Robust integration of secondary outcomes information into primary outcome analysis in the presence of missing data.

In clinical and observational studies, secondary outcomes are frequently collected alongside the primary outcome for each subject, yet their potential to improve the analysis efficiency remains underutilized. Moreover, missing data, commonly encountered in practice, can introduce bias to estimates if not appropriately addressed. This article presents an innovative approach that enhances the empirical likelihood-based information borrowing method by integrating missing-data techniques, ensuring robust data integration. We introduce a plug-in inverse probability weighting estimator to handle missingness in the primary analysis, demonstrating its equivalence to the standard joint estimator under mild conditions. To address potential bias from missing secondary outcomes, we propose a uniform mapping strategy, imputing incomplete secondary outcomes into a unified space. Extensive simulations highlight the effectiveness of our method, showing consistent, efficient, and robust estimators under various scenarios involving missing data and/or misspecified secondary models. Finally, we apply our proposal to the Uniform Data Set from the National Alzheimer's Coordinating Center, exemplifying its practical application.

Causes of death among people living with metastatic cancer.

Studying survivorship and causes of death in patients with advanced or metastatic cancer remains an important task. We characterize the causes of death among patients with metastatic cancer, across 13 cancer types and 25 non-cancer causes and predict the risk of death after diagnosis from the diagnosed cancer versus other causes (e.g., stroke, heart disease, etc.). Among 1,030,937 US (1992-2019) metastatic cancer survivors, 82.6% of patients (n = 688,529) died due to the diagnosed cancer, while 17.4% (n = 145,006) died of competing causes. Patients with lung, pancreas, esophagus, and stomach tumors are the most likely to die of their metastatic cancer, while those with prostate and breast cancer have the lowest likelihood. The median survival time among patients living with metastases is 10 months; our Fine and Gray competing risk model predicts 1 year survival with area under the receiver operating characteristic curve of 0.754 (95% CI [0.754, 0.754]). Leading non-cancer deaths are heart disease (32.4%), chronic obstructive and pulmonary disease (7.9%), cerebrovascular disease (6.1%), and infection (4.1%).

Comparison of partial-breast irradiation and intraoperative radiation to whole-breast irradiation in early-stage breast cancer patients: a Kaplan-Meier-derived patient data meta-analysis.

PURPOSE: Partial breast irradiation (PBI) and intraoperative radiation (IORT) represent alternatives to whole breast irradiation (WBI) following breast conserving surgery. However, data is mixed regarding outcomes. We therefore performed a pooled analysis of Kaplan-Meier-derived patient data from randomized trials to evaluate the hypothesis that PBI and IORT have comparable long-term rates of ipsilateral breast tumor recurrence as WBI. METHODS: In February, 2023, PubMed, EMBASE and Cochrane Central were systematically searched for randomized phase 3 trials of early-stage breast cancer patients undergoing breast-conserving surgery with PBI or IORT as compared to WBI. Time-to-event outcomes of interest included ipsilateral breast tumor recurrence (IBTR), overall survival (OS) and distant disease-free survival (DDFS). Statistical analysis was performed with R Statistical Software. RESULTS: Eleven randomized trials comprising 15,460 patients were included; 7,675 (49.6%) patients were treated with standard or moderately hypofractionated WBI, 5,413 (35%) with PBI and 2,372 (15.3%) with IORT. Median follow-up was 9 years. PBI demonstrated comparable IBTR risk compared with WBI (HR 1.20; 95% CI 0.95-1.52; p = 0.12) with no differences in OS (HR 1.02; 95% CI 0.90-1.16; p = 0.70) or DDFS (HR 1.15; 95% CI 0.81-1.64; p = 0.43). In contrast, patients treated with IORT had a higher IBTR risk (HR 1.46; 95% CI 1.23-1.72; p < 0.01) compared with WBI with no difference in OS (HR 0.98; 95% CI 0.84-1.14; p = 0.81) or DDFS (HR 0.91; 95% CI 0.76-1.09; p = 0.31). CONCLUSION: For patients with early-stage breast cancer following breast-conserving surgery, PBI demonstrated no difference in IBTR as compared to WBI while IORT was inferior to WBI with respect to IBTR.

A National Study of Expedited Partner Therapy Use in Emergency Departments: A Survey of Medical Director Knowledge, Attitudes, and Practices.

BACKGROUND: Emergency departments (EDs) are the primary source of health care for many patients diagnosed with sexually transmitted infections (STIs). Expedited partner therapy (EPT), treating the partner of patients with STIs, is an evidence-based practice for patients who might not otherwise seek care. Little is known about the use of EPT in the ED. In a national survey, we describe ED medical directors' knowledge, attitudes, and practices of EPT. METHODS: A cross-sectional survey of medical directors from academic EDs was conducted from July to September 2020 using the Academy of Academic Administrators of Emergency Medicine Benchmarking Group. Primary outcomes were EPT awareness, support, and use. The survey also examined barriers and facilitators. RESULTS: Forty-eight of 70 medical directors (69%) responded. Seventy-three percent were aware of EPT, but fewer knew how to prescribe it (38%), and only 19% of EDs had implemented EPT. Seventy-nine percent supported EPT and were more likely to if they were aware of EPT (89% vs. 54%; P = 0.01). Of nonimplementers, 41% thought EPT was feasible, and 56% thought departmental support would be likely. Emergency department directors were most concerned about legal liability, but a large proportion (44%) viewed preventing sequelae of untreated STIs as "extremely important." CONCLUSIONS: Emergency department medical directors expressed strong support for EPT and reasonable levels of feasibility for implementation but low utilization. Our findings highlight the need to identify mechanisms for EPT implementation in EDs.

Determinism, well-posedness, and applications of the ultrahyperbolic wave equation in spacekime.

Spatiotemporal dynamics of many natural processes, such as elasticity, heat propagation, sound waves, and fluid flows are often modeled using partial differential equations (PDEs). Certain types of PDEs have closed-form analytical solutions, some permit only numerical solutions, some require appropriate initial and boundary conditions, and others may not have stable, global, or even well-posed solutions. In this paper, we focus on one-specific type of second-order PDE - the ultrahyperbolic wave equation in multiple time dimensions. We demonstrate the wave equation solutions in complex time (kime) and show examples of the Cauchy initial value problem in space-kime. We extend the classical formulation of the dynamics of the wave equation with respect to positive real longitudinal time. The solutions to the Cauchy boundary value problem in multiple time dimensions are derived in Cartesian, polar, and spherical coordinates. These include both bounded and unbounded spatial domains. Some example solutions are shown in the main text with additional web-based dynamic illustrations of the wave equation solutions in space-kime shown in the appendix. Solving PDEs in complex time has direct connections to data science, where solving under-determined linear modeling problems or specifying the initial conditions on limited spatial dimensions may be insufficient to forecast, classify, or predict a prospective value of a parameter or a statistical model. This approach extends the notion of data observations, anchored at ordered longitudinal events, to complex time, where observables need not follow a strict positive-real structural arrangement, but instead could traverse the entire kime plane.

Kimesurface Representation and Tensor Linear Modeling of Longitudinal Data.

Many modern techniques for analyzing time-varying longitudinal data rely on parametric models to interrogate the time-courses of univariate or multivariate processes. Typical analytic objectives include utilizing retrospective observations to model current trends, predict prospective trajectories, derive categorical traits, or characterize various relations. Among the many mathematical, statistical, and computational strategies for analyzing longitudinal data, tensor-based linear modeling offers a unique algebraic approach that encodes different characterizations of the observed measurements in terms of state indices. This paper introduces a new method of representing, modeling, and analyzing repeated-measurement longitudinal data using a generalization of event order from the positive reals to the complex plane. Using complex time (kime), we transform classical time-varying signals as 2D manifolds called kimesurfaces. This kime characterization extends the classical protocols for analyzing time-series data and offers unique opportunities to design novel inference, prediction, classification, and regression techniques based on the corresponding kimesurface manifolds. We define complex time and illustrate alternative time-series to kimesurface transformations. Using the Laplace transform and its inverse, we demonstrate the bijective mapping between time-series and kimesurfaces. A proposed general tensor regression based linear model is validated using functional Magnetic Resonance Imaging (fMRI) data. This kimesurface representation method can be used with a wide range of machine learning algorithms, artificial intelligence tools, analytical approaches, and inferential techniques to interrogate multivariate, complex-domain, and complex-range longitudinal processes.