The asymptotic information in censored survival data

Various procedures are considered for fitting a regression model to censored survival data in continuous time with time–dependent covariate functions. These include maximum likelihood with the underlying hazard function known completelyand known up to a multiplicative constant, and the maximization of Cox's partial likelihood. Explicit formulae for the asymptotic variances of the estimators are derived informally and compared. It is shown how sample second derivatives may be used to estimate the amount of information lost through lack of knowledge of the underlying hazard function. Corresponding results for a more general parameterization which includes the Weibull hazard function are indicated.