Inferences for the distribution of the duration of response in a comparative clinical study.

Duration of response is an important endpoint used in drug development. Prolonged duration for response is often viewed as an early indication of treatment efficacy. However, there are numerous difficulties in studying the distribution of duration of response based on observed data subject to right censoring in practice. The most important obstacle is that the distribution of the duration of response is in general not identifiable in the presence of censoring due to the simple fact that there is no information on the joint distribution of time to response and time to progression beyond the largest follow-up time. In this article, we introduce the restricted duration of response as a replacement of the conventional duration of response. The distribution of restricted duration of response is estimable and we have proposed several nonparametric estimators in this article. The corresponding inference procedure and additional downstream analysis have been developed. Extensive numerical simulations have been conducted to examine the finite sample performance of the proposed estimators. It appears that a new regression-based two-step estimator for the survival function of the restricted duration of response tends to have a robust and superior performance, and we recommend its use in practice. A real data example from oncology has been used to illustrate the analysis for restricted duration of response.

Enhanced direct and synthetic estimators for domain mean with simulation and applications.

This article considers the issue of domain mean estimation utilizing bivariate auxiliary information based enhanced direct and synthetic logarithmic type estimators under simple random sampling (SRS). The expressions of mean square error (MSE) of the proposed estimators are provided to the 1 s t order approximation. The efficiency criteria are derived to exhibit the dominance of the proposed estimators. To exemplify the theoretical results, a simulation study is conducted on a hypothetically drawn trivariate normal population from R programming language. Some applications of the suggested methods are also provided by analyzing the actual data from the municipalities of Sweden and acreage of paddy crop in the Mohanlal Ganj tehsil of the Indian state of Uttar Pradesh. The findings of the simulation and real data application exhibit that the proposed direct and synthetic logarithmic estimators dominate the conventional direct and synthetic mean, ratio, and logarithmic estimators in terms of least MSE and highest percent relative efficiency.

New classes of difference cum-ratio-type exponential estimators for a finite population variance in stratified random sampling.

The problem of estimating the variance of a finite population is an important issue in practical situations where controlling variability is difficult. During experiments conducted in the fields of agriculture and biology, researchers often face this issue, resulting in outcomes that appear uncontrollable for the desired results. Using auxiliary information effectively has the potential to enhance the precision of estimators. This article aims to introduce improved classes of efficient estimators that are specifically designed to estimate the study variable's finite population variance. When stratified random sampling is used, these estimators are particularly efficient when the minimum and maximum values of the auxiliary variable are known. The bias and mean squared error (MSE) of the proposed classes of estimators are determined by a first-order approximation. In order to evaluate their performance and verify the theoretical results, we performed simulation research. The proposed estimators show higher percent relative efficiencies ( P R E s ) in all simulation scenarios compared to other existing estimators, according to the results. Three datasets are utilized in the application section, which are used to further validate the effectiveness of the proposed estimators.

Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored Weibull distribution.

This paper presents an effort to investigate the estimations of the Weibull distribution using an improved adaptive Type-II progressive censoring scheme. This scheme effectively guarantees that the experimental time will not exceed a pre-fixed time. The point and interval estimations using two classical estimation methods, namely maximum likelihood and maximum product of spacing, are considered to estimate the unknown parameters as well as the reliability and hazard rate functions. The approximate confidence intervals of these quantities are obtained based on the asymptotic normality of the maximum likelihood and maximum product of spacing methods. The Bayesian estimations are also considered using MCMC techniques based on the two classical approaches. An extensive simulation study is implemented to compare the performance of the different methods. Further, we propose the use of various optimality criteria to find the optimal sampling scheme. Finally, one real data set is applied to show how the proposed estimators and the optimality criteria work in real-life scenarios. The numerical outcomes demonstrated that the Bayesian estimates using the likelihood and product of spacing functions performed better than the classical estimates.

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques.

We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

Multimodel Approaches Are Not the Best Way to Understand Multifactorial Systems.

Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by "shrinking" parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity.

Robust analysis of stepped wedge trials using composite likelihood models.

Stepped wedge trials (SWTs) are a type of cluster randomized trial that involve repeated measures on clusters and design-induced confounding between time and treatment. Although mixed models are commonly used to analyze SWTs, they are susceptible to misspecification particularly for cluster-longitudinal designs such as SWTs. Mixed model estimation leverages both "horizontal" or within-cluster information and "vertical" or between-cluster information. To use horizontal information in a mixed model, both the mean model and correlation structure must be correctly specified or accounted for, since time is confounded with treatment and measurements are likely correlated within clusters. Alternative non-parametric methods have been proposed that use only vertical information; these are more robust because between-cluster comparisons in a SWT preserve randomization, but these non-parametric methods are not very efficient. We propose a composite likelihood method that focuses on vertical information, but has the flexibility to recover efficiency by using additional horizontal information. We compare the properties and performance of various methods, using simulations based on COVID-19 data and a demonstration of application to the LIRE trial. We found that a vertical composite likelihood model that leverages baseline data is more robust than traditional methods, and more efficient than methods that use only vertical information. We hope that these results demonstrate the potential value of model-based vertical methods for SWTs with a large number of clusters, and that these new tools are useful to researchers who are concerned about misspecification of traditional models.

Statistical mirroring: A robust method for statistical dispersion estimation.

This study introduces statistical mirroring as an innovative approach to statistical dispersion estimation, drawing inspiration from the Kabirian-based isomorphic optinalysis model, aimed at enhancing robustness and mitigating biases in estimation methods. Beyond scale-invariant characteristics, the proposed estimators emphasize scaloc-invariant robustness, thereby addressing a critical gap in dispersion estimation. By highlighting statistical meanic mirroring, alongside other forms of proposed statistical mirroring, the study underscores the adaptability and customization potential. Through extensive Monte Carlo simulations and real-life applications, in comparison with classical estimators, the results of the performance evaluation of the proposed estimators demonstrate robustness, efficiency, and transformations-invariance. The research offers a paradigm shift in addressing longstanding challenges in dispersion estimation, offering a new category of dispersion estimation and increased resistance to outliers. Notable limitations include selecting and evaluating the proposed statistical meanic mirroring under Gaussian and Gaussian mixture model distributions. This research paper significantly contributes to statistical methodologies, offering avenues for expanding knowledge in dispersion estimation. It recommends further exploration of proposed estimators across various statistical mirroring types and encourages comparative studies to establish their effectiveness, thereby advancing statistical knowledge and tools for precise data analysis.•The proposed methodology involves preprocessing transformations, statistical mirror design, and optimization to transform a univariate set into a bivariate one, facilitating the fitting of an isomorphic optinalysis model.•Estimators rely on a foundational bijective mapping of isoreflective pairs, deducing the probability of proximity or deviation from any defined center. This contrasts with classical estimators that utilize average or median deviations from a mean or median center.

Dual-type quantile regression approach for mean estimation incorporating sampled and non-sampled data.

Drawing inspiration from recent advancements in robust mean estimation within finite sampling theory, we introduce a novel dual-type class of mean estimators in a design-based framework. The dual-type class is based on quantile regression and is specifically designed to be effective in the presence of extreme observations. Significantly, it integrates the averages of both sampled observations and non-sampled observations of auxiliary variable. In the initial discussion of this class, it is presumed that the target variable is non-sensitive, signifying its relevance to subjects that respondents do not consider embarrassing when queried directly. In this standard setting, we present specific estimators within the class and determine their theoretical properties. The class's scope broadens to include scenarios where the target variable incorporates sensitive topics, giving rise to nonresponse rates and inaccurate reporting. To alleviate these errors, one can promote respondent cooperation by employing scrambled response methods that obscure the actual value of the sensitive variable. Accordingly, the article delves into discussions on additive methods. Subsequently, a numerical study is conducted using asymmetric data to evaluate the effectiveness of the dual-type class by comparing it with several existing estimators, both in the absence and presence of scrambled responses.

Calibrated EWMA estimators for time-scaled surveys with diverse applications.

Recently, several memory-type mean estimators (including ratio, product, and logarithmic) have been developed. These estimators rely on exponentially weighted moving average (EWMA), which incorporate both historical and present sample data. In this article, we propose EWMA type calibrated estimators under single and double stratified random sampling (StRS). Because calibration method enhances the estimates by modifying the stratification weight, taking advantage of supplementary information. To evaluate the performance of estimators, various real-world time-scaled data sets pertaining to stock market and weather are taken into account. Additionally, we also conduct a simulation study using a bivariate symmetric data set. The numerical results show the superiority of proposed estimators (y¯TM,y¯TaM) over the adapted ones (y¯PM,y¯PaM).

Updated Surveillance Metrics and History of the COVID-19 Pandemic (2020-2023) in Europe: Longitudinal Trend Analysis.

BACKGROUND: In this study, we built upon our initial research published in 2020 by incorporating an additional 2 years of data for Europe. We assessed whether COVID-19 had shifted from the pandemic to endemic phase in the region when the World Health Organization (WHO) declared the end of the public health emergency of international concern on May 5, 2023. OBJECTIVE: We first aimed to measure whether there was an expansion or contraction in the pandemic in Europe at the time of the WHO declaration. Second, we used dynamic and genomic surveillance methods to describe the history of the pandemic in the region and situate the window of the WHO declaration within the broader history. Third, we provided the historical context for the course of the pandemic in Europe in terms of policy and disease burden at the country and region levels. METHODS: In addition to the updates of traditional surveillance data and dynamic panel estimates from the original study, this study used data on sequenced SARS-CoV-2 variants from the Global Initiative on Sharing All Influenza Data to identify the appearance and duration of variants of concern. We used Nextclade nomenclature to collect clade designations from sequences and Pangolin nomenclature for lineage designations of SARS-CoV-2. Finally, we conducted a 1-tailed t test for whether regional weekly speed was greater than an outbreak threshold of 10. We ran the test iteratively with 6 months of data across the sample period. RESULTS: Speed for the region had remained below the outbreak threshold for 4 months by the time of the WHO declaration. Acceleration and jerk were also low and stable. While the 1-day and 7-day persistence coefficients remained statistically significant, the coefficients were moderate in magnitude (0.404 and 0.547, respectively; P<.001 for both). The shift parameters for the 2 weeks around the WHO declaration were small and insignificant, suggesting little change in the clustering effect of cases on future cases at the time. From December 2021 onward, Omicron was the predominant variant of concern in sequenced viral samples. The rolling t test of speed equal to 10 became insignificant for the first time in April 2023. CONCLUSIONS: While COVID-19 continues to circulate in Europe, the rate of transmission remained below the threshold of an outbreak for 4 months ahead of the WHO declaration. The region had previously been in a nearly continuous state of outbreak. The more recent trend suggested that COVID-19 was endemic in the region and no longer reached the threshold of the pandemic definition. However, several countries remained in a state of outbreak, and the conclusion that COVID-19 was no longer a pandemic in Europe at the time is unclear.

A memetic dynamic coral reef optimisation algorithm for simultaneous training, design, and optimisation of artificial neural networks.

Artificial Neural Networks (ANNs) have been used in a multitude of real-world applications given their predictive capabilities, and algorithms based on gradient descent, such as Backpropagation (BP) and variants, are usually considered for their optimisation. However, these algorithms have been shown to get stuck at local optima, and they require a cautious design of the architecture of the model. This paper proposes a novel memetic training method for simultaneously learning the ANNs structure and weights based on the Coral Reef Optimisation algorithms (CROs), a global-search metaheuristic based on corals' biology and coral reef formation. Three versions based on the original CRO combined with a Local Search procedure are developed: (1) the basic one, called Memetic CRO; (2) a statistically guided version called Memetic SCRO (M-SCRO) that adjusts the algorithm parameters based on the population fitness; (3) and, finally, an improved Dynamic Statistically-driven version called Memetic Dynamic SCRO (M-DSCRO). M-DSCRO is designed with the idea of improving the M-SCRO version in the evolutionary process, evaluating whether the fitness distribution of the population of ANNs is normal to automatically decide the statistic to be used for assigning the algorithm parameters. Furthermore, all algorithms are adapted to the design of ANNs by means of the most suitable operators. The performance of the different algorithms is evaluated with 40 classification datasets, showing that the proposed M-DSCRO algorithm outperforms the other two versions on most of the datasets. In the final analysis, M-DSCRO is compared against four state-of-the-art methods, demonstrating its superior efficacy in terms of overall accuracy and minority class performance.

Assessing the properties of patient-specific treatment effect estimates from causal forest algorithms under essential heterogeneity.

BACKGROUND: Treatment variation from observational data has been used to estimate patient-specific treatment effects. Causal Forest Algorithms (CFAs) developed for this task have unknown properties when treatment effect heterogeneity from unmeasured patient factors influences treatment choice - essential heterogeneity. METHODS: We simulated eleven populations with identical treatment effect distributions based on patient factors. The populations varied in the extent that treatment effect heterogeneity influenced treatment choice. We used the generalized random forest application (CFA-GRF) to estimate patient-specific treatment effects for each population. Average differences between true and estimated effects for patient subsets were evaluated. RESULTS: CFA-GRF performed well across the population when treatment effect heterogeneity did not influence treatment choice. Under essential heterogeneity, however, CFA-GRF yielded treatment effect estimates that reflected true treatment effects only for treated patients and were on average greater than true treatment effects for untreated patients. CONCLUSIONS: Patient-specific estimates produced by CFAs are sensitive to why patients in real-world practice make different treatment choices. Researchers using CFAs should develop conceptual frameworks of treatment choice prior to estimation to guide estimate interpretation ex post.

Efficient imputation methods in case of measurement errors.

This manuscript develops few efficient difference and ratio kinds of imputations to handle the situation of missing observations given that these observations are polluted by the measurement errors (ME). The mean square errors of the developed imputations are studied to the primary degree approximation by adopting Taylor series expansion. The proposed imputations are equated with the latest existing imputations presented in the literature. The execution of the proposed imputations is assessed by utilizing a broad empirical study utilizing some real and hypothetically created populations. Appropriate remarks are made for sampling respondents regarding practical applications.

A new modified biased estimator for Zero inflated Poisson regression model.

Zero-inflated Poisson (ZIP) model is widely used for counting data with excessive zeroes. The multicollinearity is the common factor in the explanatory variables of the count data. In this context, typically, maximum likelihood estimation (MLE) generates unsatisfactory results due to inflation of mean square error (MSE). In the solution of this problem usually, ridge parameters are used. In this study, we proposed a new modified zero-inflated Poisson ridge regression model to reduce the problem of multicollinearity. We experimented within the context of a specified simulation strategy and recorded the behavior of proposed estimators. We also apply our proposed estimator to the real-life data set and explore how our proposed estimators perform well in the presence of multicollinearity with the help of ZIP model for count data.

What contributes more to BRI economic growth, renewable or non-renewable energy consumption: A third generation panel data analysis.

Given the increasing investment by Belt and Road Initiative (BRI) participants in the renewable energy industry, it is imperative to ascertain how much this investment contributes to economic growth. The objective of this study is to ascertain the extent to which renewable energy contributes to economic growth within the Belt and Road Initiative compared to non-renewable energy sources. Prior studies have yet to incorporate oil prices as a variable in the production function, among other output aspects. This study integrates the inclusion of real oil prices as a variable within the production function alongside capital, labor, renewable energy consumption, and non-renewable energy consumption. A cohort including 49 Belt and Road Initiative participants was formed, encompassing data from 1990 to 2019. The data has undergone an initial examination to assess cross-sectional dependence, slope heterogeneity, and structural break(s), and are verified. Hence, third-generation panel data analysis has been utilized. The continuously updated fully modified estimator and continuously updated biased corrected estimator provide evidence supporting the notion that renewable energy plays a substantial role in fostering economic growth within nations participating in the Belt and Road Initiative. Furthermore, this contribution is found to be more pronounced when compared to the impact of non-renewable energy sources. The study's findings inform policy recommendations at both the BRI and national level.

Entropy Estimators for Markovian Sequences: A Comparative Analysis.

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data and the lack of unbiased estimators. Most existing entropy estimators are designed for sequences of independent events and their performances vary depending on the system being studied and the available data size. In this work, we compare different entropy estimators and their performance when applied to Markovian sequences. Specifically, we analyze both binary Markovian sequences and Markovian systems in the undersampled regime. We calculate the bias, standard deviation, and mean squared error for some of the most widely employed estimators. We discuss the limitations of entropy estimation as a function of the transition probabilities of the Markov processes and the sample size. Overall, this paper provides a comprehensive comparison of entropy estimators and their performance in estimating entropy for systems with memory, which can be useful for researchers and practitioners in various fields.

Ln-type estimators for the estimation of the population mean of a sensitive study variable using auxiliary information.

In this article, we offered two ln-type estimators for the population mean estimation of a sensitive study variable by using the auxiliary information under the design of basic probability sampling. The Taylor and log series were used to derive the expressions of mean square error and bias up to the first order. Improved classes of proposed estimators are obtained by using conventional parameters associated with the supplementary variable to obtained precise estimates. Mathematical comparisons of the estimators have been made with the usual mean and ratio estimators using theoretical equations of mean square error. A simulation study is conducted for the evaluation of proposed estimator's implementation using four artificial populations generated through R-software with different choices of mean vectors and variance-covariance matrices. The demonstration of proposed ln-type estimators was implemented through the real data application.

The heterogeneous well-being effects of intergenerational mobility perceptions.

Individuals make comparisons with their parents which determine their intergenerational mobility perceptions, yet very little is known about the areas used for intergenerational comparison and whether these matter for individuals' well-being. In 2021 we commissioned a nationally representative survey in Georgia in which we explicitly asked 1159 individuals an open-ended question on the most important areas in their intergenerational comparisons. More than 170 types of answers were provided by respondents and many of these responses went beyond the standard indicators of intergenerational mobility. We show that the areas of intergenerational comparison significantly differ between those who perceive themselves as being downwardly and upwardly mobile or immobile using the measure of mobility previously validated in cross-national research. Using, among other statistical approaches, treatment effects estimators, we demonstrate that some areas of intergenerational comparison, particularly in terms of income attainment, are significantly and consistently associated with internationally validated measures of well-being.

A flexible model based on piecewise linear approximation for the analysis of left truncated right censored data with covariates, and applications to Worcester Heart Attack Study data and Channing House data.

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards model. The principal advantage of the proposed model is that it does not depend on restrictive parametric assumptions while being flexible and data-driven. Likelihood inference for the model is developed. Through detailed simulation studies, the robustness property of the model is studied by fitting it to LTRC data generated from different processes covering a wide range of lifetime distributions. A sensitivity analysis is also carried out by fitting the model to LTRC data generated from a process with a piecewise constant baseline hazard. It is observed that the performance of the model is quite satisfactory in all those cases. Analyses of two real LTRC datasets by using the model are provided as illustrative examples. Applications of the model in some practical prediction issues are discussed. In summary, the proposed model provides a comprehensive and flexible approach to model a general structure for LTRC lifetime data.