Modifications of the EM algorithm for survival influenced by an unobserved stochastic process

Anatoli I. Yashin and Kenneth G. Manton

Stochastic Processes and their Applications, 1994, vol. 54, issue 2, 257-274

Abstract: Let Y=(Yt)t>=0) be an unobserved random process which influences the distribution of a random variable T which can be interpreted as the time to failure. When a conditional hazard rate corresponding to T is a quadratic function of covariates, Y, the marginal survival function may be represented by the first two moments of the conditional distribution of Y among survivors. Such a representation may not have an explicit parametric form. This makes it difficult to use standard maximum likelihood procedures to estimate parameters - especially for censored survival data. In this paper a generalization of the EM algorithm for survival problems with unobserved, stochastically changing covariates is suggested. It is shown that, for a general model of the stochastic failure model, the smoothing estimates of the first two moments of Y are of a specific form which facilitates the EM type calculations. Properties of the algorithm are discussed.

Keywords: Randomly; changing; covariates; Missing; information; principle; Survival; analysis; Unobserved; stochastic; frailty; Random; hazard; EM; algorithm; Incomplete; information; Smoothing; estimates (search for similar items in EconPapers)
Date: 1994
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