Maximum likelihood estimate, Randomizing device, Randomized response technique, Sensitive questions, Warner’s model,

We propose a new non-randomized model for assessing the association of two sensitive questions with binary outcomes. Under the new model, respondents only need to answer a non-sensitive question instead of the original two sensitive questions. As a result, it can protect a respondent's privacy, avoid the usage of any randomizing device, and be applied to both the face-to-face interview and mail questionnaire. We derive the constrained maximum likelihood estimates of the cell probabilities and the odds ratio for two binary variables associated with the sensitive questions via the EM algorithm. The corresponding standard error estimates are then obtained by bootstrap approach. A likelihood ratio test and a chi-squared test are developed for testing association between the two binary variables. We discuss the loss of information due to the introduction of the non-sensitive question, and the design of the co-operative parameters. Simulations are performed to evaluate the empirical type I error rates and powers for the two tests. In addition, a simulation is conducted to study the relationship between the probability of obtaining valid estimates and the sample size for any given cell probability vector. A real data set from an AIDS study is used to illustrate the proposed methodologies.

Abstract-Blind direction of arrival (DOA) estimation algorithms of coherent sources using multi-invariance property is presented in this paper. ESPRIT-like algorithm in [23] can estimate DOA of coherent signal, but its performance is without satisfaction. We reconstruct the received signal to form data model with multi-invariance property, and then multi-invariance ESPRIT and multi-invariance MUSIC algorithms for coherent DOA estimation are proposed in this paper. Our proposed algorithms can resolve the DOAs of coherent signals. They have much better DOA estimation performance than ESPRITlike algorithm. Meanwhile they identify more DOAs than ESPRIT-like algorithm. The simulation results demonstrate their validity.

No abstract

Clinical trials usually involve efficient and ethical objectives. Different adaptive designs have been proposed to satisfy these needs. We combine interim analysis, the sequential estimation-adjusted urn model (SEU), and sample size re-estimation (SSR) in one clinical trial. We show that the asymptotic distribution, under the null hypothesis, of the proposed sequential statistic follows Brownian motion by simultaneously addressing the three sequential procedures (allocation of patients, urn composition, and sequential parameter estimators) and the sequential statistics with revised information time due to SSR. Therefore, to control the type I error rate, traditional critical values for sequential monitoring based on Brownian motion can be used for the proposed procedure. Numerical studies with three types of urn models demonstrate that our proposed approach can control the type I error rate well and also achieve efficient and ethical objectives.

No abstract

In addition to scientific questions, clinical trialists often explore or require other design features, such as increasing the power while controlling the type I error rate, minimizing unnecessary exposure to inferior treatments, and comparing multiple treatments in one clinical trial. We propose implementing adaptive seamless design (ASD) with response adaptive randomization (RAR) to satisfy various clinical trials’ design objectives. However, the combination of ASD and RAR poses a challenge in controlling the type I error rate. In this paper, we investigated how to utilize the advantages of the two adaptive methods and control the type I error rate. We offered the theoretical foundation for this procedure. Numerical studies demonstrated that our methods could achieve efficient and ethical objectives while controlling the type I error rate.