An improved randomized response model: estimation of mean

In this paper, we suggest a new randomized response model useful for collecting information on quantitative sensitive variables such as drug use and income. The resultant estimator has been found to be better than the usual additive randomized response model. An interesting feature of the proposed model is that it is free from the known parameters of the scrambling variable unlike the additive model due to Himmelfarb and Edgell [S. Himmelfarb and S.E. Edgell, Additive constant model: a randomized response technique for eliminating evasiveness to quantitative response questions, Psychol. Bull. 87(1980), 525–530]. Relative efficiency of the proposed model has also been studied with the corresponding competitors. At the end, an application of the proposed model has been discussed.     

Scalable statistical inference for averaged implicit stochastic gradient descent

Stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates in applications involving large‐scale data or streaming data. As an alternative version, averaged implicit SGD (AI‐SGD) has been shown to be more stable and more efficient. Although the asymptotic properties of AI‐SGD have been well established, statistical inferences based on it such as interval estimation remain unexplored. The bootstrap method is not computationally feasible because it requires to repeatedly resample from the entire data set. In addition, the plug‐in method is not applicable when there is no explicit covariance matrix formula. In this paper, we propose a scalable statistical inference procedure, which can be used for conducting inferences based on the AI‐SGD estimator. The proposed procedure updates the AI‐SGD estimate as well as many randomly perturbed AI‐SGD estimates, upon the arrival of each observation. We derive some large‐sample theoretical properties of the proposed procedure and examine its performance via simulation studies.     

A pooled Bayes test of independence for sparse contingency tables from small areas

We study the association between bone mineral density (BMD) and body mass index (BMI) when contingency tables are constructed from the several U.S. counties, where BMD has three levels (normal, osteopenia and osteoporosis) and BMI has four levels (underweight, normal, overweight and obese). We use the Bayes factor (posterior odds divided by prior odds or equivalently the ratio of the marginal likelihoods) to construct the new test. Like the chi-squared test and Fisher's exact test, we have a direct Bayes test which is a standard test using data from each county. In our main contribution, for each county techniques of small area estimation are used to borrow strength across counties and a pooled test of independence of BMD and BMI is obtained using a hierarchical Bayesian model. Our pooled Bayes test is computed by performing a Monte Carlo integration using random samples rather than Gibbs samples. We have seen important differences among the pooled Bayes test, direct Bayes test and the Cressie-Read test that allows for some degree of sparseness, when the degree of evidence against independence is studied. As expected, we also found that the direct Bayes test is sensitive to the prior specifications but the pooled Bayes test is not so sensitive. Moreover, the pooled Bayes test has competitive power properties, and it is superior when the cell counts are small to moderate.     

Improved estimation under random censorship

In this article we propose a variant of the Kaplan-Meier estimator which aims at reducing the bias by adding a bootstrap based correction term to the pertaining cumulative hazard function. For the mean lifetime it is demonstrated in a simulation study that the new estimator also has a smaller variance.     

Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses

It is known that collinearity among the explanatory variables in generalized linear models (GLMs) inflates the variance of maximum likelihood estimators. To overcome multicollinearity in GLMs, ordinary ridge estimator and restricted estimator were proposed. In this study, a restricted ridge estimator is introduced by unifying the ordinary ridge estimator and the restricted estimator in GLMs and its mean squared error (MSE) properties are discussed. The MSE comparisons are done in the context of first-order approximated estimators. The results are illustrated by a numerical example and two simulation studies are conducted with Poisson and binomial responses.     

Tests for noninferiority trials with binomial endpoints: A guide to modern and quasi‐exact methods for biomedical researchers

Applied statisticians and pharmaceutical researchers are frequently involved in the design and analysis of clinical trials where at least one of the outcomes is binary. Treatments are judged by the probability of a positive binary response. A typical example is the noninferiority trial, where it is tested whether a new experimental treatment is practically not inferior to an active comparator with a prespecified margin δ. Except for the special case of δ = 0, no exact conditional test is available although approximate conditional methods (also called second‐order methods) can be applied. However, in some situations, the approximation can be poor and the logical argument for approximate conditioning is not compelling. The alternative is to consider an unconditional approach. Standard methods like the pooled z‐test are already unconditional although approximate. In this article, we review and illustrate unconditional methods with a heavy emphasis on modern methods that can deliver exact, or near exact, results. For noninferiority trials based on either rate difference or rate ratio, our recommendation is to use the so‐called E‐procedure, based on either the score or likelihood ratio statistic. This test is effectively exact, computationally efficient, and respects monotonicity constraints in practice. We support our assertions with a numerical study, and we illustrate the concepts developed in theory with a clinical example in pulmonary oncology; R code to conduct all these analyses is available from the authors.     

中国的通货膨胀及其不确定性

采用1990年1月以来居民消费价格指数(CPI)的月度数据,运用随机域回归模型、系列随机域的非线性检验方法和贝叶斯估计方法,对中国通货膨胀率与通货膨胀不确定性的关系进行了实证分析。研究发现:通货膨胀率与通货膨胀之间具有双向关系。通货膨胀率引起了通货膨胀不确定性,两者呈现U型关系;较高的通货膨胀不确定性引起通货膨胀率先升后降,呈现倒U曲线关系。     

Cystatin C as a predictor of mortality in elderly patients with chronic kidney disease

Background: The prevalence of chronic kidney disease (CKD) in the elderly is high. Serum cystatin C is an accurate marker of kidney function and it also has prognostic utility in CKD patients. The aim of our study was to determine the prediction of serum cystatin C and other markers of kidney function on long-term survival in elderly CKD patients.

Methods: Fifty eight adult Caucasian patients, older than 65 years, without known malignancy, thyroid disease and/or not on steroid therapy were enrolled in the study. In each patient, ⁵¹CrEDTA clearance, serum creatinine, serum cystatin C, and estimated glomerular filtration rate using different equations were determined on the same day and patients were then followed for 11 years or until their death.

Results: The means are as follows: ⁵¹CrEDTA clearance 53.3?±?17.4?ml/min/1.73?m², serum creatinine 1.62?±?0.5?mg/dl, serum cystatin C 1.79?±?0.5?mg/l, Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) creatinine equation 40.1?±?14?ml/min/1.73?m², Berlin Initiative Study 2 (BIS2) equation 38.9?±?10.7?ml/min/1.73?m², full age spectrum (FAS) creatinine equation 43.8?±?13.8?ml/min/1.73?m², FAS cystatin C equation 40.1?±?11.7?ml/min/1.73?m². In the follow up period, 47 (81%) patients died. Cox regression analysis showed different hazard ratios (HRs) for death: for ⁵¹CrEDTA clearance HR 1.022 (95% CI 1.004–1.042; p?=?.015), serum creatinine HR 1.013 (95% CI 1.006–1.019; p?=?.001), serum cystatin C HR 2.028 (95% CI 1.267–3.241; p?=?.003), CKD-EPI creatinine equation HR 1.048 (95% CI 1.019–1.076; p?=?.001), BIS2 equation HR 1.055 (95% CI 1.021–1.088; p?=?.001), FAS creatinine equation HR 1.046 (95% CI 1.017–1.074; p?=?.001), FAS cystatin C equation HR 1.039 (95% CI 1.010–1.071; p?=?.009).

Conclusions: Our results showed the highest HR for serum cystatin C among kidney function markers for prediction of outcome in elderly CKD patients.     

A new useful four-parameter extension of the Gumbel distribution: Properties,regression model and applications using the GAMLSS framework

In this paper we introduce a flexible extension of the Gumbel distribution called the odd log-logistic exponentiated Gumbel distribution. The new model was implemented in GAMLSS package of R software and a brief tutorial on how to use this package is presented throughout the paper. We provide a comprehensive treatment of its general mathematical properties. Further, we propose a new extended regression model considering four regression structures. We discuss estimation methods based on censored and uncensored data. Two simulation studies are presented and four real data sets are applied to illustrating the usefulness of the new model.     

Weibull inference using trimmed samples and prior information

Trimmed samples are commonly used in several branches of statistical methodology, especially when the presence of contaminated data is suspected. Assuming that certain proportions of the smallest and largest observations from a Weibull sample are unknown or have been eliminated, a Bayesian approach to point and interval estimation of the scale parameter, as well as hypothesis testing and prediction, is presented. In many cases, the use of substantial prior information can significantly increase the quality of the inferences and reduce the amount of testing required. Some Bayes estimators and predictors are derived in closed-forms. Highest posterior density estimators and credibility intervals can be computed using iterative methods. Bayes rules for testing one- and two-sided hypotheses are also provided. An illustrative numerical example is included.