1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

when formulating problems about optimal solutions concerningeverything happening in life usually very soon leads to a cul-de-sac.In addition, the cited investigation concerned a totality of men thatwas never attempted to be influenced by pharmacological means. Andit is absolutely unclear whether its quantitative characterization willpersist had it been otherwise. Most likely, not, and that anycomparison of 7mm % cholesterol with 4.5mm mercury column ofsystolic blood pressure becomes senseless.Thus, we can not at all attribute practical significance to the citedinvestigation of being able to indicate a desired way of influencing riskfactors for preventing the IHD. In my opinion, that investigation hasno purely applied medical significance at all. However, there exists acertain set of studies for which its role should be essential. I bear inmind the examination of various medicinal preparations. Statisticalinvestigation is the only way to obtain trustworthy results about theirefficacy.In the most simple case two totalities of men are formed by randomselection, one of them (the experimental group) is treated by apreparation, the other one (the control group) gets placebo, a harmlesssubstance similar in appearance. Results are compared, and neither is itforbidden to compare them with general statistical information aboutthe mean rate of the IHD in a city, country, etc. However, the so-calledplacebo effect is regrettably often revealed in modern cardiology.It consists in that the results of both groups practically coincidewhereas the mean results for a larger totality are much worse 20 . Thiscan be rather likely explained: apart from medicines, the physicianapplies other means for helping patients like advising him/her about arational way of life. During modern experiments, even the doctor doesnot know to which group does a given man belong. As a result, againstthe background of general treatment by a skilled physician, the effectof chemotherapy, if it exists, is absolutely imperceptible. On the otherhand, the overwhelming majority of the population either does notvisit physicians, or get treated by less skilled specialists, and theresults are much worse 21 .The placebo effect makes it impossible to judge the real benefit ofpharmacological means. It can be supposed that the point is, that thefrequency of the occurrence of the IHD is not so high. Whenconsidering the extreme case by supposing that some sickness rate is1% and that some preventing means lowers it to 0.5%, any reliableestimation of the efficacy of the preparation applied should be basedon at least a thousand patients (on two thousand when counting thecontrol group). And in that control group the number of people takenill µ 1 will obey the Poisson distribution with parameter 10, and in theexperimental group, their number µ 2 will obey the same distributionwith parameter 5. The probability of a wrong result (µ 2 ≥ µ 1 ) will be,roughly, Φ( − 5 / 15) = Φ( −1.29) ≈ 0.10, which is not so small 22 .However, had we been able to select for the experiment a group ofpeople with probability of being taken ill of 20%, then for the sametwofold decrease of the sickness rate (down to 10% due to the actionof the preparation) 100 patients will much better satisfy us.112