A clinic has conducted a trial in which a typical patient S referred to it on the basis of information v, and who has subsequently been diagnosed to have disease type u, is allocated treatment t (from among a set of trial treatments) and the outcome y of the treatment recorded. The clinic has therefore been able to obtain a reasonable assessment of pS(y|u, v, t). A new patient R with information vector vR but with unknown disease type uR has now been referred to the clinic which is naturally interested in how the patient will respond to treatment t, in other words to evaluate pR(yR|vR, t).

The clinic has already carried out an independent investigation into the use of the information v for diagnostic purposes and so can evaluate pR(uR|vR).

Can you provide the clinic with a means of evaluating the effect of treatment for this new patient?