Brit. J. Psychiat. (ig77), 131, 345—50
Seasonality
of Mania:
a Reappraisal
By S. D. WALTER Some recently published data on the seasonal incidence of mania are re-examrned. The reanalysis confirms a strong seasonal trend in females, but also demonstrates a similar trend in males; the latter result is at variance with an earlier finding which showed no seasonal pattern in males. A simple harmonic curve would describe the data extremely well in both sexes, and the parameters of these curves (the amplitude of variation and the time of maximum incidence) are very close for males and females.
Introduction In a recent paper by Symonds and Williams (1976) the analysis of hospital admission data by a test developed by myself and Elwood (Walter and Elwood, i@7@) indicates a very significant seasonal behaviour of the incidence rates of mania in females, but no significant seasonal trend in males. Although such a conclusion may be somewhat appealing from certain points of view, it is, I am afraid, due to erroneous calculations; a reanalysis of the data shows a very similar seasonal trend in both sexes, with peak incidences at almost the same time of year and almost equal ampli tudes in the seasonal variation. Because statis tical tests for seasonality may be unfamiliar to many readers, an outline of the calculations is given
below,
together with
some
adjustment for the differing month length, June and July still have a slight excess of admissions (column 3) there is also a secondary peak
deficit
in admissions
Christmas
in
December,
in January
period.
following a
possibly
due
to
the
A very simple test which may be applied to the rates is that of Hewitt et al (z@@',), which
uses
as test statistic
the largest
rank
sum
of the
rates for any six-month segment of the year; for the data of Table I this statistic comes from the segment May—October and is equal to 57; this is in fact the highest attainable value for the test statistic,
and
has an associated
significance
level of P = 0-0130. The Hewitt test is non-parametric, making no assumptions about the kind of seasonal variation that isanticipated. On
further
the test of Walter
comments relatingto the interpretation of such
tests.
the other hand,
and Elwood uses the actual
case frequencies
and populations
maximum
one minimum
at risk, and in
addition the parameters of the best fitting simple harmonic (i.e.sinusoidalwith one
Analysis Table I shows the data reported by Symonds and Williams (1976) for males. An initial inspec tion of the rates (column 4) reveals an excess of
and
may be simply estimated;
per year)
curve
finally the adequacy
of such a simple harmonic
may
be evaluated
cases in the months May to October, which is using a goodness-of-fit x2 statistic. The essential confirmed by a ranking of months (column @); stepin the Walter-Elwoodtestisto represent
the data by weights @/n(where n is the number of cases of mania in a given month) on the
these six consecutive months are those with the
six highest admissions
monthly rates. The total numbers of (column 2), which constitute the
denominators
similar,
of these rates, demonstrate
but more erratic
pattern.
circumference of a circlewith unit radius; arbitrarilytaking iJanuary
a
each weight
Even after
345
is placed
as the startingpoint,
at an angle
0 which
346
SEASONALITY
Admissions with
Month(i)
mania
February March
..
May
July August
..
September October
24,824
25,793
27,769 28,500
702
..
30,332
624
28,465
6i@
.. ..
November .. December.. ..617 4Total..7,196328,15121-93
26,977 27,963 26,529 25,379936
637
573 53029,024
Rank for Mania admission rate per i,ooo total admissions(3)
Average total admissions/day(4)
a6,6@,6
626 676
.. ..
Total
admissions(3)
538
..
June
(296.1)(2)
511
..
April
A REAPPRAISAL
TARI.E I hospital admissions with mania and total admissions, England and Wales 1970-73
Monthly
rateJanuary
OF MANIA:
879 86o 86o
20-58
2 i
2052
20-86
896
3
8
22'54
12 u
23-72 2314 2192 22-85 22@78 21-60
950
978
918
897 902
884 8mg21-26
7
10 g
6
20-885
corresponds to the midpoint of the appropriate
and subsequent formulae are taken directly from the Walter and Elwood paper.] Similarly, lengthof 28* days and that the year is of the expected centre of gravity under the null average length 365* days. Thus the midpoint hypothesis of no seasonal pattern is given by month.
We assume that February
has an average
of January has an angle 360 X31/(2 X3651) = 15-28°, the midpoint of February has an angle
360 X (31 +@ X28k)/365*
=
44-48°, and so on.
The test then consists of comparing the centre of gravity with its expected position under the null hypothesis of no seasonal trend (i.e. equal
=
III)
=
=
Z
Im
Cos
—¿ o-00,36
and MI
the
Cos2
0/I
@fm
(columns
= 4,
corresponding 0/[4N(Z
—¿ O-00797 5
@fm)2J
and
6 of
.variances
=
1.735
and Table
are
X I05
and o@=MZSin' 0/[4N(Z v'm)2]=I 742 X 101,. where N and M are the totals of mania and all rates in all months). Because the month angles admissions respectively (from columns 2 and 4 of and trigonometricfunctionsof them are re-@ Table II and column 4 of Table III) and m is quired for any application of this test to monthly the number of total admissions in a particular data, Table II may be useful to other investi month. This leads to a test statistic gators. It would be possible to adjust the angles
more
exactly
period
(for the
to allow
for
the
actual
Williams
data,
=8-43-1-3-37=11-80
number of leap years occurring in the study such adjustment
Symonds
and
is not required,
the data
which may be compared to the table of x2 with
but it is very unlikely that this further refine
associated probability value of P 0-5. This implies that the simple harmonic model provides an adequate description of the data, with the departures from the model not being significantly different from random. (Note: the degrees of freedom for this test were erroneously reported as i i by Walter and Elwood).
572@3
560-4 611-9
626
676
635 ‘¿ 9 681-9
31,113-8 29,221-2
161-3
metric curve to the data, it is useful to examine the goodness-of-fit of the estimated rate curve with the observed numbers of mania cases. For the month with angle 0 and total ad missions m, the expected number of cases, assuming this model, is proportional to c = m[i +a Cos(0_0*)]; the constants c are shown in column 4 of Table IV, and column 5 shows the expected frequency for each month, propor tional to c/Ic; e.g. for January the expected 619-6.
29,0131
74_I
51-0 72-2 1023 November —¿ 34.7 —¿ 107-31557 132-4—162-8 December—197'! 530Total14.8998-9328,326-37,196.07,196
Having
25,569-2 27,918-6
6@6
33'o 111-6
5!! 547 538
529-6
24,164-5 26,112-0
I6@4
—¿ 51.3
Number of(6) mania -(3)
c
702
64o@4
27,459-0 28,194.8
60i-8 6i8-o
26,375-5
5781
624 615
637 573
@6-i617
24,914-46ig-6
A further test carried out by Symonds and Williams in support of their contention that the male
data
show
no
significant
seasonality
is a
x' teston theobserved andexpectednumber
of mania periods
admissions
in the two six-month
January-June
and July-December;
the
test statistic was x' = •¿ i@ on one degree of freedom, not significant. This test may be criticized on the grounds that the choice of the
six-month
periods
is
arbitrary,
weak test; if one tests the period
leading
versus November—April, one obtains x2 =
with P