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

The Framingham investigation indeed indicates that in principlechoosing people with a many times greater probability of being takenill is possible by issuing from a simple medical examination. Note thatwe supposed that the relative efficacy of a preparation is the same forall the risk groups. If this premise seems unfounded, it was perhapsunreasonable to restrict the experiment by the group of highest risk.However, afterwards it is extremely necessary in any case to separatethe examined patients into risk groups for checking whether anythingis (more instructive than the placebo effect) will be found when groupsof roughly the same risk are compared with each other. In other words,the results of the Fromingham investigation should become aconstituent part of treating the results of examining (each or at leastmany) medical preparations.The stated above method naturally applies not only to medicalpreparations but also to many technological means intended toheighten the reliability of the work of the machinery.Because the Framingham experiment is so methodically important,the problem of its results being justified is raised. It seems that thatstudy provides an example of obtaining important results as well as ofa comprehensive discussion of possible doubts and objections by theauthors themselves.The authors published not only positive, but also some negativeresults. Thus, all the numerical estimates were based on 12 years ofobserving a certain population, but are they applicable to otherpopulations? Or, to ask quite sharply, is not the observed arrangementinto groups of different risks just an artefact connected with selecting arather large number of parameters? It is indeed known that anarrangement of an already collected material according to a largenumber of indications can be done not badly, but that the obtainedformulas quit being useful when new observations are added.The authors attempted to apply the obtained expression for ˆp toisolate those totalities in which new cases of the IHD must occur (afterthe 12 years of observation). This experiment was quite successful formen aged 30 – 39 years and women aged 30 – 49 years: 8 new casesfor men from a high risk group and 10 for women; 2 and 5 for thosefrom groups of low risk. However, for other ages the experimentproved a real failure. The possible explanation is that for groups moreadvanced in age such a simple medical examination made more than12 years ago was not indicative at all.As to the applicability of the concrete numerical values of thecoefficients of the function (2.9), this question can only be solvedexperimentally. I do not know whether that was accomplished. Usualestimates based on the model of two normal totalities do not admit thepossibility of an artefact.Thus, when analyzing one-dimensional samples (§ 2.1), it waspossible to be directly convinced in the correctness of the resultssimply by looking at the data represented in a form convenient forunderstanding. For a multivariate analysis such representation isimpossible which seriously hampers statistical studies in manydimensionalspaces.113