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Armitage P (2009). A note on the statistical analysis of the 1948 MRC streptomycin trial

Commentary on: Medical Research Council (1948). Streptomycin treatment of pulmonary tuberculosis. BMJ 2:769-82.

Cite as: Armitage P (2009). A note on the statistical analysis of the 1948 MRC streptomycin trial.. The James Lind Library (www.jameslindlibrary.org).
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© Peter Armitage, 2009.

Author contact details: Peter Armitage, 2 Reading Road, Wallingford, Oxon OX10 6DP, UK.
E-mail:armitage55@btinternet.com

I was recently asked for my opinion about the statistical analysis likely to have been used by Bradford Hill in analysing the results of Medical Research Council’s celebrated trial of streptomycin for pulmonary tuberculosis (MRC 1948). I think he would almost certainly have used the chi-square test. Or, equivalently, he might have taken the ratio of the difference in death rates to its estimated standard error, as a standard normal deviate (this being the square root of the chi-square value). Either of these would have seemed ideal examples of the techniques he would have been teaching to his Diploma in Public Health students, and which he included in successive editions of the textbook first published in 1937 (Hill 1937).

The chi-square for the differences in mortality in the two groups compared in the streptomycin trial is 7.38. On one degree of freedom, this has a P-value between .01 and .001. The difference in fatality rates is 2.72 times its standard error, 2.72 being v7.38. Bradford Hill might have considered a continuity correction to the chi-square (although I wouldn't advocate it and it wouldn't normally be done for the test on the difference in proportions). If this is done, the chi-square goes down to 6.04, with a P-value between .01 and .025, so, on the basis of the information in the paper, I guess he didn't do this.

I don't think that, at that time, Bradford Hill would normally have thought in terms of a ratio of death rates. The ratio observed in the streptomycin trial, 3.70, is very imprecise and I don't think Bradford Hill would have thought it worth estimating. The relative risk came into fashion much more with the analysis of case-control studies, where it became apparent that the population odds-ratio can be estimated from case-control data, and that for rare diseases this will be very close to the relative risk (that is, the ratio of risks).

References

Hill AB (1937). Principles of medical statistics. London: Lancet.

Medical Research Council (1948). Streptomycin treatment of pulmonary tuberculosis. BMJ 2:769-82