Classical Competing Risks

TL;DR: In this paper, Martingale et al. proposed a model for estimating the probability of failure of a small subset of survival data in a large set of small data sets, based on Bernoulli trials.

Abstract: CONTINUOUS FAILURE TIMES AND THEIR CAUSES Basic Probability Functions Some Small Data Sets Hazard Functions Regression Models PARAMETRIC LIKELIHOOD INFERENCE The Likelihood for Competing Risks Model Checking Inference Some Examples Masked Systems LATENT FAILURE TIMES: PROBABILITY DISTRIBUTIONS Basic Probability Functions Some Examples Marginal vs. Sub-Distributions Independent Risks A Risk-Removal Model LIKELIHOOD FUNCTIONS FOR UNIVARIATE SURVIVAL DATA Discrete and Continuous Failure Times Discrete Failure Times: Estimation Continuous Failure Times: Random Samples Continuous Failure Times: Explanatory Variables Discrete Failure Times Again Time-Dependent Covariates DISCRETE FAILURE TIMES IN COMPETING RISKS Basic Probability Functions Latent Failure Times Some Examples Based on Bernoulli Trials Likelihood Functions HAZARD-BASED METHODS FOR CONTINUOUS FAILURE TIMES Latent Failure Times vs. Hazard Modelling Some Examples of Hazard Modelling Nonparametric Methods for Random Samples Proportional Hazards and Partial Likelihood LATENT FAILURE TIMES: IDENTIFIABILITY CRISES The Cox-Tsiatis Impasse More General Identifiability Results Specified Marginals Discrete Failure Times Regression Case Censoring of Survival Data Parametric Identifiability MARTINGALE COUNTING PROCESSESES IN SURVIVAL DATA Introduction Back to Basics: Probability Spaces and Conditional Expectation Filtrations Martingales Counting Processes Product Integrals Survival Data Non-parametric Estimation Non-parametric Testing Regression Models Epilogue APPENDIX 1: Numerical Maximisation of Likelihood Functions APPENDIX 2: Bayesian Computation Bibliography Index