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

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  • Yashin, Anatoli I.
  • Manton, Kenneth G.

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.

Suggested Citation

  • Yashin, Anatoli I. & Manton, Kenneth G., 1994. "Modifications of the EM algorithm for survival influenced by an unobserved stochastic process," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 257-274, December.
    • Handle: RePEc:eee:spapps:v:54:y:1994:i:2:p:257-274
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