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

258 – 82 – 176 cases or 68.5% of all cases of the disease would haveoccurred in spite of our promise of the opposite. The problem ofindividual forecast is therefore far from being solved.Let us now have a look at the estimates of the coefficients informula (2.9) and at the possible conclusions. These estimates differfor different age groups and also for women and men. For the group ofmen of all ages the estimate ˆα = − 10.8986. Other estimates are shownin Table 4. It is seen there that the coefficients of two factors out ofseven (relative weight and haemoglobin) comparatively little exceedtheir mean square errors in absolute value. They should be recognizedas less influencing the IHD than the other five. One of those five, theage, can not be changed, and it is convenient to refer the action of therest of them with the influence of age.For example, a daily packet of cigarettes provides 2 points and thecorresponding increment of the linear function is 0.7220 whichapproximately means 10 years of age. In other words, smoking apacket daily brings forward by ten years the occurrence of myocardialinfraction. This figure remains approximately the same in the differentage groups of men. For women, the harm of smoking is representedessentially weaker. It is not quite clear why, either the figuresrepresent reality or the number of smoking women was small (1562women out of 2669 did not smoke at all, and only 301 used a packetdaily) and the statistics was incomplete.It is inconvenient to compare the influence of cholesterol and bloodpressure with the action of age by means of Table 4. The point is thatthe coefficients of the linear combination of any dimensionalmagnitudes are also dimensional (whereas in our case, it is demandedthat the linear combination be dimensionless). The comparison of thetype we have applied leads, for example, to such a result as 7mg % 19 ofcholesterol is equivalent to a year of life. We know very well what is ayear of life, but is 7mg % much or little?For answering that question we ought to know how large are thefluctuations of the content of cholesterol. Or, that content be dividedby its mean square deviation and thus expressed as a dimensionlessmagnitude. After accomplishing this procedure with all the riskfactors, a comparison of their coefficients provides the followingarrangement of the factors in a decreasing order of importance: age,cholesterol, smoking, blood pressure, abnormal electro-cardiogram.Weight and haemoglobin influence less. The somewhat conditionalcharacter of such norming that has only a statistical sense should beunderstandable.A question such as the following naturally comes to mind: If,according to Table 4, 7mg % cholesterol is equivalent to the samenumber of years of life as 4.5mm of mercury column of bloodpressure, then what is easier to decrease, the former by 7mg % or thelatter by 4.5mm of mercury column? Or, the question is formulatedabout dimensionless magnitudes concerning the range of the scatter,but this is not the same. Concerning the comparative possibilities ofinfluencing the cholesterol and blood pressure, we likely enter ascientific cul-de-sac: in all probability, those are quantitativelyincomparable. In general, the dominant present style of reasoning111