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