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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]

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]

• 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]