Modifications of the EM algorithm for survival influenced by an unobserved stochastic process
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.
Year of publication: |
1994
|
---|---|
Authors: | Yashin, Anatoli I. ; Manton, Kenneth G. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 54.1994, 2, p. 257-274
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Publisher: |
Elsevier |
Keywords: | Randomly changing covariates Missing information principle Survival analysis Unobserved stochastic frailty Random hazard EM algorithm Incomplete information Smoothing estimates |
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