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This paper describes estimation of the regression parameters and prediction of the cumulative incidence functions under the cause-specific proportional hazards model when some of covariates are not fully observed. Assuming that missingness mechanism is missing at random, we propose the augmented inverse probability weighted method for estimation and inference procedures. A nonparametric regression approach is adapted for estimating selection probabilities and conditional expectations of missing covariates in the augmented estimating function. We establish the asymptotic properties of the predicted cumulative incidence functions under the cause-specific proportional hazards model with missing covariates and derive consistent variance estimators of the predicted cumulative incidence functions. Simulation studies show that the procedures perform well. The proposed methods are illustrated with stage IV breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute. [ABSTRACT FROM AUTHOR]

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial. [ABSTRACT FROM AUTHOR]

Currently available risk prediction methods are limited in their ability to deal with complex, heterogeneous, and longitudinal data such as that available in primary care records, or in their ability to deal with multiple competing risks. This paper develops a novel deep learning approach that is able to successfully address current limitations of standard statistical approaches such as landmarking and joint modeling. Our approach, which we call Dynamic-DeepHit, flexibly incorporates the available longitudinal data comprising various repeated measurements (rather than only the last available measurements) in order to issue dynamically updated survival predictions for one or multiple competing risk(s). Dynamic-DeepHit learns the time-to-event distributions without the need to make any assumptions about the underlying stochastic models for the longitudinal and the time-to-event processes. Thus, unlike existing works in statistics, our method is able to learn data-driven associations between the longitudinal data and the various associated risks without underlying model specifications. We demonstrate the power of our approach by applying it to a real-world longitudinal dataset from the U.K. Cystic Fibrosis Registry, which includes a heterogeneous cohort of 5883 adult patients with annual follow-ups between 2009 to 2015. The results show that Dynamic-DeepHit provides a drastic improvement in discriminating individual risks of different forms of failures due to cystic fibrosis. Furthermore, our analysis utilizes post-processing statistics that provide clinical insight by measuring the influence of each covariate on risk predictions and the temporal importance of longitudinal measurements, thereby enabling us to identify covariates that are influential for different competing risks. [ABSTRACT FROM AUTHOR]

After the diagnosis of a disease, one major objective is to predict cumulative probabilities of events such as clinical relapse or death from the individual information collected up to a prediction time, usually including biomarker repeated measurements. Several competing estimators have been proposed, mainly from two approaches: joint modelling and landmarking. These approaches differ by the information used, the model assumptions and the complexity of the computational procedures. This paper aims to review the two approaches, precisely define the derived estimators of dynamic predictions and compare their performances notably in case of misspecification. The ultimate goal is to provide key elements for the use of individual dynamic predictions in clinical practice. Prediction of two competing causes of prostate cancer progression from the history of prostate-specific antigen is used as a motivated example. We formally define the quantity to estimate and its estimators, propose techniques to assess the uncertainty around predictions and validate them. We then conduct an in-depth simulation study compare the estimators in terms of prediction error, discriminatory power, efficiency and robustness to model assumptions. We show that prediction tools should be handled with care, in particular by properly specifying models and estimators. [ABSTRACT FROM AUTHOR]

Why would dictators purge members of their ruling coalition? Some argue that doing so can minimize the risk to dictators' political survival, while others contend that dictators who mount purges are motivated by the desire to share resources with fewer allies. In this study, we analyze an original dataset, compiled from biographical data on the subordinates of the founding emperors of seven ancient Chinese imperial dynasties. Analyzing the data with competing risks models, we find that military experience is a strong predictor of political purges. Emperors were less likely to execute officers who had fought in more battles, but more likely to execute commanders, especially those who had established military credentials prior to the founding of an empire. In addition, the incidence of political purges heightened toward the end of an emperor's life, which implies that the founding emperors were concerned about the security threats against their designated successors. Potential challengers came not only from the military, but also from the aristocracy. Indeed, we find that the blood relatives of the emperors were more likely to experience a mild form of purges: deprivation of titles. These findings suggest that dictators are more likely to use purges to reduce existential threats. [ABSTRACT FROM AUTHOR]

The cause-specific cumulative incidence function quantifies the subject-specific disease risk with competing risk outcome. With longitudinally collected biomarker data, it is of interest to dynamically update the predicted cumulative incidence function by incorporating the most recent biomarker as well as the cumulating longitudinal history. Motivated by a longitudinal cohort study of chronic kidney disease, we propose a framework for dynamic prediction of end stage renal disease using multivariate longitudinal biomarkers, accounting for the competing risk of death. The proposed framework extends the local estimation-based landmark survival modeling to competing risks data, and implies that a distinct sub-distribution hazard regression model is defined at each biomarker measurement time. The model parameters, prediction horizon, longitudinal history and at-risk population are allowed to vary over the landmark time. When the measurement times of biomarkers are irregularly spaced, the predictor variable may not be observed at the time of prediction. Local polynomial is used to estimate the model parameters without explicitly imputing the predictor or modeling its longitudinal trajectory. The proposed model leads to simple interpretation of the regression coefficients and closed-form calculation of the predicted cumulative incidence function. The estimation and prediction can be implemented through standard statistical software with tractable computation. We conducted simulations to evaluate the performance of the estimation procedure and predictive accuracy. The methodology is illustrated with data from the African American Study of Kidney Disease and Hypertension. [ABSTRACT FROM AUTHOR]

Building occupancy, which reflects occupant presence, movements and activities within the building space, is a key factor to consider in building energy modelling and simulation. Characterising complex occupant behaviours and their determinants poses challenges from the sensing, modelling, interpretation and prediction perspectives. Past studies typically applied time-dependent models to predict regular occupancy patterns for commercial buildings. However, this prevalent reliance on purely time-of-day effects is typically not sufficient to accurately characterise the complex occupancy patterns as they may vary with building's surrounding conditions, i.e. the urban environment. Therefore, this paper proposes a conceptual framework to incorporate the interactions between urban systems and building occupancy. Under the framework, we propose a novel modelling methodology relying on competing risk hazard formulation to analyse the occupancy of a case study building in London, UK. The occupancy profiles were inferred from the Wi-Fi connection logs extracted from the existing Wi-Fi infrastructure. When compared with the conventional discrete-time Markov Chain Model (MCM), the hazard-based modelling approach was able to better capture the duration dependent nature of the transition probabilities as well as incorporate and quantify the influence of the local environment on occupancy transitions. The work has demonstrated that this approach enables a convenient and flexible incorporation of urban dependencies leading to accurate occupancy predictions whilst providing the ability to interpret the impacts of urban systems on building occupancy. •Model of interactions between occupancy behaviour and urban systems is proposed. •Competing risk hazard model is used to operationalise the model using Wi-Fi logs. •The hazard model flexibly captures dependence of transition probability on duration. •The model helps gain insights into exogenous effects on occupancy behaviour. •Compared to MCM, hazard model better predicts occupancy with flexible work agendas. [ABSTRACT FROM AUTHOR]

• Random survival forest method in highway rail grade crossing safety analysis is introduced. • Long-term time effects on cumulative probability of crash severity and occurrence over 29 years is evaluated. • Contributors' long-term and instantaneous effects on crash severity and occurrence behave very different. • Adding stop sign to active controlled crossings will reduce crash risk up to 7 years. • Audible device to active crossings will reduce crash/PDO/injury/fatal likelihoods by 49 %, 52 %, 46 %, and 50 % respectively. This paper proposes a machine learning approach, the random survival forest (RSF) for competing risks, to investigate highway-rail grade crossing (HRGC) crash severity during a 29-year analysis period. The benefits of the RSF approach are that it (1) is a special type of survival analysis able to accommodate the competing nature of multiple-event outcomes to the same event of interest (here the competing multiple events are crash severities), (2) is able to conduct an event-specific selection of risk factors, (3) has the capability to determine long-term cumulative effects of contributors with the cumulative incidence function (CIF), (4) provides high prediction performance, and (5) is effective in high-dimensional settings. The RSF approach is able to consider complexities in HRGC safety analysis, e.g., non-linear relationships between HRGCs crash severities and the contributing factors and heterogeneity in data. Variable importance (VIMP) technique is adopted in this research for selecting the most predictive contributors for each crash-severity level. Moreover, marginal effect analysis results real several HRGC countermeasures' effectiveness. Several insightful findings are discovered. For examples, adding stop signs to HRGCs that already have a combination of gate, standard flashing lights, and audible devices will reduce the likelihood of property damage only (PDO) crashes for up to seven years; but after the seventh year, the crossings are more likely to have PDO crashes. Adding audible devices to crossing with gates and standard flashing lights will reduce crash likelihood, PDO, injury, and fatal crashes by 49 %, 52 %, 46 %, and 50 %, respectively. [ABSTRACT FROM AUTHOR]