Assessing mortality rates from dubious data--when to stop doing statistics and start doing mathematics

When trying to assess surgical outcomes at a particular centre, it is important to take account of case mix in terms of the types of operation performed. This is because those centres that undertake a disproportionately high number of complex operations might well be expected to have higher mortality rates than other centres whose case mix is more routine. From a statistical viewpoint, such case-mix adjustment is relatively straightforward if there are reliable risk estimates for different operation types. However this may not be the case and the risk estimates may have to be derived from several different sources which may not themselves be in agreement. Here, standard case-mix adjustment methods are no longer applicable and alternative analysis methods need to be used to make use of such unreliable risk estimates.