Journal of Epidemiology and Community Health 1993; 47: 362-367 Changing seasonality of birth-a possible J Epidemiol Community Health: first published as 10.1136/jech.47.5.362 on 1 October 1993. Downloaded from environmental effect D Russell, A S Douglas, T M Allan Abstract five decades and for all 50 years combined. Study objective-Seasonality of birth was The statistical analysis was in five stages: examined to determine whether this has (1) Correction for unequal month length. changed over the last half century. (2) Correction for secular (non-seasonal) Design-Time-series analysis was carried trend. out on retrospective data, both for the full 50 (3) Estimation of a single cyclic trend using a year period and for the five decades within sine curve model: cosinor analysis. that period. Although the primary objective (4) Modification of the sine curve model to was to investigate seasonality by fitting an allow for a second distinct peak in the data: appropriate model and examining changes modified cosinor analysis. over the period studied, non-seasonal trends (5) Analysis ofvariance to test the significance were also examined. of the components of the sine model. Setting-Data by month were obtained from the Registrar General on all births in (1) CORRECTION FOR UNEQUAL MONTH Scotland during the years 1938-87. LENGTH Subjects-There was a total of 4 325 000 Each monthly total was corrected to the value it births in the 50 years examined. would have in a month of 31 days. Measurements and main results-There are two peaks to the seasonality rhythm-one (2) CORRECTION FOR TREND wide, in spring/early summer and one nar- Long and medium term trends were present in the row, in October. Cosinor analysis, modified data. These had to be eliminated as far as possible to allow for the second peak, was used to fit a in order to test and assess the seasonal variation sine curve model. Analysis of variance independently. This was done in two stages: showed that this was adequate and estab- (a) To eliminate medium term variation lished the significance of both peaks. The between years, each month's (31 day corrected) main peak of seasonal excess rose to a value was expressed as a proportion of the whole maximum in 1948-57, and thereafter year's total, multiplied by 12 so that the average declined by two thirds. While the position of monthly value in each year was 1. the main peak moved forward two months (b) This still left a bias in the monthly over the 50 years, the October peak remained averages if there was a net increase or decrease http://jech.bmj.com/ unchanged until the final decade, when it over the 10 or 50 year period, as the December rose slightly; thus its relative importance values are on average a year later than the January increased steadily from 1948 onwards. values. This bias can be quite important when, as Conclusions-The changing biological in 1968-77, birth rates are rising or falling sharply. rhythm may be related to alterations in the Thus, the overall trend was fitted to the original climate and environment or to social dif- yearly totals by linear regression, and the pro- ferences. portional drop through one year calculated from the slope of the regression equation. This was on October 5, 2021 by guest. Protected copyright. Epidemiol Community Health 1993; 47: 362-367 used to correct the values used in (a), so that the average monthly value was still 1. For example, if Department of Public the birth rate is falling, December values will be Health During the past two centuries the seasonal increased by a proportion (5-5/12) of the yearly D Russell of births and deaths have been studied proportional drop, and January values decreased Department of rhythms Medicine and using acceptable data. These rhythms have by the same proportion (as the midpoint of a year Therapeutics altered because of social change' but also prob- is between June and July). A S Douglas ably because of climatic change. Bearing in mind Wellcome Research Library the concern about global warming, the green- (3) COSINOR ANALYSIS T M Allan house effect, the hole in the ozone layer, atmos- A computer program called cosinor analysis was Medical School, pheric pollution, and other environmental used2 3 4. This uses 12 monthly totals or averages University of Aberdeen changes, this study examines the seasonality of to determine how much of the seasonal variation births in Scotland over the 50 years 1938-87. can be explained by a sine curve and to fit the best Correspondence to: curve to the data by least squares. The output Professor A S Douglas University Department of from the program includes: Medicine and Therapeutics, Methods (a) The amplitude (largest distance from the Medical School, Polwarth Building, Foresterhill, The monthly data on births were obtained from mean) of the sine curve, and the position of the Aberdeen AB9 2ZD the Registrar General for Scotland (1938-87) peak and trough (these are six months apart, and need not be at one of the 12 Accepted for publication (table I). Males and females are considered exactly plotted June 1993 together. The data are examined for each of the points). Seasonality of birth 363 J Epidemiol Community Health: first published as 10.1136/jech.47.5.362 on 1 October 1993. Downloaded from (b) A correlation coefficient R and a corres- variability-the within month mean square is the ponding significance level. R is the proportion of average of the 11 monthly variances which are between-month variation explained by the sine assumed equal (in the basic model, October is not curve. The significance level is based on an F test; assumed to be equally variable), and thus has 99 of the (12-1 = 11) degrees of freedom available, degrees offreedom (10 year series) or 539 degrees two are used to estimate the curve, leaving nine for of freedom (50 year series); it can be compared the deviations from the curve. with mean squares for (a), (b), and (c) above. (See (c) A graph of the fitted curve, the actual table III). monthly totals, and 95% confidence intervals for deviations from the curve, based on the unex- plained variation. Results The program makes allowanvce for varying The data after month correction are presented in lengths of month, plotting eaclh point at the table I. Figure 1 shows the secular trend of births midpoint of the month on a scale of 365 days. It in Scotland over 50 years. After the 1939-45 war does not, however, take account of year to year there was an increased number of births for three variation, which is considered in (5). or four years followed by a return to the pre-war number by 1955. Thereafter, the numbers rose (4) MODIFIED COSINOR ANALYSIIS again to a peak around 1965, followed by a steady The most important deviation frorm the sine curve decline until the mid 1970s. was found to be an extra sharp peak in October. The data can be visualised in figure 2A (total 50 To see how well the sine curve fit:s the rest of the years), which shows the main, spring peak and the data, the cosinor program was rerun with the small (but persistent) subsidiary peak in October. actual October value replaced by tiie average ofthe Figure 2B shows the same data with the October September and November values3. In all cases a peak replaced by the mean of September and considerably better fit was obtaiined. The cor- November. The features of cosinor analysis are relation coefficient and its signific*ance level need shown, with 95% CI, mesor line, and amplitude. to be modified, as there are now only 11 Table II and figure 3 deal with the correction independent values. In addition oan approximate for linear trend. Table II shows the regression test of the significance of the Ocitober peak as a coefficients, while figure 3 exemplifies the cor- deviation from the modified siIne curve fit is rection for 1968-77 (a period of falling births). available. The further results are concerned with fitting a sine curve (table III, figs 2 and 4) to the data by (5) ANALYSIS OF VARIANCE decade, both without and with the October cor- The components ofthe between Inionth variations rection. Table III confirms by analysis ofvariance are (a) the sine component (es:timated for 11 that the data are well described by a sine curve. months) (b) the 11 deviations froem this, and (c) The significance levels, correlation coefficients, the October deviation. The data aire examined to and amplitudes are greater when the October determine whether these are sigriificantly larger value is modified. Over the 50 years the peak has than would be expected from thie year to year tended to move fowards from April-May to June- within month variations of the (linear trend July as the seasonal difference has become smaller. adjusted) invidual values. The wit]hin month vari- In all cases, the October deviation is signifi- 120 000- ation is an estimate of basic non-systematic cantly larger than other deviations, and is always http://jech.bmj.com/ positive. This is strong support for the overall 115000- hypothesis ofa systematic special effect in October only. No other month shows a consistent pattern of large deviations in the same direction. Thus, in 100 000- U, all decades the October peak is established as real; t moreover, its size is relatively constant, although 90 0007 the latest decade has the largest peak. Q-iu- on October 5, 2021 by guest.