mediator variables are both dichotomous. We propose using the latent variable technique which in turn will adjust for the necessary condition that indirect effect is equal to the total effect minus the direct effect. An intensive simulation study is conducted to compare the proposed method with other methods in the literature. Our theoretical derivation and simulation study show that the proposed approach is simpler to use and at least as good as other approaches provided in the literature. We illustrate our approach to test for the potential mediators on the relationship between depression and obesity among children and adolescents compared to the method in Winship and Mare using National children health survey data 2011–2012.

Notes on the overlap measure as an alternative to the Youden index: How are they related?

The receiver operating characteristic (ROC) curve is frequently used to evaluate and compare diagnostic tests. As one of the ROC summary indices, the Youden index measures the effectiveness of a diagnostic marker and enables the selection of an optimal threshold value (cut-off point) for the marker. Recently, the overlap coefficient, which captures the similarity between 2 distributions directly, has been considered as an alternative index for determining the diagnostic performance of markers. In this case, a larger overlap indicates worse diagnostic accuracy, and vice versa. This paper provides a graphical demonstration and mathematical derivation of the relationship between the Youden index and the overlap coefficient and states their advantages over the most popular diagnostic measure, the area under the ROC curve. Furthermore, we outline the differences between the Youden index and overlap coefficient and identify situations in which the overlap coefficient outperforms the Youden index. Numerical examples and real data analysis are provided.

More efficient logistic analysis using moving extreme ranked set sampling

ABSTRACT Logistic regression is the most popular technique available for modeling dichotomous-dependent variables. It has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient logistic regression analysis based on moving extreme ranked set sampling (MERSSmin) scheme with ranking based on an easy-to-available auxiliary variable known to be associated with the variable of interest (response variable). The paper demonstrates that this approach will provide more powerful testing procedure as well as more efficient odds ratio and parameter estimation than using simple random sample (SRS). Theoretical derivation and simulation studies will be provided. Real data from 2011 Youth Risk Behavior Surveillance System (YRBSS) data are used to illustrate the procedures developed in this paper.

Reducing Sample Size Needed for Accelerated Failure Time Model Using More Efficient Sampling Methods

Survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Accelerated failure time (AFT) models provide a linear relationship between the log of the failure time and covariates that affect the expected time to failure by contracting or expanding the time scale. The AFT model has intensive application in the field of social, medical, behavioral, and public health sciences. In this article we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) or an Extreme Ranked Set Sampling (ERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This article demonstrates that these approaches provide a more powerful testing procedure, as well as a more efficient estimate of hazard ratio, than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural Health Study data are used to illustrate the methods developed in this article.

On quantiles estimation based on different stratified sampling with optimal allocation

ABSTRACT This work considers the problem of estimating a quantile function based on different stratified sampling mechanism. First, we develop an estimate for population quantiles based on stratified simple random sampling (SSRS) and extend the discussion for stratified ranked set sampling (SRSS). Furthermore, the asymptotic behavior of the proposed estimators are presented. In addition, we derive an analytical expression for the optimal allocation under both sampling schemes. Simulation studies are designed to examine the performance of the proposed estimators under varying distributional assumptions. The efficiency of the proposed estimates is further illustrated by analyzing a real data set from CHNS.

Increased Fisher's Information for Parameters of Association in Count Regression via Extreme Ranks

ABSTRACT The article details a sampling scheme which can lead to a reduction in sample size and cost in clinical and epidemiological studies of association between a count outcome and risk factor. We show that inference in two common generalized linear models for count data, Poisson and negative binomial regression, is improved by using a ranked auxiliary covariate, which guides the sampling procedure. This type of sampling has typically been used to improve inference on a population mean. The novelty of the current work is its extension to log-linear models and derivations showing that the sampling technique results in an increase in information as compared to simple random sampling. Specifically, we show that under the proposed sampling strategy the maximum likelihood estimate of the risk factor’s coefficient is improved through an increase in the Fisher’s information. A simulation study is performed to compare the mean squared error, bias, variance, and power of the sampling routine with simple random sampling under various data-generating scenarios. We also illustrate the merits of the sampling scheme on a real data set from a clinical setting of males with chronic obstructive pulmonary disease. Empirical results from the simulation study and data analysis coincide with the theoretical derivations, suggesting that a significant reduction in sample size, and hence study cost, can be realized while achieving the same precision as a simple random sample.

Markov Chain Monte-Carlo Methods for Missing Data Under Ignorability Assumptions

Missing observations are a common occurrence in public health, clinical studies and social science research. Consequences of discarding missing observations, sometimes called complete case analysis, are low statistical power and potentially biased estimates. Fully Bayesian methods using Markov Chain Monte-Carlo (MCMC) provide an alternative model-based solution to complete case analysis by treating missing values as unknown parameters. Fully Bayesian paradigms are naturally equipped to handle this situation by augmenting MCMC routines with additional layers and sampling from the full conditional distributions of the missing data, in the case of Gibbs sampling . Here we detail ideas behind the Bayesian treatment of missing data and conduct simulations to illustrate the methodology. We consider specifically Bayesian multivariate regression with missing responses and the missing covariate setting under an ignorability assumption. Applications to real datasets are provided.

Using Ranked Auxiliary Covariate as a More Efficient Sampling Design for ANCOVA Model: Analysis of a Psychological Intervention to Buttress Resilience

Drawing a sample can be costly or time consuming in some studies. However, it may be possible to rank the sampling units according to some baseline auxiliary covariates, which are easily obtainable, and/or cost efficient. Ranked set sampling (RSS) is a method to achieve this goal. In this paper, we propose a modified approach of the RSS method to allocate units into an experimental study that compares L groups. Computer simulation estimates the empirical nominal values and the empirical power values for the test procedure of comparing L different groups using modified RSS based on the regression approach in analysis of covariance (ANCOVA) models. A comparison to simple random sampling (SRS) is made to demonstrate efficiency. The results indicate that the required sample sizes for a given precision are smaller under RSS than under SRS. The modified RSS protocol was applied to an experimental study. The experimental study was designed to obtain a better understanding of the pathways by which positive experiences (i.e., goal completion) contribute to higher levels of happiness, well-being, and life satisfaction. The use of the RSS method resulted in a cost reduction associated with smaller sample size without losing the precision of the analysis.

Estimation of P(X > Y) When X and Y Are Dependent Random Variables Using Different Bivariate Sampling Schemes

The stress-strength models have been intensively investigated in the literature in regards of estimating the reliability θ = P (X > Y) using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimating θ when (X, Y) are dependent random variables with a bivariate underlying distribution. The empirical and kernel estimates of θ = P (X > Y), based on bivariate ranked set sampling (BVRSS) are considered, when (X,Y) are paired dependent continuous random variables. The estimators obtained are compared to their counterpart, bivariate simple random sampling (BVSRS), via the bias and mean square error (MSE). We demonstrate that the suggested estimators based on BVRSS are more efficient than those based on BVSRS. A simulation study is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.