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

Seasonality of mania: a reappraisal.

Brit. J. Psychiat. (ig77), 131, 345—50 Seasonality of Mania: a Reappraisal By S. D. WALTER Some recently published data on the seasonal incidenc...
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