Statistical Papers最新文献

There is often a presence of random change points (RCPs) with varying timing of hazard rate change among patients in survival analysis within oncology trials. This is in contrast to fixed change points in piecewise constant hazard models, where the timing of hazard rate change remains the same for all subjects. However, currently there is a lack of appropriate statistical methods to effectively tackle this particular issue. This article presents novel statistical methods that aim to characterize these complex survival models. These methods allow for the estimation of important features such as the probability of an event occurring and being censored, and the expected number of events within the clinical trial, prior to any specific time, and within specific time intervals. They also derive expected survival time and parametric expected survival and hazard functions for subjects with any finite number of RCPs. Simulation studies validate these methods and demonstrate their reliability and effectiveness. Real clinical data from an oncology trial is also used to apply these methods. The applications of these methods in oncology trials are extensive, including estimating hazard rates and rate parameters of RCPs, assessing treatment switching, delayed onset of immunotherapy, and subsequent anticancer therapies. They also have value in clinical trial planning, monitoring, and sample size adjustment. The expected parametric survival and hazard functions provide a thorough understanding of the behaviors and effects of RCPs in complex survival models.

Symmetrical global sensitivity analysis (SGSA) can aid practitioners in reducing the model complexity by identifying symmetries within the model. In this paper, we propose a nested symmetrical Latin hypercube design (NSLHD) for implementing SGSA in a sequential manner. By combining the strengths of the nested Latin hypercube design and symmetrical design, the proposed design allows for the implementation of SGSA without the need to pre-determine the sample size of the experiment. We develop a random sampling procedure and an efficient sequential optimization algorithm to construct flexible NSLHDs in terms of runs and factors. Sampling properties of the constructed designs are studied. Numerical examples are given to demonstrate the effectiveness of the NSLHD for designing sequential sensitivity analysis.

Comparison of variability or dispersion of two distributions is the major focus of this work. To this end, we consider a two sample testing problem for detecting dominance in dispersive order and develop a test based on U-statistic approach. We also explore a link between the two measures of variability, viz. dispersive order and Gini’s mean difference (GMD). We exploit methodologies based on jackknife empirical likelihood (JEL) and adjusted JEL in order to overcome certain practical difficulties. The performance of the proposed test is assessed by means of a simulation study. Finally, we apply our test in the context of several real life situations including medical studies and insurance data.

Negative binomial related distributions have been widely used in practice. The calculation of the corresponding Fisher information matrices involves the expectation of trigamma function values which can only be calculated numerically and approximately. In this paper, we propose a trigamma-free approach to approximate the expectations involving the trigamma function, along with theoretical upper bounds for approximation errors. We show by numerical studies that our approach is highly efficient and much more accurate than previous methods. We also apply our approach to compute the Fisher information matrices of zero-inflated negative binomial (ZINB) and beta negative binomial (ZIBNB) probabilistic models, as well as ZIBNB regression models.

In this work, we develop two stable estimators for solving linear functional regression problems. It is well known that such a problem is an ill-posed stochastic inverse problem. Hence, a special interest has to be devoted to the stability issue in the design of an estimator for solving such a problem. Our proposed estimators are based on combining a stable least-squares technique and a random projection of the slope function (beta _0(cdot )in L^2(J),) where J is a compact interval. Moreover, these estimators have the advantage of having a fairly good convergence rate with reasonable computational load, since the involved random projections are generally performed over a fairly small dimensional subspace of (L^2(J).) More precisely, the first estimator is given as a least-squares solution of a regularized minimization problem over a finite dimensional subspace of (L^2(J).) In particular, we give an upper bound for the empirical risk error as well as the convergence rate of this estimator. The second proposed stable LFR estimator is based on combining the least-squares technique with a dyadic decomposition of the i.i.d. samples of the stochastic process, associated with the LFR model. In particular, we provide an (L^2)-risk error of this second LFR estimator. Finally, we provide some numerical simulations on synthetic as well as on real data that illustrate the results of this work. These results indicate that our proposed estimators are competitive with some existing and popular LFR estimators.

Traditionally, common testing problems are formalized in terms of a precise null hypothesis representing an idealized situation such as absence of a certain “treatment effect”. However, in most applications the real purpose of the analysis is to assess evidence in favor of a practically relevant effect, rather than simply determining its presence/absence. This discrepancy leads to erroneous inferential conclusions, especially in case of moderate or large sample size. In particular, statistical significance, as commonly evaluated on the basis of a precise hypothesis low p value, bears little or no information on practical significance. This paper presents an innovative approach to the problem of testing the practical relevance of effects. This relies upon the proposal of a general method for modifying standard tests by making them suitable to deal with appropriate interval null hypotheses containing all practically irrelevant effect sizes. In addition, when it is difficult to specify exactly which effect sizes are irrelevant we provide the researcher with a benchmark value. Acceptance/rejection can be established purely by deciding on the (ir)relevance of this value. We illustrate our proposal in the context of many important testing setups, and we apply the proposed methods to two case studies in clinical medicine. First, we consider data on the evaluation of systolic blood pressure in a sample of adult participants at risk for nutritional deficit. Second, we focus on a study of the effects of remdesivir on patients hospitalized with COVID-19.

Functional time series model has been the subject of the most research in recent years, and since functional data is infinite dimensional, dimension reduction is essential for functional time series. However, the majority of the existing dimension reduction methods such as the functional principal component and fixed basis expansion are unsupervised and typically result in information loss. Then, the functional time series model has an urgent need for a supervised dimension reduction method. The functional sufficient dimension reduction method is a supervised technique that adequately exploits the regression structure information, resulting in minimal information loss. Functional sliced inverse regression (FSIR) is the most popular functional sufficient dimension reduction method, but it cannot be applied directly to functional time series model. In this paper, we examine a functional time series model in which the response is a scalar time series and the explanatory variable is functional time series. We propose a novel supervised dimension reduction technique for the regression model by combining the FSIR and blind source separation methods. Furthermore, we propose innovative strategies for selecting the dimensionality of dimension reduction space and the lags of the functional time series. Numerical studies, including simulation studies and a real data analysis are show the effectiveness of the proposed methods.

In this paper, we advance the application of empirical likelihood (EL) for missing response problems. Inspired by remedies for the shortcomings of EL for parameter hypothesis testing, we modify the EL approach used for statistical inference on the mean response when the response is subject to missing behavior. We propose consistent mean estimators, and associated confidence intervals. We extend the approach to estimate the average treatment effect in causal inference settings. We detail the analogous estimators for average treatment effect, prove their consistency, and example their use in estimating the average effect of smoking on renal function of the patients with atherosclerotic renal-artery stenosis and elevated blood pressure, chronic kidney disease, or both. Our proposed estimators outperform the historical mean estimators under missing responses and causal inference settings in terms of simulated relative RMSE and coverage probability on average.

This paper explores a methodology for dimension reduction in regression models for a treatment outcome, specifically to capture covariates’ moderating impact on the treatment-outcome association. The motivation behind this stems from the field of precision medicine, where a comprehensive understanding of the interactions between a treatment variable and pretreatment covariates is essential for developing individualized treatment regimes (ITRs). We provide a review of sufficient dimension reduction methods suitable for capturing treatment-covariate interactions and establish connections with linear model-based approaches for the proposed model. Within the framework of single-index regression models, we introduce a sparse estimation method for a dimension reduction vector to tackle the challenges posed by high-dimensional covariate data. Our methods offer insights into dimension reduction techniques specifically for interaction analysis, by providing a semiparametric framework for approximating the minimally sufficient subspace for interactions.

Estimating the mean of a population is a recurrent topic in statistics because of its multiple applications. If previous data is available, or the distribution of the deviation between the measurements and the mean is known, it is possible to perform such estimation by using L-statistics, whose optimal linear coefficients, typically referred to as weights, are derived from a minimization of the mean squared error. However, such optimal weights can only manage sample sizes equal to the one used to derive them, while in real-world scenarios this size might slightly change. Therefore, this paper proposes a method to overcome such a limitation and derive approximations of flexible-dimensional optimal weights. To do so, a parametric family of functions based on extreme value reductions and amplifications is proposed to be adjusted to the cumulative optimal weights of a given sample from a symmetric distribution. Then, the application of Yager’s method to derive weights for ordered weighted average (OWA) operators allows computing the approximate optimal weights for sample sizes close to the original one. This method is justified from the theoretical point of view by proving a convergence result regarding the cumulative weights obtained for different sample sizes. Finally, the practical performance of the theoretical results is shown for several classical symmetric distributions.