EVALUATING CLUSTER EFFECTS IN MALARIA SURVIVAL ANALYSIS WITH A SIMULATED EXTENDED COX MODEL

One of the disorders of the eye that may occur to the diabetes patients is diabetic retinopathy. Diabetic retinopathy can cause vision loss and even blindness to the diabetes patients. At first, diabetic retinopathy may not have any symptoms at all. But diabetic retinopathy is the disorder which cause of blindness besides of cataracts, glaucoma and macular degeneration. The objective of this research was to determine the factors that can be used to delay diabetic retinopathy. There are several covariates that used in this research. One of the survival analysis method that can be used is Cox Proportional Hazard model. However, in this research, the result of Cox Proportional Hazard model showed that some covariates are not significant in the Cox Proportional Hazard model and the model did not fulfil the assumption, that is a constant hazard ratio over time. Therefore, an analysis was carried out using the Extended Cox Model. The results of Extended Cox model showed that all variables are concede a significant effect in delaying diabetic retinopathy in the Extended Cox model. Therefore, the Extended Cox model is more appropriate in this research than Cox Proportional Hazard model.

W.Q. Meeker and L.A. Escobar famous book Statistical Methods for Reliability Data [26] is a very well-known reference for all engineers and researchers who are interested in reliability problems. W.Q. Meeker has a long experience in modeling and solving degradation problems with the most complex features, so that it is a pleasure for me to participate in this volume in his honor. For a long time, survival data analysis and reliability studies walked their way parallel without much interpenetration. But nowadays, impulsed by several people among which Bagdonavicius and Nikulin [3, 4], one is aware of the multiple links between reliability and survival analysis, acknowledging still for some specificities. Many parametric models are available, as well as large classes of models like accelerated models, mainly in use in reliability, and extended Cox model [11], that are the favorite for survival data which have parametric as well as semi-parametric versions. In the recent years, there was an increasing interest for purely nonparametric approaches. Their advantage is that they are supposed to be able to adjust any possible data set through a vast class of regular functions. The drawbacks are first that there is generally a lack of easy interpretation for practical purposes and second that proving the required properties of the inference procedures like consistency, for example, is not trivial when censoring and truncation are present (Huber et al. [18], [19]), which is often true in the medical field. The result is that the justification of some proposed procedures is only through some simulations without any theoretical proof of their properties. What I would like to emphasize in this chapter is the need for a robust approach to survival data analysis, which means using robust procedures for flexible parametric models, still valid when the observations follow a model close, but not exactly equal, to the assumed model [22]. This always seemed to me a good compromise between a purely parametric approach and a purely nonparametric one. One of the most interesting chapter on robustness in survival analysis is the one by Kosorok et al. [24], which tackles the case of a possibly misspecified frailty model.

Timely monitoring of trends in long-term patient survival is an important task of cancer registries. Recently, a new method, denoted period analysis, has been proposed to enhance up-to-date monitoring of survival. The authors assessed the use of period analysis for advanced detection of time trends in long-term cancer patient survival based on data from the nationwide Finnish Cancer Registry by comparing estimates of 10-, 15-, and 20-year relative survival rates obtained by period analysis and by traditional (cohort) analysis of survival at various points of time between 1953 and 1997. Time trends are graphically displayed for the 15 most common forms of cancer. Long-term survival rates strongly improved over time for most forms of cancer. The slope and shape of trend curves obtained by period analysis are very similar to those obtained by traditional survival analysis. However, detection of progress in 10-, 15-, and 20-year survival rates of newly diagnosed patients could have been advanced by 5-10 years, 10-15 years, and 15-20 years, respectively, with the use of period analysis rather than traditional cohort survival analysis. The authors conclude that period analysis should be routinely used to advance detection of progress in long-term cancer patient survival.

Introduction. In medicine and related industries, bioinspired approaches are used for the survival analysis, among which the Cox regression model holds a specific place. The practice of its application is described in the theoretical and applied literature. However, a significant drawback of this method requires careful study. The fact is that the features correlate with the hazard function linearly, and the model does not use more complex dependences. This causes some difficulties in studying survival analysis. The presented work is aimed at solving this problem. The object of study is the extended Cox model, in which the hazard function includes a nonlinear combination of features.Materials and Methods. A database of prostate cancer patients was used, since this is a common diagnosis in global oncology. A class of extended Cox models with an additive/multiplicative hazard function was defined. To solve the problem using the optimization method, a fitness function was constructed that evaluated the results of prognosis, the number of features, and the degree of overtraining of the model — the complexity and load of the compiled hazard function. An algorithm of pollinating ants has been developed to optimize the fitness function. It simulates the reproduction of flowering plants using pollinating insects and consists of three parts: an ant colony algorithm, a genetic algorithm, and an ant pollinator algorithm. The quality of training of the Cox model was assessed by C-index.Results. A metaheuristic algorithm for ant pollinator optimizing was proposed, providing for the construction of hazard functions of the extended Cox model. The set of parameters for training the standard Cox model was the entire set of features used: TNM, prostate-specific antigen doubling time (PSADT), Gleason score, serum PSA concentration at diagnosis, patient age and education, Rh factor. C-index value of the trained model was 0.853691. The extended Cox model with the found additive/multiplicative hazard function had a higher C-index value — 0.856241 with a smaller number of features used (TNM, PSADT, and Gleason score). In terms of quality, this approach is not inferior to or superior to the classical Cox model. Reducing the number of features involved should improve the efficiency of medical decisions and speed up the start of treatment.Discussion and Conclusion. The presented algorithm for constructing survival analysis models increased the accuracy of predicting the occurrence of a terminal event, and reduced the number of features used for this purpose. The difference in accuracy for the studied data set seemed insignificant — C-index increased from 0.853691 to 0.856241 (by 0.3%). At this, the number of features taken into account was reduced from 7 to 3 (by 57.1%). Consequently, the proposed method effectively solves the problem of feature selection, and can be applied to improve the quality of prognostication.

Traditional survival analysis was developed to investigate the occurrence and timing of a single event, but researchers have recently begun to ask questions about the order and timing of multiple events. A multiple event process survival mixture model is developed here to analyze nonrepeatable events measured in discrete-time that may occur at the same point in time. Building on both traditional univariate survival analysis and univariate survival mixture analysis, the model approximates the underlying multivariate distribution of hazard functions via a discrete-point finite mixture in which the mixing components represent prototypical patterns of event occurrence. The model is applied in an empirical analysis concerning transitions to adulthood, where the events under study include parenthood, marriage, beginning full-time work, and obtaining a college degree. Promising opportunities, as well as possible limitations of the model and future directions for research, are discussed.

Background: Poisoning is a medical emergency, and is considered as a common cause of morbidity and mortality worldwide. In this study, the extended Cox model was used to determine the factors affecting the length of hospitalization in those with drug poisoning. Methods: The sample size included 2408 patients with opioids poisoning referring to the Emergency Department of Imam Reza Hospital in Mashhad, Iran from March 21, 2018 to March 20, 2019. Extended Cox model was fitted to determine the effect of five covariates (age, gender, marital status, type of poisoning, and type of opioids). In survival analysis, the length of hospitalization was considered as a time covariate (T). Patients’ recovery was also regarded as an event. Results: Of 2408 patients, 399 (16.6%) were censored and 2009 (83.4%) were uncensored. The risk of failure in complete recovery from poisoning in males was 1.189 times more compared to females. The risk of failure in complete recovery for the 15-24, 25-44, 45-64, and >65 years age groups were 0.277, 0.241, 0.289, and 0.481 times lower, respectively compared to the <2 years age group. For the married patients, the risk was 0.291 times lower compared to the divorced patients. For those poisoned accidentally, the risk was 0.490 times lower than compared to those poisoned intentionally. For those used methadone, morphine, opium, and tramadol, the risk was 1.195, 1.243, 1.193, and 1.147 times more, respectively compared to those used marijuana. By increasing the time (day) of hospital stay, the risk of failure for the 25-44, 45-64, and >65 years age groups were 1.024, 1.028, and 1.040 times more, respectively compared to the <2 years age group. Moreover, for those poisoned accidentally, the risk was 1.197 times more compared to those poisoned intentionally by the time (day) of hospital stay. Conclusion: The factors affecting the length of hospitalization in those poisoned by drugs are gender, marital status, and type of opioids covariate as time-independent covariate, and age and type of poisoning as time-dependent covariates. Since the complications of drug poisoning impose many costs on the health system, knowledge of these covariates can help take some measures for complete recovery of poisoned patients in a shorter length of hospital stay.

Background: Poisoning is a medical emergency, and is considered as a common cause of morbidity and mortality worldwide. In this study, the extended Cox model was used to determine the factors affecting the length of hospitalization in those with drug poisoning. Methods: The sample size included 2408 patients with opioids poisoning referring to the Emergency Department of Imam Reza Hospital in Mashhad, Iran from March 21, 2018 to March 20, 2019. Extended Cox model was fitted to determine the effect of five covariates (age, gender, marital status, type of poisoning, and type of opioids). In survival analysis, the length of hospitalization was considered as a time covariate (T). Patients’ recovery was also regarded as an event. Results: Of 2408 patients, 399 (16.6%) were censored and 2009 (83.4%) were uncensored. The risk of failure in complete recovery from poisoning in males was 1.189 times more compared to females. The risk of failure in complete recovery for the 15-24, 25-44, 45-64, and >65 years age groups were 0.277, 0.241, 0.289, and 0.481 times lower, respectively compared to the <2 years age group. For the married patients, the risk was 0.291 times lower compared to the divorced patients. For those poisoned accidentally, the risk was 0.490 times lower than compared to those poisoned intentionally. For those used methadone, morphine, opium, and tramadol, the risk was 1.195, 1.243, 1.193, and 1.147 times more, respectively compared to those used marijuana. By increasing the time (day) of hospital stay, the risk of failure for the 25-44, 45-64, and >65 years age groups were 1.024, 1.028, and 1.040 times more, respectively compared to the <2 years age group. Moreover, for those poisoned accidentally, the risk was 1.197 times more compared to those poisoned intentionally by the time (day) of hospital stay. Conclusion: The factors affecting the length of hospitalization in those poisoned by drugs are gender, marital status, and type of opioids covariate as time-independent covariate, and age and type of poisoning as time-dependent covariates. Since the complications of drug poisoning impose many costs on the health system, knowledge of these covariates can help take some measures for complete recovery of poisoned patients in a shorter length of hospital stay.

The aim of logistic regression is to estimate genetic effects on disease risk, while survival analysis aims to determine effects on age of onset. In practice, genetic variants may affect both types of outcomes. A cure survival model analyzes logistic and survival effects simultaneously. The aim of this simulation study is to assess the performance of logistic regression and traditional survival analysis under a cure model and to investigate the benefits of cure survival analysis. We simulated data under a cure model and varied the percentage of subjects at risk for disease (cure fraction), the logistic and survival effect sizes, and the contribution of genetic background risk factors. We then computed the error rates and estimation bias of logistic, Cox proportional hazards (PH), and cure PH analysis, respectively. The power of logistic and Cox PH analysis is sensitive to the cure fraction and background heritability. Our results show that traditional Cox PH analysis may erroneously detect age of onset effects if no such effects are present in the data. In the presence of genetic background risk even the cure model results in biased estimates of both the odds ratio and the hazard ratio. Cure survival analysis takes cure fractions into account and can be used to simultaneously estimate the effect of genetic variants on disease risk and age of onset. Since genome-wide cure survival analysis is not computationally feasible, we recommend this analysis for genetic variants that are significant in a traditional survival analysis.

Size-dependent quantum confinement effect on electronic structure of hydrogen-terminated carbon nanodiamond (ND) cluster has been investigated at the hybrid density functional theory level. Large scale all-electron calculations have been carried out for ND clusters of 0.76 nm (29 carbons) to 7.3 nm (20 959 carbons) in diameter. It is demonstrated that the quantum confinement effect in these clusters shows strong structural dependence. An important structural factor, describing the ratio between the number of atoms within the inner core and outer shell of the cluster, is identified which dictates the size-dependent behavior of the electronic states. For ND clusters with diameter smaller than 1.5 nm, the core-shell ratio changes fast with the increase in cluster size, and the evolution of electronic properties does not follow conventional quantum confinement models. For ND clusters exceeding the threshold of 1.5 nm in diameter, the change in the core-shell ratio saturates and quantum confinement effect becomes visible. Electronic states within the inner core and surface show different size dependence, but a general formula is proposed and describes their structure dependent quantum confinement effects. This formula provides useful insights into quantum confinement behavior in ND clusters, and thereby leads to important physical property information. The calculated electron effective masses for core and surface states of ND clusters are in very good agreement with the experiments.

This study provides an in-depth examination of the critical role that survival analysis plays across various disciplines, with a particular emphasis on its applications in clinical research, public policy, and economics. The research is designed to offer a comprehensive overview of traditional survival analysis methods, highlight emerging trends, explore practical applications, and discuss the challenges and future directions for the field. By conducting a thorough review of existing literature and analyzing contemporary advancements, this study employs a robust and methodical approach. Key findings suggest that traditional survival analysis techniques, such as the Kaplan-Meier estimator and the Cox (1072) proportional hazards model, continue to serve as foundational tools in the field. However, the integration of big data and advanced computational technologies has significantly enhanced the precision and broadened the applicability of survival analysis, facilitating more accurate predictions and wider applications. In clinical research, survival analysis remains indispensable for assessing patient outcomes and guiding treatment decisions. Furthermore, the study highlights the growing importance of cross-disciplinary collaborations, which are increasingly essential for addressing both ethical and methodological challenges, thereby enhancing the utility of survival analysis across various sectors. The study concludes that while traditional methods retain their relevance, the future of survival analysis will be shaped by the integration of modern computational tools and the promotion of cross-disciplinary collaborations. Recommendations include further exploration of machine learning and artificial intelligence within survival analysis, as well as encouraging collaborative efforts across diverse fields to address current challenges and expand the application of survival analysis in new and innovative ways.

Cancer causes immense suffering globally, and data constitute the cornerstone of cancer research. Analyzing data is pivotal, but manual analysis of vast datasets within constrained time frames is challenging and error-prone. Even minor inaccuracies can lead to false interpretations, affecting lives. This review explores the free, open-source, and widely acclaimed R software. Our goal was to facilitate data analysis and visualization in the scientific writing of clinical projects. R offers a wide range of features and packages for tasks like data manipulation, cleaning, analysis, and creating informative graphs, including traditional statistics, hypothesis testing, regression, time series, survival analysis, machine learning, and medical image analysis. These capabilities aid in accurate data analysis, facilitating a deeper understanding of cancer mechanisms and predicting outcomes. To prepare this review, we performed an online literature search in Scopus, PubMed, and Google for articles and books related to R software published between March 2012 and January 2024, using specific keywords such as “medical data analysis,” “RStudio,” “statistical software,” “clinical data management,” “R programming,” and “research tools.” Articles, books, and online sources lacking full-text options in English or complete information were excluded. A total of 66 articles and book chapters were retrieved, 22 were excluded, and 44 were included in this review. Through this article, our goal was to provide a user-friendly guide to employing R software for fundamental analysis with dummy data, making it accessible even to non-programmers. This will empower individuals to perform statistical analyses independently, contributing to cancer research with flexibility and accuracy.

BackgroundSkull base chordoma (SBC) is a rare, locally aggressive malignant bone tumor with a poor prognosis due to its location and recurrence. Despite advances in surgery and radiotherapy (RT), long-term survival remains uncertain. Traditional survival analyses are limited by their static nature, failing to capture the dynamic changes in survival probabilities over time. To address this, we applied conditional survival (CS) analysis for more precise evaluation of evolving survival rates in SBC patients.MethodsData of 717 SBC patients [2000–2019] from SEER (Surveillance, Epidemiology, and End Results) database were obtained. Using CS analysis, we evaluated survival probabilities over time and developed the first SBC-specific CS-nomogram. Key clinicopathological factors were incorporated into the model via least absolute shrinkage and selection operator (LASSO) and multivariate Cox analysis. The nomogram was validated with training and validation cohorts. Calibration curves, C-index, time-dependent receiver operating characteristic (ROC) curves and decision curve analysis (DCA) were used to evaluate model performance.ResultsCS analysis showed a steady overall survival (OS) improvement in SBC patients over time. The 10-year survival probability rose from 61% at diagnosis to 98% after 9 years. Eight clinicopathological factors, significant predictors of OS, were incorporated into the CS-nomogram. The model had robust predictive accuracy, with C-index values of 0.703 (training) and 0.731 (validation). Calibration curves and DCA indicated good agreement between predicted and actual outcomes with significant net clinical benefit.ConclusionsCombining CS analysis and a nomogram, we developed a new tool for dynamic, individualized survival predictions in SBC patients. The CS-nomogram can improve clinical decision-making and patient counseling, bringing hope and more precise prognostic evaluations for long-term survivors.

BackgroundSurvival prediction for cervical cancer is usually based on its stage at diagnosis or a multivariate nomogram. However, few studies cared whether long-term survival improved after they survived for several years. Meanwhile, traditional survival analysis could not calculate this dynamic outcome. We aimed to assess the improvement of survival over time using conditional survival (CS) analysis and developed a novel conditional survival nomogram (CS-nomogram) to provide individualized and real-time prognostic information.MethodsCervical cancer patients were collected from the Surveillance, Epidemiology, and End Results (SEER) database. The Kaplan–Meier method estimated cancer-specific survival (CSS) and calculated the conditional CSS (C-CSS) at year y+x after giving x years of survival based on the formula C-CSS(y|x) =CSS(y+x)/CSS(x). y indicated the number of years of further survival under the condition that the patient was determined to have survived for x years. The study identified predictors by the least absolute shrinkage and selection operator (LASSO) regression and used multivariate Cox regression to demonstrate these predictors’ effect on CSS and to develop a nomogram. Finally, the CSS possibilities predicted by the nomogram were brought into the C-CSS formula to create the CS-nomogram.ResultsA total of 18,511 patients aged <65 years with cervical cancer from 2004 to 2019 were included in this study. CS analysis revealed that the 15-year CSS increased year by year from the initial 72.6% to 77.8%, 84.5%, 88.8%, 91.5%, 93.5%, 94.8%, 95.7%, 96.4%, 97.3%, 98.0%, 98.5%, 99.1%, and 99.4% (after surviving for 1-13 years, respectively), and found that when survival exceeded 5-6 years, the risk of death from cervical cancer would be less than 5% in 10-15 years. The CS-nomogram constructed using tumor size, lymph node status, distant metastasis status, and histological grade showed strong predictive performance with a concordance index (C-index) of 0.805 and a stable area under the curve (AUC) between 0.795 and 0.816 over 15 years.ConclusionsCS analysis in this study revealed the gradual improvement of CSS over time in long-term survived cervical cancer patients. We applied CS to the nomogram and developed a CS-nomogram successfully predicting individualized and real-time prognosis.

BART-Survival is a Python package that allows time-to-event (survival) analyses in discrete-time using the non-parametric machine learning algorithm, Bayesian Additive Regression Trees (BART). BART-Survival combines the performance of the BART algorithm with the complementary data and model formatting required to complete the survival analyses. The library contains a convenient application programming interface (API) that allows a simple approach when using the library for survival analyses, while maintaining capabilities for added complexity when desired. The package is intended for analysts exploring use of flexible non-parametric alternatives to traditional (semi-)parametric survival analyses.

BackgroundComposite outcomes that weight each component equally are commonly used to study treatment effects. We hypothesized that each component of a composite outcome would differentially affect patients’ overall health-related quality of life (HRQL).MethodsWe tested our hypothesis using data from 2 published clinical studies of treatment for heart failure, one comparing metformin and sulfonylurea and the other comparing digoxin and placebo. We applied the quality-adjusted survival (QAS) approach, which incorporates HRQL data to accommodate differential weights for 2 components (in this analysis, death or admission to hospital) of a commonly used composite end point. For each of the 2 studies, the composite outcome was partitioned into its components, to which utility weights derived from the literature were assigned. Total QAS time determined for each treatment by the QAS analysis was compared with the results from traditional survival analyses based on Cox proportional hazards regression.ResultsIn the observational study of metformin in heart failure, the risk of the composite outcome of death or admission to hospital was lower for those receiving metformin therapy than for those who received sulfonylurea (event rate 160 [77%] v. 658 [85%]; hazard ratio [HR] 0.83, 95% confidence interval [CI] 0.70–0.99). With traditional survival analysis, the net gain was 0.82 years (95% CI 0.26–1.37), whereas the difference in QAS time was less, at 0.54 years (95% CI 0.20–0.89). In the randomized trial of digoxin therapy, the risk of the composite outcome was lower for those receiving the intervention than for those receiving placebo (event rate 1291 [38%] v. 1041 [31%]; HR 0.75, 95% CI 0.69–0.82). With traditional survival analysis, the net gain was 0.06 years (95% CI 0.02–0.16), whereas the difference in QAS time was greater, at 0.11 years (95% CI 0.06–0.16).InterpretationStudies that assume equal weights for the components of composite outcomes may overestimate or underestimate treatment effects. By incorporating HRQL into survival analyses, the impact of the various components of the outcome can be assessed more directly.