This study shows that spontaneously initiated births are well modelled by a time-dependent Poisson process when variations by month and day of the week are included. The variations by month and day of the week have a high predictive value: the frequency of births is highest in the months of June and July, and Fridays and Tuesdays stand out as the busiest days of the week. The birth frequency is at its lowest during weekends. Furthermore, we found that the sums of the digits of date numbers do not follow the Benford distribution. There is no clustering of births on days with a low sum of their digits. The digit sum has no explanatory force and can be omitted from models of birth frequency.
One possible source of error in this context is the practice followed in periods with a high number of expected births of sending women to other nearby hospitals with expected free capacity. This may lead to observation of a lower variance than would be predicted by a Poisson model, since there will be fewer days with a very high number of births than the model would indicate.
There is no reason to reject the hypothesis that a Poisson process constitutes an appropriate mathematical model for the expected number of non-elective births. The hypothesis put forward that the digit sum of the date number has an effect on birth rates (12, 13), with a Benford distribution or otherwise, can be rejected. The goodness-of-fit tests with a view to a Poisson distribution lends strong support to the results of Gam and collaborators (9), and our findings confirm the general pattern of seasonal variability described by Aarnes and Andersen (10).
This may have implications for decision-makers in the health services. With regard to the activity planning in maternity wards, some economies of scale may be reaped with a view to the variations in the number of births from one day to the next. If we assume that the arrival of new mothers-to-be follows the Poisson distribution, the standard deviation will increase by the square root of the expected number of births. This means that if some excess capacity is included in planning in order to cope with the peaks, these will be relatively lower in one large ward than in two smaller ones. For example, a ward with an expected number of eight births daily would presume that the number of daily births will exceed fifteen on only one per cent of all days. Similarly, a ward with ten expected births daily may anticipate that the number of births will exceed eighteen on only one per cent of the days. In a large ward with eighteen births expected daily, this figure will amount to 29. In other words, the two smaller wards will need to plan for a total capacity of 33 births, four more than the large one. For a general discussion of the advantages of larger units in terms of predictability of arrivals when these constitute a Poisson process, see Kirkwood and Sterne (11, p. 234). Another possibility could be to schedule some elective births to Wednesdays and Thursdays, or make provisions for elective «weekend sections».
The fact that birth rates vary with the seasons is well known and well understood. Like those of Aarnes and Andersen (10), our findings show that the September peak described by Ødegård (1) has moved to earlier in the year. One possible explanation for this shift could be that the admission to day-care in any one year requires the child to have been born before 1 September of the previous year.
The finding of a strong and significant variation by day of the week for births confirms the somewhat unexpected finding of such a variation in the Danish study (9). Why does it seem that even non-elective births «get done with» on Fridays and/or are delayed until Monday or Tuesday? One possible explanation could be that pregnant women have different ways of living on weekends and weekdays, with a differing effect on the start of labour. Other possible explanations could be that perinatal care practices may differ slightly on weekends as opposed to weekdays, or that pregnant women are more often referred to other hospitals on weekends than on weekdays.
Beyond lending support to the hypothesis that births follow the Poisson distribution, the analyses of birth data from Akershus University Hospital should not be over-interpreted. We have only analysed the number of non-elective births, and we have not controlled for other variables.
To sum up, we found that births follow a (time trend-adjusted) Poisson distribution, with variations by month and day of the week, and that the date number has no explanatory force.