J. Soc. Cosmetic Chemists 18 455-467 (1967) ¸ 1967 Society of Cosmetic Chemists of Great Britain The evaluation clinical trials of placebos in P. MACDONALD* Presented at the Symposium on "Product Testing", organised by the Society of Cosmetic Chemists of Great Britain in Eastbourne, Sussex, on 15th November, 1966 Synopsis--A model is proposed for the response of living organisms to the action of drugs when placebo reaction is likely to occur. The estimation of the parameters in the model is discussed together with tests of hypotheses about the parameter values. INTRODUCTION The clinical evaluation of drugs and medicaments is as old as medicine itself but it is comparatively recently in the history of the subject that the actions of various drugs have been recorded and compared in a quantitative and scientific fashion. The value of a treatment can only be expressed in meaningful terms by reference to the state of affairs when the treatment is not used, either because of an alternative treatment or because of the absence of any treatment. If a disease is severe so that the mortality rate for sufferers from the disease is high and if no treatment is currently known it is clear that any substantial reduction in the mortality rate is a sufficient indication of the value of a new treatment. A more common state of affairs is the case of a well established treatment for a disease where two questions may arise: i. Is the customary treatment more effective than no treatment? it. Is the customary treatment less effective than one or more new possible treatments? 'Dept. of Mathematics, Brunel University, London. 455

456 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS The second question may usually be answered by comparison in a clinical trial but ethical considerations require that new treatments are admitted to a trial only if there are good grounds for expecting them to be as least as effective as the old treatment. The first question is more subject to ethical difficulties in the answering, since only in the mildest diseases may treatment be stopped in order to study the effect of no treatment. The ethical considerations referred to above are not unequivocably interpreted, as has been pointed out by Hill (1), since the only well estab- lished treatment may actually be inferior to the absence of treatment, as in the use of anti-coagulant in cerebrovascular disturbances. No scientist is completely free from the ethical implications of his work and this applies to the statistician as much as to any other scientist. We may, however, consider the scientific aspects of a problem without reference to its ethical context. When attempting to answer the first of the two questions above, a placebo is frequently administered instead of merely neglecting those patients who are to receive no treatment. One of the original meanings of placebo is derived from the same root as placate, that is the placebo is given in order to please the patient or to keep him from the knowledge that he is being neglected. Lasagna (2) has given several meanings for placebo we are at present concerned with the administration of a dummy treatment (3), which may also and incidentally please the patient either consciously or in more subtle ways. There is little to be gained by distinguishing form- ally between placebos and dummies (4). QUANTITATIVE RESPONSES TO DRUGS When a drug or medicament is administered to a patient the response is likely to be quantitative if the treatment has pharmacological properties but it may be quantitative or qualitative if the effect of the treatment is psychological or psychosomatic. The effect of a pharmacological preparation on a living organism must depend on the potency of the preparation and on the dose used but the mode of observation of the effect may either be quantitative as well or it may only be possible to observe success and failure of the treatment. The psychological results of the administration are likely to be qualitative the treatment either pleases or it does not, although degrees of pleasure may sometimes occur. Both pharmacological and psychological effects are probably present in most clinical trials, each to a greater or lesser extent. If the observed