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LETTERS: W J Edmunds and N J Gay Health professionals do not understand mathematical models BMJ 2000; 320: 581a [Full text]

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But the teaching has to be right!

G H Hall   (25 February 2000)

Re: But the teaching has to be right!

B. Burt Gerstman   (17 July 2002)

But the teaching has to be right! 25 February 2000
G H Hall, Retired Send response to journal: Re: But the teaching has to be right!	Edmunds and Gay's concern about the lack of understanding of mathematical models by health workers leading to neglect of possible benefits seems well founded. One difficulty with their solution- education of decision makers- is that the lessons in this area 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 literature. 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. Statisticians and mathematicians can't do this. We've got to find and use the skills of those doctors who have a foot in both camps. In the meantime, it would be helpful if the "literature" got it right, especially in didactic articles and books, and even more importantly, were ready to admit and correct mistakes. GH Hall MD FRCP (Rtd. physician)
Re: But the teaching has to be right! 17 July 2002
B. Burt Gerstman, Professor San Jose State University, San Jose, CA, US, 95192-0052 Send response to journal: Re: 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 literature." 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 cites: "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. Sincerely, Bud Gerstman San Jose State University San Jose, California, USA 95192-0052 References 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 - 169.