Estimation Of Survival Function Research Articles

Competing risks and multivariate outcomes in epidemiological and clinical trial research.

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women's Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

Random forests for survival data: which methods work best and under what conditions?

Few systematic comparisons of methods for constructing survival trees and forests exist in the literature. Importantly, when the goal is to predict a survival time or estimate a survival function, the optimal choice of method is unclear. We use an extensive simulation study to systematically investigate various factors that influence survival forest performance - forest construction method, censoring, sample size, distribution of the response, structure of the linear predictor, and presence of correlated or noisy covariates. In particular, we study 11 methods that have recently been proposed in the literature and identify 6 top performers. We find that all the factors that we investigate have significant impact on the methods' relative accuracy of point predictions of survival times and survival function estimates. We use our results to make recommendations for which methods to use in a given context and offer explanations for the observed differences in relative performance.

Improvement of Midpoint Imputation for Estimation of Median Survival Time for Interval-Censored Time-to-Event Data.

Progression-free survival (PFS) is used to evaluate treatment effects in cancer clinical trials. Disease progression (DP) in patients is typically determined by radiological testing at several scheduled tumor-assessment time points. This produces a discrepancy between the true progression time and the observed progression time. When the observed progression time is considered as the true progression time, a positively biased PFS is obtained for some patients, and the estimated survival function derived by the Kaplan-Meier method is also biased. While the midpoint imputation method is available and replaces interval-censored data with midpoint data, it unrealistically assumes that several DPs occur at the same time point when several DPs are observed within the same tumor-assessment interval. We enhanced the midpoint imputation method by replacing interval-censored data with equally spaced timepoint data based on the number of observed interval-censored data within the same tumor-assessment interval. The root mean square error of the median of the enhanced method is almost always smaller than that of the midpoint imputation regardless of the tumor-assessment frequency. The coverage probability of the enhanced method is close to the nominal confidence level of 95% in most scenarios. We believe that the enhanced method, which builds upon the midpoint imputation method, is more effective than the midpoint imputation method itself.

Meteorological and Agricultural Drought Risk Assessment via Kaplan–Meier Survivability Estimator

Dry periods and drought are inherent natural occurrences. However, due to the increasing pressures of global warming and climate change, these events have become more frequent and severe on a global scale. These phenomena can be traced with various indicators and related indices proposed by various scholars. In general, drought risk assessment is done by modeling these indicators and determining the drought occurrence probabilities. The proposed adaptation introduces the “Kaplan–Meier estimator”, a non-parametric statistic traditionally used in medical contexts to estimate survival functions from lifetime data. The study aims to apply this methodology to assess drought risk by treating past droughts as “events” and using drought indicators such as the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI). Mapping these results for a better understanding of the drought risks on larger spatial scales such as a river basin is also within the expected outcomes. The adapted method provides the probability of non-occurrence, with inverted results indicating the likelihood of drought occurrence. As a case study, the method is applied to SPI and SPEI values at different time steps (3, 6, and 12 months) across 27 meteorological stations in the Gediz River Basin, located in Western Turkey—a region anticipated to be profoundly affected by global climate change. The results are represented as the generated drought risk maps and curves, which indicate that (i) drought risks increase as the considered period extends, (ii) drought risks decrease as the utilized indicator timescales increase, (iii) locally plotted drought curves indicate higher drought risks as their initial slope gets steeper. The method used enables the generation of historical evidence based spatially distributed drought risk maps, which expose more vulnerable areas within the river basin.

A Framework for Leveraging Machine Learning Tools to Estimate Personalized Survival Curves

The conditional survival function of a time-to-event outcome subject to censoring and truncation is a common target of estimation in survival analysis. This parameter may be of scientific interest and also often appears as a nuisance in nonparametric and semiparametric problems. In addition to classical parametric and semiparametric methods (e.g., based on the Cox proportional hazards model), flexible machine learning approaches have been developed to estimate the conditional survival function. However, many of these methods are either implicitly or explicitly targeted toward risk stratification rather than overall survival function estimation. Others apply only to discrete-time settings or require inverse probability of censoring weights, which can be as difficult to estimate as the outcome survival function itself. Here, we employ a decomposition of the conditional survival function in terms of observable regression models in which censoring and truncation play no role. This allows application of an array of flexible regression and classification methods rather than only approaches that explicitly handle the complexities inherent to survival data. We outline estimation procedures based on this decomposition, empirically assess their performance, and demonstrate their use on data from an HIV vaccine trial. Supplementary materials for this article are available online.

Deep survival analysis model for incident clearance time prediction

Incident clearance time prediction is a key task for traffic incident management. A hazard-based duration model is a prevalent approach for predicting and analyzing the incident clearance time, which considers “duration dependence” of which the probability of an incident clearance ending depends on the time the clearance has lasted. However, the performance is limited due to its model assumptions for clearance time distribution, linear relationship, and the time-invariant effects of influential factors. This study proposes a deep survival analysis model that relaxes the assumptions of the hazard-based duration model while considering duration dependence based on a multi-task deep neural network (MTDNN). The MTDNN can consider the duration dependence when predicting incident clearance time by simultaneously estimating the survival function based on the concept of multi-task learning. The effects of influential factors on the prediction of MTDNN are also investigated using a post-analysis method. The proposed model is evaluated by its predictive performance and the estimated effects of influential factors using the freeway incident data collected in Korea from 2014 to 2019. These evaluations show that, compared to the baseline hazard-based duration model, the proposed MTDNN improves the predictive performance by 29.7% in terms of mean absolute percent error, and outperforms all statistical and machine learning models for both incident clearance time prediction and the survival function estimation. The analysis of the influential factors reveals that the hazard-based duration model and MTDNN had major influencing factors in common, but the impact of some factors is considerably different.

Health Disparities in Time to Diagnosis and Survival Post-Diagnosis of Cirrhosis in Individuals with Alcohol Use Disorder: A Retrospective Cohort Study

ObjectiveThis study investigates the impact of race, gender, and ethnicity on the progression from diagnosis to cirrhosis and subsequent survival in patients with alcohol use disorder, with a specific focus on identifying potential disparities in health outcomes. MethodEmploying a STROBE-compliant, retrospective cohort design, we analyzed data from patients diagnosed with alcohol use disorder from January 2000 to December 2022, using the University of California Health Data Warehouse. We estimated survival functions using the Kaplan-Meier method and assessed demographic associations using both bivariate and multivariate Cox proportional hazards models. ResultsThe analysis highlighted a significant association between Hispanic ethnicity and an accelerated timeline for both the diagnosis of alcohol-related cirrhosis following diagnosis of alcohol use disorder and mortality post-cirrhosis diagnosis. The former was evident only in bivariate analysis, but the latter association persisted in multivariate analysis. Gender did not demonstrate a significant correlation with the time to these outcomes, though multiracial identification emerged as a protective factor. ConclusionsThe study reveals critical health disparities in the progression and outcomes of cirrhosis, particularly between Hispanic and non-Hispanic patients. These findings underscore the urgent need for targeted healthcare interventions and policies that address these disparities. Future research should delve deeper into the multifaceted factors influencing these outcomes, facilitating the development of more nuanced and effective prevention and treatment strategies for alcohol use disorder and its severe complications.

Camrelizumab combined with apatinib for unresectable, metastatic esophageal squamous cell carcinoma: a single-center, single-arm, prospective study.

The prognosis for esophageal cancer (EC), a common malignant tumor, is poor. The new oral small-molecule tyrosine kinase inhibitor apatinib has shown an excellent therapeutic effect on treating EC. Camrelizumab is a humanized programmed death 1 (PD-1) inhibitor with high affinity. Immune checkpoint inhibitors combined with chemotherapy have become the standard first-line treatment for advanced EC. The new combination strategy of anti-angiogenic therapy combined with immunotherapy has great application prospects in the treatment of tumors. We aimed to assess camrelizumab in combination with apatinib as a new combination regimen for advanced or metastatic esophageal squamous cell carcinoma (ESCC). In this study, we recruited patients with an Eastern Cooperative Oncology Group (ECOG) performance status ≤2, with pathologically confirmed unresectable, locally advanced, locally recurrent, or metastatic ESCC. Each patient received an intravenous infusion of camrelizumab 200 mg and oral administration of apatinib 250 mg once a day, every 21 days, as a cycle until disease progression, intolerance, or death. The primary endpoint was the objective response rate (ORR), while the Kaplan-Meier method and LIFETEST procedure were used to estimate survival functions for overall survival (OS) and progression-free survival (PFS). The National Cancer Institute Common Terminology Criteria for Adverse Events, version 4.03, was used to evaluate adverse events. Between December 1, 2019 and July 31, 2022, 35 patients were enrolled, with 29 patients in the efficacy and safety analysis. The ORR was 34.5%, and the disease control rate (DCR) reached 82.8%. Median OS was 13.8 months (95% CI: 11.2-16.2), and the estimated 6-, 9-, and 12-month OS rates were 85.5% (95% CI: 65.7-94.3%), 80.9% (95% CI: 60.3-91.5%), and 67.0% (95% CI: 43.8-82.4%), respectively. Median PFS was 9.5 months (95% CI: 7.0-13.6). The most prominent grade ≥3 adverse events associated with treatments were alanine aminotransferase (ALT) increase (10.3%), hypertension (10.3%), and reactive cutaneous capillary endothelial proliferation (CCEP) (6.9%), and no deaths occurred due to adverse events. Among patients with advanced or metastatic ESCC, camrelizumab combined with apatinib showed a reasonable remission rate and survival benefit with a manageable safety profile.

Estimating several survival functions under uniform stochastic ordering

El Barmi and Mukerjee (2016, Journal of Multivariate Analysis 144, 99–109) studied the estimation of survival functions of k samples under uniform stochastic ordering constraints. There were two crucial errors in the consistency proof. Here, we provide alternative estimators and show consistency.

Revascularization Outcomes Stratified by Glycemic Control in Patients with Diabetes Mellitus and Chronic Limb-Threatening Ischemia

The prevalence of chronic limb-threatening ischemia (CLTI) has increased alongside rising rates of diabetes mellitus (DM). While diabetic patients with CLTI have worse outcomes compared to patients without diabetes, conflicting data exist on the relationship between the severity of DM and CLTI outcomes. Close inspection of the relationship between DM severity and outcomes in CLTI may benefit surgical decision-making and patient education. We retrospectively reviewed patients who received endovascular intervention or surgical bypass for CLTI at our multidisciplinary Limb Preservation Program from 2013 to 2019 to collect patient characteristics using Society for Vascular Surgery (SVS) reporting standards, arterial lesion characteristics from recorded angiograms, and outcomes, including survival, amputation, wound healing, and revascularization patency. Controlled DM was defined as SVS Grade 1 (controlled, not requiring insulin) and Grade 2 (controlled, requiring insulin), while uncontrolled DM was defined as SVS Grade 3 (uncontrolled), and DM severity was assessed using preoperative hemoglobin A1c (HgbA1c) values. Product-limit Kaplan-Meier was used to estimate survival functions. Univariable Cox proportional hazards analyses guided variable selection for multivariable analyses. Our Limb Preservation Program treated 177 limbs from 141 patients with DM. Patients with uncontrolled DM were younger (60.44±10.67 vs. 65.93±10.89years old, P=0.0009) and had higher HgbA1c values (8.97±1.85% vs. 6.79±1.10%, P<0.0001). Fewer patients with uncontrolled DM were on dialysis compared to patients with controlled DM (15.6% vs. 30.9%, P=0.0278). By Kaplan-Meier analysis, DM control did not affect time to mortality, limb salvage, wound healing, or loss of patency. However, multivariable proportional hazards analysis demonstrated increased risk of limb loss in patients with increasing HgbA1C (hazard ratio (HR)=1.96 [1.42-2.80], P<0.0001) or dialysis dependence (HR=15.37 [3.44-68.73], P=0.0003), increased risk of death in patients with worsening pulmonary status (HR=1.70 [1.20-2.39], P=0.0026), and increased risk of delayed wound healing in patients who are male (HR=0.48 [0.29-0.79], P=0.0495). No independent association existed between loss of patency with any of the variables we collected. Patients with uncontrolled DM, as defined by SVS reporting standards, do not have worse outcomes following revascularization for CLTI compared to patients with controlled DM. However, increasing HgbA1c is associated with a greater risk for early amputation. Before revascularization, specific attention to the level of glycemic control in patients with DM is important, even if DM is "controlled." In addition to aggressive attempts at improved glycemic control, those with elevated HgbA1c should receive careful education regarding their increased risk of amputation despite revascularization. Future work is necessary to incorporate the severity of DM into risk models of revascularization for the CLTI population.

Statistical inference for time-to-event data in non-randomized cohorts with selective attrition.

In multi-season clinical trials with a randomize-once strategy, patients enrolled from previous seasons who stay alive and remain in the study will be treated according to the initial randomization in subsequent seasons. To address the potentially selective attrition from earlier seasons for the non-randomized cohorts, we develop an inverse probability of treatment weighting method using season-specific propensity scores to produce unbiased estimates of survival functions or hazard ratios. Bootstrap variance estimators are used to account for the randomness in the estimated weights and the potential correlations in repeated events within each patient from season to season. Simulation studies show that the weighting procedure and bootstrap variance estimator provide unbiased estimates and valid inferences in Kaplan-Meier estimates and Cox proportional hazard models. Finally, data from the INVESTED trial are analyzed to illustrate the proposed method.

Biomechanical comparison of titanium alloy additively manufactured and conventionally manufactured plate-screw constructs

ABSTRACTAimTo biomechanically compare the bending stiffness, strength, and cyclic fatigue of titanium additively manufactured (AM) and conventionally manufactured (CM) limited contact plates (LCP) of equivalent dimensions using plate-screw constructs.MethodsTwenty-four 1.5/2.0-mm plate constructs (CM: n = 12; AM: n = 12) were placed under 4-point bending conditions. Data were collected during quasi-static single cycle to failure and cyclic fatigue testing until implants plastically deformed or failed. Bending stiffness, bending structural stiffness, and bending strength were determined from load–displacement curves. Fatigue life was determined as number of cycles to failure. Median test variables for each method were compared using the Wilcoxon rank sum test within each group. Fatigue data was also analysed by the Kaplan–Meier estimator of survival function.ResultsThere was no evidence for a difference in bending stiffness and bending structural stiffness between AM and CM constructs. However, AM constructs exhibited greater bending strength (median 3.07 (min 3.0, max 3.4) Nm) under quasi-static 4-point bending than the CM constructs (median 2.57 (min 2.5, max 2.6) Nm, p = 0.006). Number of cycles to failure under dynamic 4-point bending was higher for the CM constructs (median 164,272 (min 73,557, max 250,000) cycles) than the AM constructs (median 18,704 (min 14,427, max 33,228) cycles; p = 0.02). Survival analysis showed that 50% of AM plates failed by 18,842 cycles, while 50% CM plates failed by 78,543 cycles.Conclusion and clinical relevanceAdditively manufactured titanium implants, printed to replicate a conventional titanium orthopaedic plate, were more prone to failure in a shorter fatigue period despite being stronger in single cycle to failure. Patient-specific implants made using this process may be brittle and therefore not comparable to CM orthopaedic implants. Careful selection of their use on a case/patient-specific basis is recommended.

Analysis of cox proportional hazard model for dropout students in university: case study from SIMAD university

PurposeThe main purpose of this study is to evaluate the extent of dropout students and identify the relationship between risk factors of dropout and the survival time of students.Design/methodology/approachThe Kaplan–Meier estimator (KM), also known as the product-limit technique, is a nonparametric model function that is commonly used in estimating survival function events (Kaplan and Meier, 1958). The survival function's Kaplan–Meier estimators are used to estimate and graph survival probabilities as a function of time, as well as explanatory data analysis (EDA) for the survival data, including the median survival time, and compare for two or more of the survival events. In addition, Cox proportional hazards model is employed for modelling purpose.FindingsResults of the Kaplan–Meier curves show that male students have lower survival rates than female, researchers have found that there is a difference between the survival times of the student's school types, results show students from English-based schools are higher than Arabic-based schools as suggested by the survival curve. Similarly, there is a difference between the survival times of students aging equal or greater than 25 and students aging less than 25 and survival function estimates of dropout according to high school grade marks has huge difference. These results were confirmed using log rank test as age, school type and marks were statistically significantly different while gender is not statistically significant.Research limitations/implicationsThere is no study of this kind from the Somalia context about the student's dropout. Subsequent to the outbreak of civil war in 1988 and the collapse of the central government in 1991, all public social services in Somalia including education centers were severely disrupted.Originality/valueThe statistical methods discussed in the previous section will be applied on a real dataset obtained from different offices of the university; most of the data were extracted from faculty of economics office and admission and record office. The data set comprised of 70 students from SIMAD university, consists of full-time faculty of economics students who enrolled at the university in the academic year of 2017–2018 until two years of diploma, students either complete 24 months of diploma or leave the university and that is the event of interest.

Estimating a discrete distribution subject to random left-truncation with an application to structured finance

Proper econometric analysis should be informed by data structure. Many forms of financial data are recorded in discrete-time and relate to products of a finite term. If the data is sampled from a financial trust, it will often be further subject to random left-truncation. The estimation of a distribution function from left-truncated data has been extensively addressed, but the case of discrete data over a known, finite number of possible values has not yet been thoroughly investigated. A precise discrete framework and suitable sampling procedure for the Woodroofe-type estimator for discrete data over a known, finite number of possible values is therefore established. Subsequently, the resulting vector of hazard rate estimators is proved to be asymptotically normal with independent components. Asymptotic normality of the survival function estimator is then established. Sister results for the left-truncating random variable are also proved. Taken together, the resulting joint vector of hazard rate estimates for the lifetime and left-truncation random variables is proved to be the maximum likelihood estimate of the parameters of the conditional joint lifetime and left-truncation distribution given the lifetime has not been left-truncated. A hypothesis test for the shape of the distribution function based on our asymptotic results is derived. Such a test is useful to formally assess the plausibility of the stationarity assumption in length-biased sampling. The finite sample performance of the estimators is investigated in a simulation study. Applicability of the theoretical results in an econometric setting is demonstrated with a subset of data from the Mercedes-Benz 2017-A securitized bond.

Inference for Treatment-Specific Survival Curves Using Machine Learning

ABSTRACT In the absence of data from a randomized trial, researchers may aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves, that is, the survival curves were the population under study to be assigned to receive the treatment or not. Under certain conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival curve can be identified with a covariate-adjusted survival curve. In this article, we propose a novel cross-fitted doubly-robust estimator that incorporates data-adaptive (e.g., machine learning) estimators of the conditional survival functions. We establish conditions on the nuisance estimators under which our estimator is consistent and asymptotically linear, both pointwise and uniformly in time. We also propose a novel ensemble learner for combining multiple candidate estimators of the conditional survival estimators. Notably, our methods and results accommodate events occurring in discrete or continuous time, or an arbitrary mix of the two. We investigate the practical performance of our methods using numerical studies and an application to the effect of a surgical treatment to prevent metastases of parotid carcinoma on mortality. Supplementary materials for this article are available online.

The natural history of chronic limb-threatening ischemia after technical failure of endovascular intervention

ObjectivesThe treatment for chronic limb-threatening ischemia (CLTI) has changed dramatically in the last few decades with a shift toward an endovascular-first approach and aggressive revascularization to achieve limb salvage. As the size of the CLTI population and intervention rates increase, patients will continue to experience technical failure (TF). Here, we describe the natural history of patients after TF of endovascular intervention for CLTI. MethodsWe conducted a retrospective cohort study of patients with CLTI who attempted endovascular intervention or bypass at our multidisciplinary limb salvage center from 2013 to 2019. Patient characteristics were collected according to the Society for Vascular Surgery’s reporting standards. Primary outcomes included survival, limb salvage, wound healing, and revascularization patency. Product-limit Kaplan-Meier estimated survival functions for these outcomes, and between-group comparisons were made using Mantel-Cox log-rank nonparametric tests. ResultsWe identified 242 limbs from 220 unique patients who underwent primary bypass (n = 30) or attempted endovascular intervention (n = 212) at our limb salvage center. Endovascular intervention was a TF in 31 (14.6%) limbs. After TF, 13 limbs underwent secondary bypass and 18 limbs were managed medically. Patients who experienced TF tended to be older (P < .001), male (P = .003), current tobacco users (P = .014), have longer lesions (P = .001), and have chronic total occlusions of target arteries (P < .001) as compared with those who experienced technical success. Furthermore, the TF group had worse limb salvage (P = .047) and slower wound healing (P = .028), but their survival was not different. Survival, limb salvage, and wound healing were not different in patients who received secondary bypass or medical management after TF. The secondary bypass group was older (P = .012) and had a lower prevalence of tibial disease (P = .049) than the primary bypass group and trended toward decreased survival, limb salvage, and wound healing (P = .059, P = .083, and P = .051, respectively). ConclusionsIncreased age, male sex, current tobacco use, longer arterial lesions, and occluded target arteries are associated with TF of endovascular intervention. Limb salvage and wound healing are relatively poor after TF of endovascular intervention, but survival appears comparable with patients who experience technical success. Secondary bypass may not always rescue patients after TF, though our sample size limits statistical power. Interestingly, patients who received a secondary bypass after TF trended toward decreased survival, limb salvage, and wound healing compared with primary bypass.

Copula graphic estimation of the survival function with dependent censoring and its application to analysis of pancreatic cancer clinical trial.

In this article, we consider a survival function estimation method that may be suitable for analyses of clinical trials of cancer treatments whose prognosis is known to be poor such as pancreatic cancer treatment. Typically, these kinds of trials are not double-blind, and patients in the control group may drop out in more significant numbers than in the treatment group if their disease progresses (DP). If disease progression is associated with a higher risk of death, then censoring becomes dependent. To estimate the survival function with dependent censoring, we use copula-graphic estimation, where a parametric copula function is used to model the dependence in the joint survival function of the event and censoring time. In this article, we propose a novel method that one can use in choosing the copula parameter. As an application example, we estimate the survival function of the overall survival time of the KG4/2015 study, the phase 3 clinical trial of the efficacy of GV1001 as a treatment for pancreatic cancer. We provide both statistical and clinical pieces of evidence that support the violation of independent censoring. Applying the estimation method with dependent censoring, we obtain that the estimates of the median survival times are 339 days in the treatment group and 225.5 days in the control group. We also find that the estimated difference of the medians is 113.5 days, and the difference is statistically significant at the one-sided level with size 2.5.

An Expectation-Maximization Algorithm for Including Oncological COVID-19 Deaths in Survival Analysis.

We address the problem of how COVID-19 deaths observed in an oncology clinical trial can be consistently taken into account in typical survival estimates. We refer to oncological patients since there is empirical evidence of strong correlation between COVID-19 and cancer deaths, which implies that COVID-19 deaths cannot be treated simply as non-informative censoring, a property usually required by the classical survival estimators. We consider the problem in the framework of the widely used Kaplan-Meier (KM) estimator. Through a counterfactual approach, an algorithmic method is developed allowing to include COVID-19 deaths in the observed data by mean-imputation. The procedure can be seen in the class of the Expectation-Maximization (EM) algorithms and will be referred to as Covid-Death Mean-Imputation (CoDMI) algorithm. We discuss the CoDMI underlying assumptions and the convergence issue. The algorithm provides a completed lifetime data set, where each Covid-death time is replaced by a point estimate of the corresponding virtual lifetime. This complete data set is naturally equipped with the corresponding KM survival function estimate and all available statistical tools can be applied to these data. However, mean-imputation requires an increased variance of the estimates. We then propose a natural extension of the classical Greenwood's formula, thus obtaining expanded confidence intervals for the survival function estimate. To illustrate how the algorithm works, CoDMI is applied to real medical data extended by the addition of artificial Covid-death observations. The results are compared with the estimates provided by the two naïve approaches which count COVID-19 deaths as censoring or as deaths by the disease under study. In order to evaluate the predictive performances of CoDMI an extensive simulation study is carried out. The results indicate that in the simulated scenarios CoDMI is roughly unbiased and outperforms the estimates obtained by the naïve approaches. A user-friendly version of CoDMI programmed in R is freely available.

A new flexible regression model with application to recovery probability Covid-19 patients

The aim of this study is to propose a generalized odd log-logistic Maxwell mixture model to analyze the effect of gender and age groups on lifetimes and on the recovery probabilities of Chinese individuals with COVID-19. We add new properties of the generalized Maxwell model. The coefficients of the regression and the recovered fraction are estimated by maximum likelihood and Bayesian methods. Further, some simulation studies are done to compare the regressions for different scenarios. Model-checking techniques based on the quantile residuals are addressed. The estimated survival functions for the patients are reported by age range and sex. The simulation study showed that mean squared errors decay toward zero and the average estimates converge to the true parameters when sample size increases. According to the fitted model, there is a significant difference only in the age group on the lifetime of individuals with COVID-19. Women have higher probability of recovering than men and individuals aged ≥ 60 years have lower recovered probabilities than those who aged < 60 years. The findings suggest that the proposed model could be a good alternative to analyze censored lifetime of individuals with COVID-19.

Bed Allocation Optimization Based on Survival Analysis, Treatment Trajectory and Costs Estimations

The intensive care units are a key element of patient flow, but due to high demand and an alternating rate of arriving patients, these units are often challenged by insufficient capacity, very high expenses, and in some cases, an unfair distribution of resources. Proper allocation of resources to match demand is, therefore, a vital task for many wards in these units. The patient bed assignment problem consists of managing in the best possible way a set of beds with equipment to be assigned to a particular type of patient. However, in real-world scenarios, constraints like a possible treatment trajectory are violated in most cases. In this paper, we present a new approach for solving patient bed assignment problems constrained by targets on survival function estimation, cost estimation, and possible treatment trajectory estimation for patients with cardiovascular diseases. For survival function estimations, we used the nave estimator and Kaplan-Meier, and for treatment effect estimations, we used logistic regression and T-learning. Estimations of the three components are used as weights in a genetic algorithm. This technique allows for the consideration of various constraints, which, unlike other techniques, allows for the selection of dominant solutions as solutions that satisfy dominant constraints. In addition, we demonstrate the robustness of our approach by testing the algorithms with multiple classes of patients, testing multiple sets of parameters, and comparing our results with several similar research studies showing the added value of working on this management axis in hospitals using the new approach to bed allocation.