Re: But the teaching has to be right!
I was browsing one day, in the summer of 2002, when my search led me
to the article by Panagiotopoulos et al. (1999)--the electronic version--
about the herd immunity effects of a vaccination program gone awry. Just a
click away was an interesting letter by Edmunds and Gay (1999), and just
one click from this, the Rapid Response by Hall (1999). While this now
hardly qualifies as a Rapid Response, some two years too late for that,
the timeliness of the Internet is somehow cross-sectional. Sadly, we shall
call it just a Response.
Regardless, the remarks by Hall bear witness! He begins with a
grouse, but who can blame him?
"One difficulty . . . is that the lessons in [using advanced
mathematics in medicine] are often wrong, even when given by experts and
published by leading journals. For example, incorrect substitution of
probability for odds (BMJ,1997,30 Aug, p540), and definition of likelihood
ratios as sensitivities (Lancet,1999,Nov 13, p1721). Incredibly, although
both these errors were acknowledged by the authors and the editors, their
corrections were faulty as well. No wonder ordinary mortals are puzzled by
the inconsistencies and contradictions which beset their attempts to grasp
and interpret the figures and formulae now ornamenting medical
Is it no wonder that epidemiology has been proclaimed "dead on
arrival"--to have faced its limits (Taubes, 1995). As epidemiologists have
stewed in their own juices, they fear their's a junk science, unworthy of
trust and support, or, worse yet, funding. But are these misuses of
numbers the cause or the result of a junk science? These thought are
tormenting to epidemiologists (Susser, 1989), and apparently to medical
men and women as well (Hall, 2000). I have myself wondered the value of
using simple numerical expressions to explain complex biological
phenomena. But as a matte of faith, I cannot turn my back on my
discipline. (I am an epidemiologist, after all.)
All is not lost, however, as this is not a new problem, and some of
the best insights into it solution are historical. One of the most
succinct statements on this conundrum was found in an old article in my
files which written by the renown epidemiologists Abraham Lilienfeld
(1973). The article quotes Robert Solo's critical assessment of an
econometric model, which represents a similar approach to economics. He
"Ultimately, the mode of expression that will most conform to the
scientific ideal will not be the image-free symbols of mathematics but
rather the imagery of normal communication and intercourse with its
reference base in the specifics of experience, for only if the general
statement is so framed can it be continuously bridged into direct
observations and contrasted with ongoing experience."
This statement corresponds nearly perfectly with Hall's intuitive
appeal, in which he states
The notorious resistance of doctors to "sums" may be due to the left-
right brain dichotomy, and therefore partly incorrigible. I have found,
however, that by working backwards from clinical examples to a
quantitative representation greatly enhances comprehension and
appreciation of the advantages of numerical methods.
I am therefore hoping that you publish Hall's extraordinarily
illuminating eLetter in hard copy, as it would be a shame to have this
insights buried in the ether of bmj.com without proper indexing by
Medline. Of course this would have to be preceded by a brief introduction
to provide some context, which might be provided in part by this letter.
San Jose State University
San Jose, California, USA 95192-0052
Edmunds, W. J., & Gay, N. J. (2000). Health professionals do not
understand mathematical models. BMJ, 320(7234), 581a-.
Hall, G. H. (2000). But the teaching has to be right! Available:
http://bmj.com/cgi/eletters/320/7234/581/a#6833 [2002, July 16].
Lilienfeld, A. M. (1973). Epidemiology of infectious and non-
infectious disease: some comparisons. Am J Epidemiol, 97(3), 135-147.
Panagiotopoulos T, Antoniadou I, Valassi-Adam E. Increase in
congenital rubella occurrence after immunisation in Greece: retrospective
survey and systematic review [with science commentary by A Berger]. BMJ
1999; 319: 1462-1466
Susser, M. (1989). Epidemiology today: 'a thought-tormented world'.
International Journal of Epidemiology, 18(3), 481-488.
Taubes. (1995). Epidemiology faces its limits. Science, 269, 164 -
Competing interests: No competing interests