Breast cancer remains a leading malignancy among women globally, necessitating precise monitoring of therapeutic outcomes to improve survival and quality of life. Conventional statistical quality control tools often face limitations due to patient heterogeneity. This study proposes a novel log-logistic risk-adjusted cumulative sum (RACUSUM) control chart for monitoring breast cancer treatments, incorporating an accelerated failure time (AFT) model to adjust for individual patient risk factors. This risk adjustment enhances the chart’s sensitivity and specificity in detecting deviations in treatment effectiveness. A significant advancement is the multi-objective optimization of the RACUSUM design, balancing rapid detection of process shifts with cost-efficiency. Multi-objective particle swarm optimization (MOPSO) generates optimal solution sets, which are prioritized using the data envelopment analysis (DEA) and weighted aggregated sum product assessment (WASPAS) methods to support clinical decision-making. Validation through a case study at a breast cancer center demonstrated superior performance compared to traditional models, achieving improved monitoring accuracy with minimal incremental cost. This integrated approach offers clinicians and healthcare administrators a robust tool for enhancing breast cancer care quality, ultimately aiming to reduce adverse events and improve patient outcomes.

Detecting the change in community structure has many important applications. In this paper, we consider the quickest detection problem when the network data may change from the Erdős-Rényi (ER) model to the stochastic block model (SBM) with two clusters. We first propose a CUSUM-type computationally and statistically efficient procedure by using the number of k-cycles in the network. Then, we investigate the theoretical detection performance of our procedure when the pre-change and post-change model parameters are fully specified and provide guidelines about the optimal choices of tuning parameters in our proposed method. Furthermore, we develop an adaptive detection procedure to address the problem when model parameters are unknown. Finally, extensive simulations are conducted to illustrate the advantages of our proposed procedures.

In this paper, our aim is to compare the scale parameters of two independent Pareto distributions using the hypothesis testing approach. We develop testing procedures for the ratio of scale parameters of two independent Pareto populations with unknown but proportional shape parameters and establish that such a comparison is not possible with any fixed sample size procedure. Hence, we implement a practical accelerated sequential sampling design to obtain the required sample sizes while controlling both type I and type II error probabilities. The first and second-order asymptotic properties of the proposed procedure are studied in detail. A large-scale simulation analysis is carried out to validate the theoretical findings under different parameter configurations. In addition to the extensive simulations, we provide two real-data illustrations (incomes of two occupations and rice production of two regions) to complement the practical utility of the proposed study.

This article provides a two-stage procedure to develop a partial sequential test procedure for both the location and scale parameters of a normal distribution. The first stage is taken to be of a fixed sample size. The stopping rule is obtained by adopting a two-stage procedure on the number of index subjects using an inverse sampling scheme in the second stage. Different asymptotic results associated with the procedure are obtained. The findings are supported by detailed simulation studies followed by three data illustrations.

In this article, the concept of asymptotic pointwise optimality in a single continuous-time process provided by Hwang (2001) is extended to more than one continuous-time process. We propose an asymptotically pointwise optimal (APO) rule, which consists of a sequential allocation procedure and a stopping time, and derive some properties of asymptotic optimality of the rule. In particular, some APO rules are proposed in the Bayes sequential estimation problem for several Poisson processes under both squared error loss and linear exponential loss functions. They are shown to be asymptotically optimal for arbitrary priors and asymptotically nondeficient for conjugate priors.

Score-based algorithms are proposed for the quickest detection of changes in unnormalized statistical models. These are models where the densities are known within a normalizing constant. These algorithms can also be applied to score-based models where the score, i.e., the gradient of log density, is known to the decision maker. Bayesian performance analysis is provided for these algorithms and compared with their classical counterparts. It is shown that strong performance guarantees can be provided for these score-based algorithms where the Kullback-Leibeler divergence between pre- and post-change densities is replaced by their Fisher divergence.

Sampling strategies with fractional acceleration 0 < ρ < 1 achieve substantial operational savings compared with purely sequential counterparts. But, acceleration customarily yielded second-order (s.o.) lower and upper bounds for requisite characteristics when ρ − 1 was not an integer. First time in the literature, we have recently designed acceleration with asymptotic s.o. expansions in normal mean problems with ρ − 1 arbitrary. In this article, a general unified theory is now developed leading to asymptotic s.o. expansions for customarily studied characteristics with arbitrary ρ − 1 . That is, the previously known s.o. lower/upper bounds can be replaced with appropriate s.o. expansions in a variety of inference problems with prescribed accuracy. We emphasize the theoretical foundation and ensuing analyses with a series of interesting inference problems from (a) a number of non-normal distributions as well as (b) one- and two-sample distribution-free scenarios. These prove a desirable breadth of coverage under our proposed big tent.

In this study, we consider disorder detection problems for statistical models with dependent observations defined by Markov chains in a Bayesian setting for a uniform prior distribution when the number of observations is limited by some known quantity. To achieve this, a new optimal sequential detection procedure is constructed using optimal stopping methods. This procedure minimizes the average delay time in the class of sequential procedures with false alarm probabilities that do not exceed a fixed value. The main difference between the proposed detection procedure and the conventional ones is that it is based not on the posterior probabilities but on the weighted Shiryaev-Roberts statistic. This allows for optimal detection in a nonasymptotic sense over any bounded time interval. Thereafter, we applied the constructed procedures to the early detection problem for the beginning of the epidemic spread. We used two epidemic models: the binomial model proposed by Baron, Choudhary, and Yu (2013) and the model based on the Gaussian approximation introduced by Pergamenchtchikov, Tartakovsky, and Spivak (2022). The theoretical results were confirmed through numerical simulations using the Monte Carlo method.

Detecting change points sequentially in a streaming setting, especially when both the mean and the variance of the signal can change, is often a challenging task. A key difficulty in this context often involves setting an appropriate detection threshold, which for many standard change statistics may need to be tuned depending on the prechange and postchange distributions. This presents a challenge in a sequential change detection setting when a signal switches between multiple distributions. Unfortunately, change point detection schemes that use the log-likelihood ratio, such as cumulative sum (CUSUM) and the generalized log-likelihood ratio (GLR), are quick to react to changes but are not symmetric when both the mean and the variance of the signal change. This makes it difficult to set a single threshold to detect multiple change points sequentially in a streaming setting. We propose a modified version of CUSUM that we call data-adaptive symmetric CUSUM (DAS-CUSUM). The DAS-CUSUM procedure is symmetric for changes between distributions, making it suitable to set a single threshold to detect multiple change points sequentially in a streaming setting. We provide results that relate the expected detection delay and average run length for our proposed procedure when both prechange and postchange distributions are normally distributed. Experiments on simulated and real-world data show the utility of DAS-CUSUM.

Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fixed time interval. It is assumed that the pre-change law is known to the decision maker but the post-change law is unknown. In this framework, three families of problems are studied: robust quickest change detection, joint quickest change detection and classification, and multi-slot quickest change detection. In the multi-slot problem, the exact slot within a period where a change may occur is unknown. Algorithms are proposed for each problem, and either exact optimality or asymptotic optimality in the low false alarm regime is proved for each of them. The developed algorithms are then used for anomaly detection in traffic data and arrhythmia detection and identification in electrocardiogram (ECG) data. The effectiveness of the algorithms is also demonstrated on simulated data.