Dr. Dublin

In re: Correlation Between Deathrate from Heart Disease

and Deathrate from Scarlet Fever, Diphtheria and
Rheumatic Fever

 

 

I have made a preliminary study of these correla-
tions and append below a statement of the results. I wish, however, to
preface these results with a word of caution. Correlations in time series
of this sort must be viewed with a good deal of suspicion. There is no
satisfactory technique for measuring the reliability of the results. This
is a well known fact and is especially discussed in Rietz's "Handbook of

Mathematical Statistics" page 163: "There is great danger that coeffi-
cients based on time series may be wrongly interpreted. For instance a
high coefficient may result if two series fit their secular trends badly
and the badness of fit in the two cases is similar."

The probable error of the coefficient of corre.
lation in .time series does not furnish a test for significance. Here again
I quote Ré&tz, page 163: "The significance of the-probable error of a
constant computed from time series is not know." UThe coefficients of cor-
relation computed for several cases from the data for the United States
1910 to 1928 are as follows:

lag r
l. Scarlet fever Heart disease 0 ~ e224 15
2- Scarlet fever Heart disease + 5 013 + .18
3. Scarlet fever Heart disease + 4 «35 # 215
4. Rheumatic fever Heart disease +1 324 14
5. Diphtheria Heart disease - 3 299 + 012

Attention is particularly drawn to the last item
in which merely by the way of illustration a computation was made correlating
diphtheria in a given year with heart disease three years prior. Note that
this gives the highest correlation in the series, namely, .55, yet this is an
absurd way of comparing observations for it would imply that heart disease
in one year causes deaths by diphtheria three years later. This example was |
done merely to show how unjustified it is to conclude from a relatively high
correlation obtained in this manner that there is causal relation between
the two phenomena correlated. The correlation coefficient of e35 such as
observed in example three would, in itself, be regarded as fairly important.
For example, this is the degree of correlation observed between stature of
brother and sister, (See Pearl, Medical Biometry, page,310)but as just
— the case of time series, such correlation cannot be taken ser-
iously. .
—

It is easy to explain why there is no very clear cut

relation between the deathrates from the several diseases mentioned above

and that from heart disease,in spite of the fact that we have every reason
to believe that actually these diseases are frequently followed by heart
impairments. The fact is that such heart impairments, if they become the
reported cause of death at a later stage, do so at all kinds of irregular
intervals varying from perhaps a few weeks to fifteen or twenty years or
even more, The consequence is that the picture becomes blurred beyond
recognition.

This is my provisional report. If after consideration of
the facts submitted it is desired to proceed to complete analysis of the
figures, considerable additional work would be required to cover both United
States and Metropolitan figures and to go into some detail in the way of
trying out varying lags between the deathrates in question. I have every
reason to believe that the samples given above are quits representative of
the results that would be obtained if the work were extended in greater
detail °

 

July 17,1931