A note on efficient estimation from case-control data

It is well known that it is valid to treat case-control data as if they had been obtained by random sampling when estimating the odds-ratio parameters of logistic regression models. The result has been generalised to estimation of the regression parameters in multiplicative intercept models and it has further been pointed out that the approach may be applied to non-multiplicative intercept models if the parameter space is first enlarged to include a multiplicative intercept term. This note is concerned with the efficiency of the approach.