Query: BAYESIAN RANDOMIZED RESPONSE 

title: Bayesian randomized response technique with multiple sensitive attributes: The case of information systems resource misuse
abstract: The randomized response technique (RRT) is a classical and effective method used to mitigate the distortion arising from dishonest answers. The traditional RRT usually focuses on the case of a single sensitive attribute, and discussion of the case of multiple sensitive attributes is limited. Here, we study a business case to identify some individual and organizational determinants driving information systems (IS) resource misuse in the workplace. People who actually engage in IS resource misuse are probably not willing to provide honest answers, given the sensitivity of the topic. Yet, to develop the causal relationship between IS resource misuse and its determinants, a version of the RRT for multivariate analysis is required. To implement the RRT with multiple sensitive attributes, we propose a Bayesian approach for estimating covariance matrices with incomplete information (resulting from the randomization procedure in the RRT case) The proposed approach (i) accommodates the positive definite condition and other intrinsic parameter constraints in the posterior to improve statistical precision, (ii) incorporates Bayesian shrinkage estimation for covariance matrices despite incomplete information, and (iii) adopts a quasi likelihood method to achieve Bayesian semiparametric inference for enhancing flexibility. We show the effectiveness of the proposed method in a simulation study. We also apply the Bayesian RRT method and structural equation modeling to identify the causal relationship between IS resource misuse and its determinants.

title: Bayesian Randomized Response Technique
abstract: When sensitive attributes are investigated, Randomized Response Technique (RRT) is a popular approach to reduce the bias arisen from untruthful response. Nonetheless, traditional RRT has weakness that it mainly focuses on estimating the moments of univariate random variables but not dependence among multiple random variables. This paper is to introduce a new method to estimate the covariance matrix of random vectors under the framework of RRT. Modified Cholesky decomposition is applied to reparameterize the covariance matrix so that the parameters of the covariance matrix can be expressed as regression on a row by row basis. This simplifies the structure of the matrix and ensures the positive definiteness of the estimator. To keep inference nonparametric, moment equations of the randomized realizations are adopted as the quasi likelihood. Moreover, Bayesian lasso is applied to impose shrinkage effect in estimation. This helps reduce estimation error when the covariance matrix is sparse. An easy to implement Gibbs sampling scheme is proposed for the inference. A simulation study is conducted to evaluate the accuracy of estimation. An empirical study related to software piracy behavior is conducted to compare the difference of the estimates under randomized and non randomized settings.

title: Bayesian Randomized Response as a Class Project
abstract: This article describes multiple learning opportunities stemming from a classroom project about psychological therapy analyzed through the Bayesian framework. Because the dataset is rather small, students focus naturally on prior elicitation, issues of identifiability and sensitivity analysis. In addition, because there is not a familiar closed form solution, students are forced to apply relevant simulation techniques, including rejection sampling, Metropolis Hastings algorithm, data augmentation, simulation of Bayes factors, and other model selection criteria. Comparison with surprising frequentist results prompts a reflection of the pros and cons of either approach. Key features for project success (writing skills, feedback) are discussed.

title: Anti Thrombotic Therapy to Ameliorate Complications of COVID 19 (ATTACC) Study design and methodology for an international, adaptive Bayesian randomized controlled trial
abstract: Mortality from COVID 19 is high among hospitalized patients and effective therapeutics are lacking. Hypercoagulability, thrombosis and hyperinflammation occur in COVID 19 and may contribute to severe complications. Therapeutic anticoagulation may improve clinical outcomes through anti thrombotic, anti inflammatory and anti viral mechanisms. Our primary objective is to evaluate whether therapeutic dose anticoagulation with low molecular weight heparin or unfractionated heparin prevents mechanical ventilation and/or death in patients hospitalized with COVID 19 compared to usual care.  An international, open label, adaptive randomized controlled trial. Using a Bayesian framework, the trial will declare results as soon as pre specified posterior probabilities for superiority, futility, or harm are reached. The trial uses response adaptive randomization to maximize the probability that patients will receive the more beneficial treatment approach, as treatment effect information accumulates within the trial. By leveraging a common data safety monitoring board and pooling data with a second similar international Bayesian adaptive trial (REMAP COVID anticoagulation domain) treatment efficacy and safety will be evaluated as efficiently as possible. The primary outcome is an ordinal endpoint with three possible outcomes based on the worst status of each patient through day 30: no requirement for invasive mechanical ventilation, invasive mechanical ventilation or death.  Using an adaptive trial design, the Anti Thrombotic Therapy To Ameliorate Complications of COVID 19 trial will establish whether therapeutic anticoagulation can reduce mortality and/or avoid the need for mechanical ventilation in patients hospitalized with COVID 19. Leveraging existing networks to recruit sites will increase enrollment and mitigate enrollment risk in sites with declining COVID 19 cases.

title: On Bayesian Analysis of a General Class of Randomized Response Models In Social Surveys about Stigmatized Traits
abstract: While conducting a social survey on stigmatized/sensitive traits, obtaining efficient (truthful) data is an intricate issue and estimates are generally biased in such surveys. To obtain trustworthy data and to reduce false response bias, a technique, known as randomized response technique, is now being used in many surveys. In this study, we performed a Bayesian analysis of a general class of randomized response models. Suitable simple Beta prior and mixture of Beta priors are used in a common prior structure to obtain the Bayes estimates for the proportion of a stigmatized/sensitive attributes in the population of interest. We also extended our proposal to stratified random sampling. The Bayes and the maximum likelihood estimators are compared. For further understanding of variability, we have also compared the prior and posterior distributions for different values of the design constants through graphs and credible intervals. The condition to develop a new randomized response model is also discussed.

title: Bayesian Analysis of Kim and Warde Randomized Response Technique Using Alternative Priors
abstract: In this paper, we developed the Bayesian estimators of the population proportion of a stigmatized attribute using Kumaraswamy and Generalised Beta prior distributions when data were obtained through the Randomized Response Technique (RRT) proposed by Kim and Warde (15) We validated our newly developed Bayesian estimators for a wide range of the designed values of the population proportion at varying sample sizes. It was observed that our newly developed Bayesian estimators performed significantly better than the Bayesian estimator developed by Hussain and Shabbir (12) for relatively small as well as moderate sample sizes. However, the reverse was the case for very large sample sizes.

title: BAYESIAN ESTIMATION OF POPULATION PROPORTION IN KIM AND WARDE MIXED RANDOMIZED RESPONSE TECHNIQUE
abstract: In this study, we have developed the Bayesian estimator of the population proportion of a sensitive characteristic when data are obtained through the Randomized Response Technique (RRT) proposed by Kim and Warde (2005) Superiority of the Bayesian estimators is established for a wide range of the values of the population proportion using simple Beta prior information. It is observed that Bayesian estimators are better than the usual Maximum Likelihood Estimator (MLE) for small as well as moderate samples. The Proposed estimator is also compared with the Warner (1965) Kim and warde (2005) and Kim et al. (2006) estimators.

title: Bayesian Analysis of Randomized Response Sum Score Variables
abstract: The randomized response (RR) technique is an effective survey method when collecting sensitive information. In this technique, a probability mechanism using randomization devices is commonly involved in answering to sensitive questions. In order to evaluate the survey at the most accurate extend, self protection (SP) is introduced to describe the responses by participants who give the evasive answer without taking the result of the randomization device into account. In this study, we propose a Bayesian approach to modeling RR sum score variables under SP assumption. RR data from a Dutch survey on non compliance with social security regulation in 2004 is used to demonstrate the proposed models.

title: Bayesian estimation of proportion and sensitivity level in randomized response procedures
abstract: A Bayesian approach to the joint estimation of population proportion and sensitivity level of a stigmatizing attribute is proposed by adopting a two stage randomized response procedure. In the first stage the direct question method is carried out for each respondent, while in the second stage the randomization is exclusively carried out for those individuals declaring their membership in the non sensitive group. The randomization is implemented on the basis of Franklin's procedure. The proposed Bayesian method avoids the drawbacks usually connected with the use of maximum likelihood or moment estimation.

title: Bayesian Estimation Using Warner's Randomized Response Model through Simple and Mixture Prior Distributions
abstract: Bayesian estimation of population proportion of a sensitive characteristic is proposed by adopting a simple beta distribution and a mixture of Beta distributions as quantification of prior information using simple random sampling with replacement. In the sequel application of the stratified random sampling is also studied in Bayesian scenario. It is assumed that data are collected through Warner (1965) randomized response technique. To study the performance of Bayesian estimators we have used Mean Squared Error (MSE) and/or Relative Efficiency (RE) as performance criterion. Further, comparison of the suggested estimator is made with Kim et al. (2006) stratified estimator and usual maximum likelihood estimator in case of stratified random sampling. It is observed that unlike the moment and maximum likelihood methods, proposed Bayesian estimation method is free of the problems of having an estimate of population proportion outside the interval (0, 1) and large variance when the sample proportion of yes responses is very low or very high.