## Irvine Loudon

Print publication date: 1992

Print ISBN-13: 9780198229971

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780198229971.001.0001

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# (p.532) appendix 4 Numbers of Births and Statistical Significance

Source:
Death in Childbirth
Publisher:
Oxford University Press

An important question, sometimes overlooked in studies of maternal mortality, is the size of the population and the number of births. Although in the past maternal deaths were common in relation to other causes of death amongst women of childbearing age, maternal deaths seen in the context of total deliveries were uncommon events. Even a level of maternal mortality as high as 100 per 10,000 births can be turned round and expressed as a survival rate of 99 per cent. In the comparison of MMRs a large number of births is needed to achieve statistical confidence. This is shown in the table accompanying this appendix which assumes an MMR of 50 deaths per 10,000 births.

If there was no such thing as random variation the figures in the third column under the heading ‘critical range of variation’ would all be 50. What, then, is the range of random variation? Common sense would tell us that if we had data from two towns, A and B, which showed that in a certain year there were two maternal deaths in town A and three in town B, it is unlikely that such a small difference had any validity. If on the other hand we had data from two large countries and found that in country A there were 20,000 maternal deaths a year while in country B there were 30,000 maternal deaths a year, it would be highly probable that the risk of dying in childbirth in country B was genuinely higher than it was in country A. We would feel that such a large difference was unlikely to be due to chance; in other words it could not be attributed to random variation.

Table A4.1 shows the extent of random variation in MMRs in a selection of places in which the annual number of births varied from as few as 1,000 to as many as 100,000. It is assumed that in all of them the average rate of maternal mortality was 50 per 10,000 births. Supposing for the sake of argument that we could identify a large

Table A4.1 Showing the Range of Random Variation (Critical Range of Variation) in Maternal Mortality Rates in Relation to the Number of Births, assuming a Rate of Maternal Mortality of 50 Maternal Deaths per 10,000 births

Annual births

Maternal deaths

Critical range of variation

Regions with birth rates close to these values during the 1930s

1,000

5

5–95

Doncaster, Darlington

5,000

25

30–70

Bristol, Newcastle upon Tyne

10,000

50

35–65

Manchester, Amsterdam

25,000

125

40–60

Lancashire, Middlesex, New Zealand

50,000

250

43–57

Paris

100,000

500

45–55

Sweden, Belgium, Australia

(p.533) series of towns which, like Manchester and Amsterdam, had 10,000 births a year, and from which we had accurate vital statistics. Let us also suppose that through some form of God-like omniscience we knew that the true MMRs in all these towns was exactly the same: 50 per 10,000 births. It would be very odd if, in practice, the actual number of maternal deaths was exactly 50 for every 10,000 births. Random variation would be certain to destroy such neatness, and mortality rates would vary. But by how much? Here the answer is 35–65. This means that there is a 95 per cent likelihood that although the rates would vary, they would not stray outside that range.

Putting it another way, if one town (Manchester, for instance) recorded a rate of 64, while another (Amsterdam) recorded a rate of 36, although at first sight it would look as if Amsterdam was a much safer town to have a baby in, the difference is not statistically significant at the 95 per cent level. We could say Amsterdam was probably safer, but no more. Of course the degree of statistical certainty (and thus the range of critical variation) depends on the degree of statistical significance that we choose. It may be 90 per cent, 95 per cent, 99 per cent, or 99.9 per cent; there never is or can be absolute certainty. Here, in this table, we have chosen 95 per cent certainty and the calculation for that degree of certainty (‘statistical confidence’) is based on twice the standard error.

The practical lesson is that generally speaking comparisons of annual values of maternal mortality are only useful if populations and the number of births are very large. Differences revealed by local studies based on counties and small towns generally achieve significance only when they show consistent trends over a period of several years in order to accumulate enough births for differences in mortality rates to be significant. Comparisons have been made and false conclusions drawn by ignoring the factor of statistical significance. It also means that a time-series of rates of maternal mortality will, other things being equal, show wider swings on either side of the average rate if the number of maternal deaths is small than if the number is large. This can often be seen in the nineteenth century when graphs of annual rates of maternal mortality in lying-in institutions are compared with graphs of maternal mortality in whole countries.