In this paper, we develop a family of bivariate beta distributions that encapsulate both positive and negative correlations, and which can be of general interest for Bayesian inference. We then invoke a use of these bivariate distributions in two contexts. The first is diagnostic testing in medicine, threat detection, and signal processing. The second is system survivability assessment, relevant to engineering reliability, and to survival analysis in biomedicine. In diagnostic testing one encounters two parameters that characterize the efficacy of the testing mechanism, {\it test sensitivity}, and {\it test specificity}. These tend to be adversarial when their values are interpreted as utilities. In system survivability, the parameters of interest are the component reliabilities, whose values when interpreted as utilities tend to exhibit co-operative (amiable) behavior. Besides probability modeling and Bayesian inference, this paper has a foundational import. Specifically, it advocates a conceptual change in how one may think about reliability and survival analysis. The philosophical writings of de Finetti, Kolmogorov, Popper, and Savage, when brought to bear on these topics constitute the essence of this change. Its consequence is that we have at hand a defensible framework for invoking Bayesian inferential methods in diagnostics, reliability, and survival analysis. Another consequence is a deeper appreciation of the judgment of independent lifetimes. Specifically, we make the important point that independent lifetimes entail at a minimum, a two-stage hierarchical construction.
We present a new backfitting algorithm estimating the complex structured non-parametric survival model of Scheike (2001) without having to use smoothing. The considered model is a non-parametric survival model with two time-scales that are equivalent up to a constant that varies over the subjects. Covariate effects are modelled linearly on each time scale by additive Aalen models. Estimators of the cumulative intensities on the two time-scales are suggested by solving local estimating equations jointly on the two time-scales. We are able to estimate the cumulative intensities solving backfitti…
Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）
Purpose: To utilize high-resolution quantitative CT (QCT) imaging features for prediction of diagnosis and prognosis in fibrosing interstitial lung diseases (ILD). Approach: 40 ILD patients (20 usual interstitial pneumonia (UIP), 20 non-UIP pattern ILD) were classified by expert consensus of 2 radiologists and followed for 7 years. Clinical variables were recorded. Following segmentation of the lung field, a total of 26 texture features were extracted using a lattice-based approach (TM model). The TM model was compared with previously histogram-based model (HM) for their abilities to classify …
In survival analysis, the hazard function often depends on a set of covariates. Martingale and deviance residual are most widely used for examining the validity of the function form of covariates by checking whether there is a discernible trend in their scatterplot against continuous covariates. However, visual inspection of martingale and deviance residuals is often subjective. In addition, these residuals lack a reference distribution due to censoring. It is therefore challenging to derive numerical statistical tests based on martingale or deviance residuals. In this paper, we extend the ide…
In the process of clinical diagnosis and treatment, the restricted mean survival time (RMST), which reflects the life expectancy of patients up to a specified time, can be used as an appropriate outcome measure. However, the RMST only calculates the mean survival time of patients within a period of time after the start of follow-up and may not accurately portray the change in a patient's life expectancy over time. The life expectancy can be adjusted for the time the patient has already survived and defined as the conditional restricted mean survival time (cRMST). A dynamic RMST model based on …
The goals in clinical and cohort studies often include evaluation of the association of a time-dependent binary treatment or exposure with a survival outcome. Recently, several impactful studies targeted the association between aspirin-taking and survival following colorectal cancer diagnosis. Due to surgery, aspirin-taking value is zero at baseline and may change its value to one at some time point. Estimating this association is complicated by having only intermittent measurements on aspirin-taking. Naive, commonly-used, methods can lead to substantial bias. We present a class of calibration…
Technische Universität Kaiserslautern（凯泽斯劳滕工业大学）；University of Cambridge（剑桥大学）；Imperial College London（帝国理工学院）；Ludwig-Maximilians-Universität München（慕尼黑大学）；J.P. Morgan AI Research（摩根大通人工智能研究院）；Chalmers Technical University（查尔姆斯理工大学）；University of Gothenburg（哥德堡大学）；Leibniz Institute for Prevention Research and Epidemiology - BIPS GmbH（莱布尼茨预防研究与流行病学研究所-BIPS有限公司）；Birla Institute of Technology and Science（贝拉理工学院）
Algorithmic fairness is an increasingly important field concerned with detecting and mitigating biases in machine learning models. There has been a wealth of literature for algorithmic fairness in regression and classification however there has been little exploration of the field for survival analysis. Survival analysis is the prediction task in which one attempts to predict the probability of an event occurring over time. Survival predictions are particularly important in sensitive settings such as when utilising machine learning for diagnosis and prognosis of patients. In this paper we expl…
Survival analysis is a critical tool for the modelling of time-to-event data, such as life expectancy after a cancer diagnosis or optimal maintenance scheduling for complex machinery. However, current neural network models provide an imperfect solution for survival analysis as they either restrict the shape of the target probability distribution or restrict the estimation to pre-determined times. As a consequence, current survival neural networks lack the ability to estimate a generic function without prior knowledge of its structure. In this article, we present the metaparametric neural netwo…
In Survival Analysis, the observed lifetimes often correspond to individuals for which the event occurs within a specific calendar time interval. With such interval sampling, the lifetimes are doubly truncated at values determined by the birth dates and the sampling interval. This double truncation may induce a systematic bias in estimation, so specific corrections are needed. A relevant target in Survival Analysis is the hazard rate function, which represents the instantaneous probability for the event of interest. In this work we introduce a flexible estimation approach for the hazard rate u…
The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether disparities in BMI is partially responsible for obser…
Comparison of the Cox proportional hazards model and Random Survival Forest algorithm for predicting patient-specific survival probabilities in clinical trial data
University of Augsburg（奥格斯堡大学）；University of Reading（雷丁大学）
What Risk Factors to Cause Long COVID and Its Impact on Patient Survival Outcomes when Combined with the Effect from Organ Transplantation in the Acute COVID
A Temporal Machine Learning-Based Time-to-Event Model for Predicting ALS Progression and Healthcare Utilization
Harrison College of Pharmacy, Auburn University（奥本大学哈里森药学院）；Fisk University（菲斯克大学）；Lewis Katz School of Medicine, Temple University（天普大学刘易斯·卡茨医学院）；Emory University（埃默里大学）；Barnett College of Public Health, Temple University（天普大学巴尼特公共卫生学院）
Bayesian causal inference offers a principled approach to policy evaluation of proposed interventions on mediators or time-varying exposures. We outline a general approach to the estimation of causal quantities for settings with time-varying confounding, such as exposure-induced mediator-outcome confounders. We further extend this approach to propose two Bayesian data fusion (BDF) methods for unmeasured confounding. Using informative priors on quantities relating to the confounding bias parameters, our methods incorporate data from an external source where the confounder is measured in order t…
