The EM Algorithm for Cox's Regression Model Using Glim

The methods described by Aitkin and Clayton (1980) for fitting parametric regression models to survival data consist of a two‐step recursive algorithm. In the first step a transformation of the observed failure times is found such that the transformed times obey a model which may be simply fitted, i.e. the exponential model. The second step updates the estimates of the parameters by fitting the simple model to the transformed observations. The steps are repeated until convergence. We have suggested elsewhere (Clayton and Cuzick, 1985) that estimation in a very general class of semi‐parametric models may be carried out using a similar algorithm in which the transformation is non‐parametric. Here we apply this idea to the proportional hazards model and show that in this case the iteration is an EM algorithm and leads to maximum partial likelihood estimates. It is shown how this algorithm allows the Cox model to be fitted using the computer program GLIM (Baker and Nelder, 1975).