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Background The first trimester of pregnancy is critical for fetal development, making early antenatal care visits essential for timely check-ups and managing potential complications. However, delayed antenatal care initiation remains a public health challenge in sub-Saharan Africa, including Kenya. Therefore, this study aimed to assess and provide up-to-date information on time to first antenatal care visit and its predictors among women in Kenya, using data from the most recent 2022 Kenya Demographic and Health Survey (KDHS). Methods This community-based cross-sectional study analyzed data from 19,530 birth histories in the 2022 Kenya Demographic and Health Survey (KDHS). The primary outcome was the timing of the first antenatal care (ANC) visit, classified as timely if it occurred in the first trimester. Shared frailty survival models were used to account for the hierarchical data structure and unobserved heterogeneity, with the Weibull gamma model identified as the best fit based on Information Criteria (AIC), and Bayesian Information Criteria (BIC). Variables with p  < 0.2 entered multivariable analysis, and results were reported as Adjusted Hazard Ratios (AHR) with 95% Confidence Intervals (CI) using the Weibull gamma model. Results The study found that the median time for the first antenatal care (ANC) visit in Kenya was four months. Significant predictors of ANC timing included women’s age (35–49 years: AHR 0.83; 95% CI: 0.72–0.95), education level (higher: AHR 1.45; 95% CI: 1.17–1.78), media exposure (yes: AHR 1.21; 95% CI: 1.05–1.39), parity (four or more children: AHR 0.81; 95% CI: 0.72–0.91), wealth status (richest: AHR 2.00; 95% CI: 1.63–2.43), desire for more children (did not want more: AHR 0.64; 95% CI: 0.54–0.77), residence (rural: AHR 1.22; 95% CI: 1.07–1.39), and religion (Islam: AHR 0.76; 95% CI: 0.64–0.89). Conclusion The median time for the first ANC visit exceeds the World Health Organization’s recommendation of initiating care within the first trimester. These findings underscore the need for targeted interventions to promote timely ANC, especially among women with limited media exposure, high parity, lower socioeconomic status, and specific religious followers.

Background Time to benefit (TTB) has emerged as a clinically interpretable estimand for characterizing when treatment effects become meaningful over time. Unlike conventional survival summaries, TTB is implicitly defined through marginal differences in survival probabilities and is therefore highly sensitive to modeling assumptions. In multicenter studies involving clustered time-to-event data, unobserved heterogeneity and misspecification of the baseline hazard present additional challenges for coherent TTB estimation. Methods We propose a unified framework for estimating TTB in clustered survival settings using marginal survival modeling with shared frailty. Specifically, TTB is defined on the marginal population scale by integrating over the frailty distribution, ensuring coherence between the estimand and its clinical interpretation. Both parametric and flexible spline-based baseline hazard models are evaluated. Uncertainty is quantified using the Delta method and Monte Carlo (MC)-based inference procedures. Extensive simulation studies are conducted to characterize estimator behavior under varying degrees of heterogeneity, censoring, and hazard misspecification. Furthermore, the framework is illustrated using data from the Systolic Blood Pressure Intervention Trial (SPRINT), a large multicenter randomized clinical trial. Results Simulation results indicate that ignoring latent heterogeneity or misspecifying the baseline hazard can bias TTB estimation and produce miscalibrated confidence intervals, particularly under small absolute risk reduction thresholds. Flexible hazard models combined with MC-based inference yield more stable estimates and improved coverage in the presence of model misspecification. In the SPRINT application, TTB point estimates remained relatively consistent across modeling approaches, while statistically significant frailty effects revealed meaningful between-site heterogeneity, highlighting its importance for accurate uncertainty quantification. Conclusions TTB is a model-sensitive implicit estimand; reliable estimation in clustered survival settings requires explicit alignment among the estimand definition, the survival model, and the inference strategy. The proposed framework provides a principled and practical approach to TTB estimation in multicenter studies, facilitating transparent and interpretable reporting of TTB in both clinical and real-world research contexts.

Background Despite its declining incidence, gastric cancer (GC) is one of the world’s leading malignancies and a major global health concern due to its high prevalence and fatality rate. Furthermore, it is the world’s fourth most common cancer and the second leading cause of cancer death. Studying the determinants of time to death of gastric cancer patients will give clinicians more information to develop specific treatment plans, forecast prognosis, and track the progress of death cases. The application of the frailty model can help account for random variation in survival that may exist due to unobserved factors, as well as show the impact of latent factors on death risk. As a result, the purpose of this study was to assess the determinants of time to death of GC patients’ by applying the parametric shared frailty models. Methods The data for this study were obtained from gastric cancer patients admitted to the Tikur Anbesa Specialized Hospital, Addis Ababa, from January 1, 2015, to February 29, 2020. With the aim of coming up with an appropriate survival model that determines factors that affect the time to death of gastric cancer patients, various parametric shared frailty models were compared. In all of the frailty models, patient regions were used as a clustering variable. The current study implemented exponential, Weibull, log-logistic, and lognormal distributions for baseline hazard functions with gamma and inverse Gaussian’s frailty distributions. The performance of all models was compared using the AIC and BIC criteria. R statistical software was used to conduct the analysis. Results A retrospective study was undertaken on a total of 407 gastric cancer patients under follow-up at Tikur Anbesa Specialized Hospital. Of all 407 GC patients, 56.3% died while the remaining 43.7% were censored. The patients’ median time to death was 21.9 months, with a maximum survival time of 49.6 months. In the current study, the clustering effect was significant in modeling the time to death from gastric cancer. The Weibull model with inverse Gaussian frailty has the minimum AIC and BIC value among the candidate models compared. The dependency within the clusters for the Weibull–inverse Gaussian frailty model was k e n d a l l ′ s t a u ( τ ) = 0.134 (13.4%). According to the results of our best model (Weibull–inverse Gaussian), the sex of the patient, the smoking status, the tumor size, the treatment taken, the vascular invasion, and the disease stage was found to be statistically significant at an alpha = 0.05 significance level. Conclusion Time to death of GC patient’s data set was well described by the Weibull–inverse Gaussian shared frailty. Furthermore, Weibull baseline distribution best fits the GC data set as it enables proportional hazard and accelerated failure time model, for time to failure data. There is unobserved heterogeneity between clusters (patient regions), indicating the need to account for this clustering effect. In this study, survival time to death among GC patients was discovered to be small. Covariates like older age, being male, having higher (advanced) stage of GC disease (stage three and stage four), advanced tumor size, being smoker, infected by Helicobacter pylori , and existence of vascular invasion significantly accelerate the time to death of GC patients. In contrast, talking combination of more treatments prolongs the time to death of patients. To improve the health of patients, interventions should be taken based on significant prognostic factors, with special attention dedicated to patients with such factors to prevent GC death.

Background Neonatal hypothermia is a major public health concern that threatens the survival and well‐being of newborns, particularly those admitted to neonatal intensive care units. In Ethiopia, where the burden of neonatal hypothermia remains high, it contributes substantially to neonatal morbidity and mortality. This study aimed to model the time to recovery from neonatal hypothermia and identify its predictors using a shared frailty survival analysis among neonates admitted to the neonatal intensive care unit at Pawe General Hospital. Methods A retrospective follow‐up study was conducted among 425 neonates admitted with hypothermia to the NICU of Pawe General Hospital. Time to recovery was analyzed using survival analysis techniques. Non‐parametric methods were used to compare recovery experiences across demographic and clinical characteristics, and parametric accelerated failure time and shared frailty models were fitted to identify significant predictors while accounting for unobserved heterogeneity. Model selection was based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Results The log‐logistic gamma shared frailty model was identified as the best‐fitting model. The frailty effect at the level of place of childbirth was statistically significant (θ = 1.228; χ² = 84.24, p < 0.001), indicating substantial unobserved heterogeneity with moderate intra‐cluster dependence (τ = 0.38). Maternal age 20–29 years (AF = 0.842) and 30–39 years (AF = 0.707), urban residence (AF = 0.823), and above‐average family income (AF = 0.834) were associated with shorter recovery times. Female neonates had slightly prolonged recovery (AF = 1.110). Very low and low birth weight, as well as preterm and post‐term gestational ages, were associated with delayed recovery. Early initiation of breastfeeding (AF = 0.365) and skin‐to‐skin contact (AF = 0.801) accelerated recovery, whereas CPR at birth (AF = 0.857) and admission‐related complications, including prematurity, low birth weight, sepsis, respiratory distress syndrome, asphyxia, and congenital malformations, were strong predictors of prolonged recovery time from neonatal hypothermia. Conclusion The findings indicate that recovery from neonatal hypothermia is influenced by maternal, socioeconomic, neonatal, clinical, and contextual factors. The significant frailty effect underscores the importance of accounting for clustering by place of childbirth when modeling recovery time. Interventions aimed at improving early breastfeeding practices, promoting skin‐to‐skin contact, and strengthening neonatal care, particularly for preterm and low birth weight infants, may substantially reduce recovery time and improve neonatal outcomes.

Panel counts are often encountered in longitudinal, such as diary, studies where individuals are followed over time and the number of events occurring in time intervals, or panels, is recorded. This article develops methods for situations where, in addition to the counts of events, a mark, denoting a measure of severity of the events, is recorded. In many situations there is an association between the panel counts and their marks. This is the case for our motivating application that studies the effect of two hormone therapy treatments in reducing counts and severities of vasomotor symptoms in women after hysterectomy/ovariectomy. We model the event counts and their severities jointly through the use of shared random effects. We also compare, through simulation, the power of testing for the treatment effect based on such joint modeling and an alternative scoring approach, which is commonly employed. The scoring approach analyzes the compound outcome of counts times weighted severity. We discuss this approach and quantify challenges which may arise in isolating the treatment effect when such a scoring approach is used. We also show that the power of detecting a treatment effect is higher when using the joint model than analysis using the scoring approach. Inference is performed via Markov chain Monte Carlo methods.

Background: Human immune virus/tuberculosis co-infection in one's immune system potentiates each other and hastening the weakening of the host's immunological capabilities while growing active TB, which will increase susceptibility to primary contamination, re-contamination, and/or reactivation for sufferers with latent TB. The goal of this study was to identify determinant factors associated with the survival time to death of HIV/TB co-infected adult patients under HAART at Debre Tabor referral hospital. Methods: A retrospective follow-up analysis was undertaken for 243 HIV/TB coinfected patients who were receiving ART treatment and had follow-ups between January 2014 and December 2019. To compare the survival experiences of different patient groups, the Log rank test was performed. The Weibull accelerated failure time gamma shared frailty model was used to find determinants of HIV/TB co-infected patients' survival time. Results: Among HIV/TB co-infected patients, 87 (35.39%) died of whom 77 (88.5%) patients were females. The Weibull AFT gamma shared frailty model showed that sex, baseline age, adherence status, educational status of respondents, functional status, WHO clinical stage, baseline hemoglobin and type of TB were among the potential determinants of survival time of HIV/TB co-infected patients. Furthermore, the findings of this study demonstrated that there is a clustering impact on patient time to death that results from the residency of HIV/TB co-infected patients' survival time. Conclusion and Recommendation: The majority of patients reside in rural area, have poor adherence to treatment, and have low CD4 cell counts. Educational status, WHO clinical stages, adherence status, and hemoglobin levels of patients are all important determinants of HIV/TB co-infected patients' survival. As a result, to improve the survival of HIV/TB co-infected patients at the start of and during some stages of anti-TB treatment, the concerned body, FMOH, in collaboration with Regional Health Bureau, should emphasize the importance of following treatment for HIV/TB coinfected patients with poor adherence status, advanced WHO clinical stages, and a low CD4+ count. Keywords: Weibull, accelerated failure time gamma shared frailty model, survival time, human immune virus/tuberculosis co-infection

Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. Taking the Cardiovascular Health Study as a motivating example, patients can experience recurrent events of myocardial infarction (MI) or stroke during follow-up, which, however, can be truncated by death. Since death could be a devastating complication of MI or stroke recurrences, ignoring dependent censoring when analysing recurrent events may lead to invalid inference. The joint shared frailty model is widely used but with several limitations: two event processes are conditionally independent given the subject level frailty, which could be violated because the dependence may rely on unknown covariates varying across recurrences; the correlation between recurrent events and death is constant over time because of the same frailty within subject, but MI or stroke recurrences could have a time-varying influence on death due to higher risk of another event of MI or stroke after the first. We propose a time-varying joint hierarchical copula model under the Bayesian framework to accommodate correlation between recurrent events and dependence between two event processes which may change over time. The performance of our method is extensively evaluated by simulation studies, and lastly by the Cardiovascular Health Study for illustration.

Background Empirical evidence from European countries has shown that economic conditions in early life are associated with mortality risk. This study aims to assess the effects of economic conditions in early life, as well as their interaction with parental education, on the risk of adult mortality in the U.S. Methods To capture exogenous variation of economic conditions early in life, we use the Gross Domestic Product (GDP) cyclical deviation during a respondent’s birth year. Using the linked U.S. General Social Survey and National Death Index data (1979–2008), we employed parametric frailty survival models to examine the effects of economic conditions in early life on all-cause and cause-specific mortality. Results We found that exposure to recession in the first year of life was associated with increased all-cause mortality only among women (hazard ratio = 1.54, 95% CI 1.03–2.31). This adverse effect was also found in women’s mortality from cancers (hazard ratio = 2.24, 95% CI 1.18–4.28). We also found a significant interaction between economic conditions in infancy and paternal education on women’s mortality risk—higher paternal education was protective against mortality under good economic conditions in infancy; however, higher paternal education was associated with greater mortality risk under poor economic conditions in infancy. We discuss how aspiration theory may explain these results. Conclusion Our study concludes that worse macroeconomic conditions early in life heighten the risk of mortality among women, and paternal education moderates this relationship.

(1) Background: Tuberculosis is a bacterial disease mainly caused by Mycobacterium tuberculosis. It is one of the major public health problems in the world and now ranks alongside human immunodeficiency virus (HIV) as the leading infectious cause of death. The objective of this study was to investigate the potential risk factors affecting the time to death of TB patients in southwest Ethiopia using parametric shared frailty models. (2) Methods: A retrospective study design was used to collect monthly records of TB patients in three selected hospitals in southwest Ethiopia. The data used in the study were obtained from patients who took part in the directly observed treatment, short-course (DOTS) program from 1 January 2015 to 31 December 2019. The survival probability was analyzed by the Kaplan–Meier method. Log-rank tests and parametric shared frailty models were applied to investigate factors associated with death during TB treatment. (3) Results: Out of the total sample of 604 registered TB patients, 46 (7.6%) died during the study period and 558 (92.4%) were censored. It was found that the median time of death for TB patients was 5 months. Hospitals were used to assess the cluster effect of the frailty model. A Gamma shared frailty model with Weibull distribution for baseline hazard function was selected among all models considered and was used for this study. It was found that the covariates, age, initial weight, extrapulmonary type of TB patient, patient category, and HIV status of TB patient were significant risk factors associated with death status among TB patients. (4) Conclusions: The risk of death was high, especially with cases of HIV co-infected, retreated, and returned-after-treatment categories of TB patients. During the treatment period, the risk of death was high for older TB patients and patients with low baseline body weight measurements. Therefore, health professionals should focus on the identified factors to improve the survival time of TB patients.

The relative frailty variance among survivors provides a readily interpretable measure of how the heterogeneity of a population, as represented by a frailty model, evolves over time. We discuss the properties of the relative frailty variance, show that it characterizes frailty distributions and that, suitably rescaled, it may be used to compare patterns of dependence across models and data sets. In shared frailty models, the relative frailty variance is closely related to the cross-ratio function, which is estimable from bivariate survival data. We investigate the possible shapes of the relative frailty variance function for the purpose of model selection, and we review available frailty distribution families in this context. We introduce several new families with contrasting properties, including simple but flexible time varying frailty models. The benefits of the approach that we propose are illustrated with two applications to bivariate current status data obtained from serological surveys.