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SUMMARYThe properties of an estimator based on a proportional hazards model are investigated when the model is incorrect. The estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly. The results are used to investigate the effects on estimation if the true model is accelerated failure time, or if covariates are omitted from the proportional hazards model.
Longitudinal studies, in which individuals are measured repeatedly in time, are often incomplete. We model continuous-time longitudinal data from the Multicenter AIDS Cohort Study using a diffusion model in which the diffusion parameters are functions of the covariates. These data are jointly modeled with the process of time-to-death due to AIDS. We show that, even for large data sets with a large number of missing variables, a Bayesian analysis is feasible using Gibbs sampling and compare a complete case analysis with a Bayesian treatment of missing values.
Let Y be a response variable, possibly multivariate, with a density function f (y|x, v; β) conditional on vectors x and v of covariates and a vector β of unknown parameters. The authors consider the problem of estimating β when the values taken by the covariate vector v are available for all observations while some of those taken by the covariate x are missing at random. They compare the profile estimator to several alternatives, both in terms of bias and standard deviation, when the response and covariates are discrete or continuous.
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