Estimating marginal survival function by adjusting for dependent censoring using many covariates

One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric model or a nonparametric model of the conditional survival function can be problematic due to the high dimensionality of the auxiliary information. In this paper, we use two working models to condense these high-dimensional covariates in dimension reduction; then an estimate of the marginal survival function can be derived nonparametrically in a low-dimensional space. We show that such an estimator has the following double robust property: when either working model is correct, the estimator is consistent and asymptotically Gaussian; when both working models are correct, the asymptotic variance attains the efficiency bound.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000050

A Fully Nonparametric Modelling Approach to Binary Regression

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random variables through discretization, and we model the joint distribution of these latent responses and the covariates using a Dirichlet process mixture of multivariate normals. We show that the kernel of the induced mixture model for the observed data is identifiable upon a restriction on the latent variables. To allow for appropriate dependence structure while facilitating identifiability, we use a square-root-free Cholesky decomposition of the covariance matrix in the normal mixture kernel. In addition to allowing for the necessary restriction, this modeling strategy provides substantial simplifications in implementation of Markov chain Monte Carlo posterior simulation. We present two data examples taken from areas for which the methodology is especially well suited. In particular, the first example involves estimation of relationships between environmental variables, and the second develops inference for natural selection surfaces in evolutionary biology. Finally, we discuss extensions to regression settings with multivariate ordinal responses

Models of Firm Dynamics and the Hazard Rate of Exits: Reconciling Theory and Evidence using Hazard Regression Models

This paper considers empirical work relating to models of firm dynamics. We show that a hazard regression model for firm exits, with a modification to accommodate age-varying covariate effects, provides an empirical framework accommodating many of the features of interest in studies on firm dynamics. Modelling implications of some of the popular theoretical models are considered and a set of empirical procedures for verifying testable implications of the theoretical models are proposed. The proposed hazard regression models can accommodate negative effects of initial size that go to zero with age (active learning model), negative initial size effects that fall with age but stay permanently negative (passive learning model), conditional and unconditional hazard rates that decrease with age at higher ages, and adverse effects of macroeconomic shocks that decrease with age of the firm. The methods are illustrated using data on quoted UK firms. Consistent with the active learning model, the effect of initial size is significantly negative for a young firm and falls to zero with age. The hazard function conditional on size, other firm- and industry-level characteristics, and macroeconomic conditions decreases with age only at higher ages, but shows the weaker property of Increasing Mean Residual Life over its entire life-duration. Instability in exchange rates affects survival of very young firms strongly, and the effect decreases to insignificant levels for older firms.Firm exit, Learning, Firm Dynamics, Non-proportional hazards, Hazard regression models

A Simple Test for the Absence of Covariate Dependence in Hazard Regression Models

This paper extends commonly used tests for equality of hazard rates in a two-sample or k-sample setup to a situation where the covariate under study is continuous. In other words, we test the hypothesis that the conditional hazard rate is the same for all covariate values, against the omnibus alternative as well as more specific alternatives, when the covariate is continuous. The tests developed are particularly useful for detecting trend in the underlying conditional hazard rates or changepoint trend alternatives. Asymptotic distribution of the test statistics are established and small sample properties of the tests are studied. An application to the e¤ect of aggregate Q on corporate failure in the UK shows evidence of trend in the covariate e¤ect, whereas a Cox regression model failed to detect evidence of any covariate effect. Finally, we discuss an important extension to testing for proportionality of hazards in the presence of individual level frailty with arbitrary distribution