Least squares type estimation for Cox regression model and specification error

A new estimation procedure for the Cox proportional hazards model is introduced. The method proposed employs the sample covariance matrix of model covariates and alternates between estimating the baseline cumulative hazard function and estimating model coefficients. It is shown that the estimating equation for model parameters resembles the least squares estimate in a linear regression model, where the outcome variable is the transformed event time. As a result an explicit expression for the difference in the parameter estimates between nested models can be derived. Nesting occurs when the covariates of one model are a subset of the covariates of the other. The new method applies mainly to the uncensored data, but its extension to the right censored observations is also proposed.