Man-Lai Tang

Testing the Ratio of Two Poisson Rates

In this paper we compare the properties of four different general approaches for testing the ratio of two Poisson rates. Asymptotically normal tests, tests based on approximate p -values, exact conditional tests, and a likelihood ratio test are considered. The properties and power performance of these tests are studied by a Monte Carlo simulation experiment. Sample size calculation formulae are given for each of the test procedures and their validities are studied. Some recommendations favoring the likelihood ratio and certain asymptotic tests are based on these simulation results. Finally, all of the test procedures are illustrated with two real life medical examples.

Sample surveys with sensitive questions: a nonrandomized response approach

Since the Warners randomized response (RR) model to solicit sensitive information was proposed in 1965, it has been used and extended in a broad range of surveys involving sensitive questions. However, it is limited, for example, by a lack of reproducibility and trust from the interviewees as well as higher cost due to the use of randomizing devices. Recent developments of the alternative non-randomized response (NRR) approach have shown the promise to alleviate or eliminate such limitations. However, the efficiency and feasibility of the NRR models have not been adequately studied. This article introduces briefly the NRR approach, proposes several new NRR models, compares the efficiency of the NRR and RR models and studies the feasibility of the NRR models. In addition, we propose the concept of the degree of privacy protection between the NRR model and the Warner model to reflect the extent the privacy is protected. These studies show that not only the NRR approach is free of the limitations of the randomized approach but also the NRR model actually increases the relative efficiency and the degree of privacy protection. Thus, the non-randomized response approach offers an attractive alternative to the randomized response approach.

Variable selection in high-dimensional partially linear additive models for composite quantile regression

A new estimation procedure based on the composite quantile regression is proposed for the semiparametric additive partial linear models, of which the nonparametric components are approximated by polynomial splines. The proposed estimation method can simultaneously estimate both the parametric regression coefficients and nonparametric components without any specification of the error distributions. The proposed estimation method is empirically shown to be much more efficient than the popular least-squares-based estimation method for non-normal random errors, especially for Cauchy error, and almost as efficient for normal random errors. To achieve sparsity in high-dimensional and sparse additive partial linear models, of which the number of linear covariates is much larger than the sample size but that of significant covariates is small relative to the sample size, a variable selection procedure based on adaptive Lasso is proposed to conduct estimation and variable selection simultaneously. The procedure is shown to possess the oracle property, and is much superior to the adaptive Lasso penalized least-squares-based method regardless of the random error distributions. In particular, two kinds of weights in the penalty are considered, namely the composite quantile regression estimates and Lasso penalized composite quantile regression estimates. Both types of weights perform very well with the latter performing especially well in terms of precisely selecting significant variables. The simulation results are consistent with the theoretical properties. A real data example is used to illustrate the application of the proposed methods.

A comparative study of tests for the difference of two Poisson means

We investigate different test procedures for testing the difference of two Poisson means. Asymptotic tests, tests based on an approximate p-value method, and a likelihood ratio test are considered. Size and power performance of these tests are studied by means of Monte Carlo simulation under different settings. If one wants to control the actual significance level at or below the pre-chosen nominal level, tests based on approximate p-value method are the desirable candidates. If one allows tests whose actual significance levels may occasionally exceed the pre-chosen nominal level by an acceptable margin, asymptotic tests based on an unbiased estimate and constrained maximum likelihood estimate are reasonable alternatives. We illustrate these testing procedures with a breast cancer example.

Predictive analyses for nonhomogeneous Poisson processes with power law using Bayesian approach

Nonhomogeneous Poisson process (NHPP) also known as Weibull process with power law, has been widely used in modeling hardware reliability growth and detecting software failures. Although statistical inferences on the Weibull process have been studied extensively by various authors, relevant discussions on predictive analysis are scattered in the literature. It is well known that the predictive analysis is very useful for determining when to terminate the development testing process. This paper presents some results about predictive analyses for Weibull processes. Motivated by the demand on developing complex high-cost and high-reliability systems (e.g., weapon systems, aircraft generators, jet engines), we address several issues in single-sample and two-sample prediction associated closely with development testing program. Bayesian approaches based on noninformative prior are adopted to develop explicit solutions to these problems. We will apply our methodologies to two real examples from a radar system development and an electronics system development.

Image Segmentation Using Fuzzy Region Competition and Spatial/Frequency Information

This paper presents a multiphase fuzzy region competition model that takes into account spatial and frequency information for image segmentation. In the proposed energy functional, each region is represented by a fuzzy membership function and a data fidelity term that measures the conformity of spatial and frequency data within each region to (generalized) Gaussian densities whose parameters are determined jointly with the segmentation process. Compared with the classical region competition model, our approach gives soft segmentation results via the fuzzy membership functions, and moreover, the use of frequency data provides additional region information that can improve the overall segmentation result. To efficiently solve the minimization of the energy functional, we adopt an alternate minimization procedure and make use of Chambolles fast duality projection algorithm. We apply the proposed method to synthetic and natural textures as well as real-world natural images. Experimental results show that our proposed method has very promising segmentation performance compared with the current state-of-the-art approaches.

Statistical inference and prediction for the Weibull process with incomplete observations

In this article, statistical inference and prediction analyses for the Weibull process with incomplete observations via classical approach are studied. Specifically, observations in the early developmental phase of a testing program cannot be observed. We derive the closed-form expressions for the maximum likelihood estimates of the parameters in both the failure- and time-truncated Weibull processes. Confidence interval and hypothesis testing for the parameters of interest are considered. In addition, predictive inferences on future failures and the goodness-of-fit test of the model are developed. Two real examples from an engine system development study and a Boeing air-conditioning system development study are presented to illustrate the proposed methodologies.

Confidence intervals for a difference between proportions based on paired data

We construct several explicit asymptotic two-sided confidence intervals (CIs) for the difference between two correlated proportions using the method of variance of estimates recovery (MOVER). The basic idea is to recover variance estimates required for the proportion difference from the confidence limits for single proportions. The CI estimators for a single proportion, which are incorporated with the MOVER, include the Agresti-Coull, the Wilson, and the Jeffreys CIs. Our simulation results show that the MOVER-type CIs based on the continuity corrected Phi coefficient and the Tango score CI perform satisfactory in small sample designs and spare data structures. We illustrate the proposed CIs with several real examples.

Testing the equality of proportions for correlated otolaryngologic data

In otolaryngologic (or ophthalmologic) studies, each subject usually contributes information for each of two ears (or eyes), and the values from the two ears (or eyes) are generally highly correlated. Statistical procedures that fail to take into account the correlation between responses from two ears could lead to incorrect results. On the other hand, asymptotic procedures that overlook small sample designs, sparse data structures, or the discrete nature of data could yield unacceptably high type I error rates even when the intraclass correlation is taken into consideration. In this article, we investigate eight procedures for testing the equality of proportions in such correlated data. These test procedures will be implemented via the asymptotic and approximate unconditional methods. Our empirical results show that tests based on the approximate unconditional method usually produce empirical type I error rates closer to the pre-chosen nominal level than their asymptotic tests. Amongst these, the approximate unconditional score test performs satisfactorily in general situations and is hence recommended. A data set from an otolaryngologic study is used to illustrate our proposed methods.

Tests of Noninferiority via Rate Difference for Three-Arm Clinical Trials with Placebo

Abstract In assessing a noninferiority trial, the investigator intends to show efficacy by demonstrating that a new experimental drug/treatment is not worse than a known active control/reference by a small predefined margin. If it is ethically justifiable, it may be advisable to include an additional placebo group for internal validation purpose. This constitutes the well-known three-arm clinical trial with placebo. In this paper, we study two asymptotic statistical methods for testing of noninferiority in three-arm clinical trials with placebo for binary outcomes based on rate difference. They are sample-based estimation method and restricted maximum likelihood estimation method, respectively. We investigate the performance of the proposed test procedures under different sample size allocation settings via a simulation study. Both methods perform satisfactorily under moderate to large sample settings. However, the restricted maximum likelihood estimation method usually possesses slightly smaller actual type I error rates, which are relatively close to the prespecified nominal level, while the sample-based method can be expressed in a simple closed-form format. Real examples from a pharmacological study of patients with functional dyspepsia and a placebo- controlled trail of subjects with acute migraine are used to demonstrate our methodologies.