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Covariate-adaptive randomization is popular in clinical trials with sequentially arrived patients for balancing treatment assignments across prognostic factors that may have influence on the response. However, existing theory on tests for the treatment effect under covariate-adaptive randomization is limited to tests under linear or generalized linear models, although the covariate-adaptive randomization method has been used in survival analysis for a long time. Often, practitioners will simply adopt a conventional test to compare two treatments, which is controversial since tests derived under simple randomization may not be valid in terms of type I error under other randomization schemes. We derive the asymptotic distribution of the partial likelihood score function under covariate-adaptive randomization and a working model that is subject to possible model misspecification. Using this general result, we prove that the partial likelihood score test that is robust against model misspecification under simple randomization is no longer robust but conservative under covariate-adaptive randomization. We also show that the unstratified log-rank test is conservative and the stratified log-rank test remains valid under covariate-adaptive randomization. We propose a modification to variance estimation in the partial likelihood score test, which leads to a score test that is valid and robust against arbitrary model misspecification under a large family of covariate-adaptive randomization schemes including simple randomization. Furthermore, we show that the modified partial likelihood score test derived under a correctly specified model is more powerful than log-rank-type tests in terms of Pitman’s asymptotic relative efficiency. Simulation studies about the type I error and power of various tests are presented under several popular randomization schemes.

The time-to-event relationship for survival modeling is considered when designing a study in clinical trials. However, because time-to-event data are mostly not normally distributed, survival analysis uses non-parametric data processing and analysis methods, mainly Kaplan-Meier (KM) estimation models and Cox proportional hazards (CPH) regression models. At the same time, the log-rank test can be applied to compare curves from different groups. However, resorting to conventional survival analysis when fundamental assumptions, such as the Cox PH assumption, are not met can seriously affect the results, rendering them flawed. Consequently, it is necessary to examine and report more sophisticated statistical methods related to the processing of survival data, but at the same time, able to adequately respond to the contemporary real problems of clinical applications. On the other hand, the frequent misinterpretation of survival analysis methodology, combined with the fact that it is a complex statistical tool for clinicians, necessitates a better understanding of the basic principles underlying this analysis to effectively interpret medical studies in making treatment decisions. In this review, we first consider the basic models and mechanisms behind survival analysis. Then, due to common errors arising from the inappropriate application of conventional models, we revise more demanding statistical extensions of survival models related to data manipulation to avoid wrong results. By providing a structured review of the most representative statistical methods and tests covering contemporary survival analysis, we hope this review will assist in solving problems that arise in clinical applications.

South Asia is home to nine species of vultures, and Nepal hosts all of them. Remarkably, all these species have also been recorded in Pokhara. This could be attributed to Pokhara's location along bird migration pathways and the year‐round availability of food sources for most of the vulture species, including the landfill. This landfill site has been translocated due to the construction of Pokhara regional international airport. In this context, we aimed to estimate the seasonal abundance of vultures as well as understand the discrepancy in people's perception on vulture conservation before and after the landfill site is shifted to another location. Data were collected using key informant interviews, household surveys, and direct field observations. The collected data were analyzed employing chi‐squared and Wilcoxon‐signed rank tests. The relative abundance of the Egyptian vulture (Neophron percnopterus) was found to be the highest among observed species. We found an association between people's perception toward vultures and their socioeconomic factors (age, education, and income source). Older people, individuals with higher levels of formal education, and people involved in farming showed greater appreciation for vultures. Our study revealed that the perceived threat of electrocution increased slightly after the landfill site was relocated. Despite the relocation, the old landfill area continues to provide a suitable habitat for vultures, likely due to consistent food availability and the proximity of nesting habitats near forests, cliffs, and rivers. The risk of collisions with airplanes is likely to increase in the future highlighting the need for proactive management and prioritization.

Optimization algorithms have made considerable advancements in solving complex problems with the ability to be applied to innumerable real-world problems. Nevertheless, they are passed through several challenges comprising of equilibrium between exploration and exploitation capabilities, and departure from local optimums. Portioning the population into several sub-populations is a robust technique to enhance the dispersion of the solution in the problem space. Consequently, the exploration would be increased, and the local optimums can be avoided. Furthermore, improving the exploration and exploitation capabilities is a way of increasing the authority of optimization algorithms that various researches have been considered, and numerous methods have been proposed. In this paper, a novel hybrid multi-population algorithm called HMPA is presented. First, a new portioning method is introduced to divide the population into several sub-populations. The sub-populations dynamically exchange solutions aiming at balancing the exploration and exploitation capabilities. Afterthought, artificial ecosystem-based optimization (AEO) and Harris Hawks optimization (HHO) algorithms are hybridized. Subsequently, levy-flight strategy, local search mechanism, quasi-oppositional learning, and chaos theory are utilized in a splendid way to maximize the efficiency of the HMPA. Next, HMPA is evaluated on fifty unimodal, multimodal, fix-dimension, shifted rotated, hybrid, and composite test functions. In addition, the results of HMPA is compared with similar state-of-the-art algorithms using five well-known statistical metrics, box plot, convergence rate, execution time, and Wilcoxon’s signed-rank test. Finally, the performance of the HMPA is investigated on seven constrained/unconstrained real-life engineering problems. The results demonstrate that the HMPA is outperformed the other competitor algorithms significantly.

The salp swarm algorithm (SSA) is a well-known optimization algorithm that is increasingly being utilized to solve many sorts of optimization problems. However, SSA may converge to sub-optimal solutions when it is applied to discrete problems such as the feature selection (FS) problem. This paper presents the enhanced opposition-based learning salp swarm algorithm (EOSSA), which is an improved SSA algorithm for solving the FS problem in intrusion detection systems (IDS). EOSSA incorporates four improvements into the original SSA algorithm. Firstly, the opposition-based learning (OBL) method is used in the initialization step of SSA to boost its population diversity. Secondly, the Elite opposition-based learning (EOBL) is used in the improvement loop of SSA to improve its exploration ability. Third, a variable neighborhood search (VNS) method is used in the improvement loop of SSA to improve its exploration mechanism to improve the local search space. Lastly, the Sigmoid binary transform function is used to convert the continuous candidate solutions produced by SSA into discrete binary solutions . EOSSA was evaluated against eighteen popular optimization algorithms (e.g., improved salp swarm algorithm based on opposition-based learning (ISSA), SSA, particle swarm algorithm (PSO), cuckoo search (CS), bat algorithm (BA), and Harris Hawk Optimization (HHO)) using eleven popular intrusion detection datasets (CICIDS2017, CSE-CIC-IDS2018, CICDDOS2019, CIRA-CIC-DoH, Intrusion detection 2018, UNSW-NB15, NSL-KDD, Phishing Legitimate, Malmem2022, IoT, and LUFlow Network) to Detect IoT Botnet Attacks. Moreover, EOSSA was compared with four machine learning algorithms (Decision Tree (DT), logistic regression (LR), Naive Bayes (NB), and K-Nearest Neighborhood (KNN)). The overall simulation results suggested that the proposed method is superior to the other algorithms in terms of the accuracy and number of selected features. The statistical analysis of the simulation results using the Friedman and Wilcoxon signed-rank test confirms the superiority of the proposed method.

A Kolmogorov–Smirnov-type test for the two-sample problem with left-truncated data is proposed. The asymptotic null distribution of the test statistic and its omnibus consistency are established. A bootstrap resampling plan to approximate the null distribution of the test statistic is introduced. The finite sample performance of the proposed test is investigated through simulations. Comparison to the well-known log-rank test and a real data illustration are included.

The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of many experiments in applied statistics. As a starting point for this robust analysis, we propose, analyze, and apply a new definition of depth for functional observations based on the graphic representation of the curves. Given a collection of functions, it establishes the \"centrality\" of an observation and provides a natural center-outward ordering of the sample curves. Robust statistics, such as the median function or a trimmed mean function, can be defined from this depth definition. Its finite-dimensional version provides a new depth for multivariate data that is computationally feasible and useful for studying high-dimensional observations. Thus, this new depth is also suitable for complex observations such as microarray data, images, and those arising in some recent marketing and financial studies. Natural properties of these new concepts are established and the uniform consistency of the sample depth is proved. Simulation results show that the corresponding depth based trimmed mean presents better performance than other possible location estimators proposed in the literature for some contaminated models. Data depth can be also used to screen for outliers. The ability of the new notions of depth to detect \"shape\" outliers is presented. Several real datasets are considered to illustrate this new concept of depth, including applications to microarray observations, weather data, and growth curves. Finally, through this depth, we generalize to functions the Wilcoxon rank sum test. It allows testing whether two groups of curves come from the same population. This functional rank test when applied to children growth curves shows different growth patterns for boys and girls.

We propose a non-parametric change-point test for long-range dependent data, which is based on the Wilcoxon two-sample test. We derive the asymptotic distribution of the test statistic under the null hypothesis that no change occurred. In a simulation study, we compare the power of our test with the power of a test which is based on differences of means. The results of the simulation study show that in the case of Gaussian data, our test has only slightly smaller power than the 'difference-of-means' test. For heavy-tailed data, our test outperforms the 'difference-of-means' test.

Phase synchronization has been an effective measurement of functional connectivity, detecting similar dynamics over time among distinct brain regions. However, traditional phase synchronization-based functional connectivity indices have been proved to have some drawbacks. For example, the phase locking value (PLV) index is sensitive to volume conduction, while the phase lag index (PLI) and the weighted phase lag index (wPLI) are easily affected by noise perturbations. In addition, thresholds need to be applied to these indices to obtain the binary adjacency matrix that determines the connections. However, the selection of the thresholds is generally arbitrary. To address these issues, in this paper we propose a novel index of functional connectivity, named the phase lag based on the Wilcoxon signed-rank test (PLWT). Specifically, it characterizes the functional connectivity based on the phase lag with a weighting procedure to reduce the influence of volume conduction and noise. Besides, it automatically identifies the important connections without relying on thresholds, by taking advantage of the framework of the Wilcoxon signed-rank test. The performance of the proposed PLWT index is evaluated on simulated electroencephalograph (EEG) datasets, as well as on two resting-state EEG datasets. The experimental results on the simulated EEG data show that the PLWT index is robust to volume conduction and noise. Furthermore, the brain functional networks derived by PLWT on the real EEG data exhibit a reasonable scale-free characteristic and high test–retest (TRT) reliability of graph measures. We believe that the proposed PLWT index provides a useful and reliable tool to identify the underlying neural interactions, while effectively diminishing the influence of volume conduction and noise.