SCOPUA Journal of Applied Statistical Research
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Deep Learning-Based Survival Analysis and Recurrence Prediction in Breast Cancer Patients Using Clinical and Genomic Data
Get PDFReliable survival prediction is essential for personalised management of breast cancer, yet conventional models often fail to capture complex interactions among clinical, pathological, and genomic features. This study applied a deep learning framework (DeepSurv) to a cohort of 2,509 breast cancer patients, integrating clinical, histopathological, and genomic data to predict overall survival (OS) and relapse-free survival (RFS). Exploratory analysis revealed a median age at diagnosis of 60.4 years, a median tumour size of 26 mm, and a median of 0 positive lymph nodes, with a relapse rate of ~40%. DeepSurv demonstrated superior predictive performance compared to classical Cox regression, achieving C-index values of 0.7567 (OS) and 0.6495 (RFS) versus 0.7038 (OS) and 0.6403 (RFS) for Cox models. SHAP analysis identified positive lymph nodes, tumour grade, tumour size, age, and Nottingham Prognostic Index (NPI) as the most influential predictors, while mutation count and treatment variables contributed moderately. Survival curves indicated higher individualised survival probabilities with DeepSurv, reflecting improved sensitivity to patient-specific risk patterns. Classical Cox regression performed adequately but exhibited reduced discriminatory power, particularly for RFS. These findings demonstrate that deep learning models can integrate multi-modal data, enhance predictive accuracy, and maintain interpretability, supporting patient stratification and informed clinical decision-making. Future work should incorporate additional molecular and treatment-response data to improve relapse prediction further
A new generalized Logistic class of distributions: Properties and applications on flood and earthquake data sets with bivariate extension
Get PDFFor univariate and bi-variate data, we propose a new generalized logistic class of distributions exible enough to exhibit monotone and non-monotone hazard rates shapes. The physical interpretation of the new family preludes in the context of series-parallel structures. Its mathematical features, including a valuable expansion for the density, explicit formulations for the quantile function, ordinary and incomplete moments, and generating function, are all derived. The parameter estimation of the new family is done using the maximum likelihood method. One of the unique model, called the generalized logistic Burr-III, is thoroughly investigated in applied sense. The exible density and hazard rate shapes capacitates the model to be applicable in extreme value theory. For univariate case, two real-life data sets related to hydrology and seismic activity have been employed to solidify the superiority of the proposed distribution to ve well established families. For bivariate data, initially a bivariate extension of the proposed family is established analytically with the help of empirical ndings. Then, a real bi-variate data related to operational lifespan of two components of a computer, has been studied using bivariate generalized logistic Burr-III model and the results are reported
Power Comparison of Modality Tests
Get PDFIn this paper, the power of each test of unimodality/multimodality is estimated. The power of each test is estimated on the basis of the alternative hypothesis that there is bimodality. The Power Curve and Power Envelope of each test of unimodality /multimodality are also shown by using a graphical representation. The most stringent test of all the four tests of unimodality/multimodality is also recognised and finally finds the Conclusion about the most powerful, best test, worst test and most stringent test among these four stated tests
A new Bartlett-based homogeneity test for linear regression models
Get PDFThe assumption of homogeneous residuals is crucial in linear regression analysis. In fact, all statistical inferences around regression coefficients are built on the basis of this fundamental assumption. As a result, having a linear model with heterogeneous residuals would destruct all those beneficial reliable inferences, and this specifically means that all extracted predicted values, confidence regions and any other conclusions are then false, misleading and far from reality. Also, heterogeneity underestimates true significance levels, which could lead to considering the importance of an explanatory variable whereas truth is not. These are a few consequences of handling a linear regression model with heterogeneous residuals, and hence, researchers have focused on two things: first, defining a consistent statistical tool to catch deviations from homogeneity, and second, proposing approaches to deal with that violation efficiently. We are not interested here in the last goal, and rather, we are focusing on the first one. Indeed, there were enormous and remarkable efforts seeking to fulfil the first goal in different ways, from plotting residuals against fitted values to applying statistical tests, such as the Breusch-Pagan test, Koenker test, and other related tests. But in effect, analysing plots is highly dependent on self-experience and how one would draw conclusions and thoughts about the plot and, in fact, it is not an easy task in many real-world studies. On the other hand, each of the Breusch-Pagan and Koenker tests has its own deficiencies and misleading conclusions. Other related tests, which we will summarise shortly, are not easily implemented or programmed. So, we aim in the present paper to present a simple statistical method for testing the homogeneity assumption of linear regression residuals, by just employing the well-known Bartlett\u27s test, on the basis of defining two suitable disjoint subsets driven from the original dataset. We evaluate the proposed approach by a series of simulation studies and analysing a previous historic case study, and it will be shown that the proposed method controls the error rate in a nominal level and has high performance in sense of both homogeneity and heterogeneity detections
Transformation to Achieve Perfect Correlation
Get PDFCorrelation and linear regression are common means to evaluate association and empirical relationships between two or more variables. Such relationships often show significant departure of |r_XY | from unity. Existing transformations to increase correlation fail to achieve perfect correlation. For a bivariate data, the paper proposes transforming Y to y=G.‖x‖‖y‖, which gives r_(X y)=1 where G is the G-inverse of the matrix A=x.x^Tand x, y denote vectors of deviation scores. The concept is extended to perfect linearity between a dependent variable (Y) and a set of independent variables (Multiple linear regressions) or between set of dependent variables and set of independent variables (Canonical regression), avoiding problems of insignificant beta coefficients in univariate and multivariate regression models and outliers. Empirical illustration of G-inverse and extensions for multiple linear regressions and Canonical regressions are also given. The proposed transformation is a novel method of introducing perfect correlation between two variables. Extension of the concept in multiple linear regressions and canonical regression will go a long way in empirical researches in various branches of science. Future studies may include finding distribution of the proposed perfect correlations and comparison of efficacy of our suggested approach against other traditional ones by providing quantitative evidences
Sum of Weighted Gamma Distribution: Properties and Applications in Reliability Engineering
Get PDFApplications of the lifetime continuous distributions in the reliability field are always in demand to improve the performance of electronic components. In this paper, we proposed a new method which is used to obtain a single-parameter lifetime distribution named “Sum of Weighted Gamma Distribution” (SWG distribution). The newly proposed distribution is obtained by weighing the gamma distribution with varying shape and constant scale parameters. The idea has been taken from the formation of the Lindley distribution, which is a mixture of exponential (with scale parameter ) and gamma (with shape parameter 2 and scale parameter ) distributions. Various mathematical properties of the SWG distribution have been derived. A few reliability and inequality measures, such as survival function, hazard rate, reversed hazard rate, cumulative hazard rate, Ginni indices, Lorenz and Bonferroni inequalities have been developed. Order statistics and upper record values from the SW-Gamma distribution have been studied. The parameter is estimated by using the method of maximum likelihood estimation (MLE), moreover, a simulation is conducted. Finally, the applications of the SWG distribution have been shown on three different lifetime data sets and compared with famous single-parameter lifetime distributions. It is shown that the SWG distribution is more flexible comparatively
Repetitive Sampling Plans for Life Tests Based on Percentiles of the Half-Normal Distribution with Applications to Software Reliability and Device Lifetime Data
Get PDFAcceptance Sampling Plans (ASPs) are indispensable statistical tools in quality control for making decisions regarding the acceptance or rejection of product lots. While traditional plans often rely on the mean lifetime, percentile-based criteria offer a more robust measure, particularly for capturing tail behavior in lifetime distributions. This paper introduces a novel repetitive sampling plan (RSP) for life tests based on percentiles of the Half-Normal Distribution (HND). The plan is designed to verify that a specified quantile of the product lifetime exceeds a predefined standard. The design parameters, namely the sample size, acceptance number, and rejection number, are obtained through an optimization model that minimizes the Average Sample Number (ASN) while ensuring that both the producer’s risk and the consumer’s risk constraints are satisfied. Comprehensive tables are presented for various practical scenarios, examining the effects of the percentile ratio, termination time multiplier, and life percentile on the performance of plan. A comparative analysis demonstrates that the proposed RSP consistently requires a smaller ASN than the comparable single sampling plan, confirming its superior efficiency in reducing inspection effort and cost. The practical utility of the methodology is illustrated through a real-life example using software reliability data, showcasing its straightforward implementation and significant advantages for quality assurance in industrial settings
Development of a Repetitive Control Chart for Monitoring Processes with Dagum-Distributed Data
Get PDFThis paper presents a repetitive control chart designed for monitoring processes where the quality characteristic follows a Dagum distribution a flexible, skewed distribution often used in income, finance, and reliability data. Traditional control charts assume normality, resulting in poor performance with heavy-tailed or skewed distributions. To address this, we introduce a repetitive control chart based on quantiles of the Dagum distribution. The approach includes deriving control limits, implementing an optimised repetitive sampling scheme, and evaluating performance using ARL. Simulation studies demonstrate that the proposed chart outperforms existing charts in detecting small to moderate shifts in data distributed according to a Dagum distribution
On the Mathematical Expectation of the Sample Variance in Simple Sampling Technique
Get PDFDrawing random samples is the core of modern life jobs. In manufacturing, it is important to inspect deficiencies by only sampling items from a production line, to meet quality worldwide standards and to maintain sufficient statistical quality control. Furthermore, in today\u27s survey research, the theory of sampling technique is foundational to ensure that all inquired and essential information is gathered. In effect, one may name thousands of practical applications that rely on taking samples, like climatic studies, industry, ecology, and so on. In effect, many studies were designed and proposed in searching for an effective sampling technique. It is, in fact, both an art and a robust science. So many strategies and considerations were plotted to determine the proper sample size and the proper sampling technique, like simple sampling and stratified sampling. This paper is a brief study focusing on the behaviour of the mathematical expectation of the sample variance in sampling without replacement and in sampling with replacement. Formally, we show that when sampling is with replacement, there exists a crucial difference between the two situations, namely, distinct samples and indistinct samples. Namely, by a series of simulation studies and a famous historical example, it will be shown that there is a faulty fact concerning the unbiasedness of sample variance when drawing indistinct samples with replacement
Power Generalized KM-Transformation for Non-Monotone Failure Rate Distribution
Get PDFA more useful transformation model, KM Transformation, for reliability and lifetime data analysis is introduced by Kavya & Manoharan (2021). Power generalization technique is the best approach for analysing a parallel system. In this article, we present a new transformation called Power Generalized KM-Transformation (PGKM) to obtain a more appropriate model while monotone and non-monotone behaviour for the failure rate function occurs. We derived the moments, moment generating function, characteristic function, quantiles, etc. for the PGKM transformation of Exponential distribution (PGKME). Distributions of minimum and maximum are obtained. Estimation of parameters of the PGKME distribution is performed via maximum likelihood method, method of moment, and least square estimation method. A simulation study is performed to validate the maximum likelihood estimator (MLE). Analysis of three sets of real data is provided