RELATIONSHIP BETWEEN SICKNESS ABSENCE AND METEOROLOGICAL ... · relationship between the weather and sickness absence. The object of this investigation is to develop a model to illustrate

Brit. J. prev. soc. Med. (1972), 26, 238-245

RELATIONSHIP BETWEEN SICKNESS ABSENCE ANDMETEOROLOGICAL FACTORS

S. J. POCOCK*

TUC Centenary Institute ofOccupational Health, London School ofHygiene and Tropical Medicine, London W.C.1

Sickness absence rates are higher in winter than insummer and also the incidence of many diseases isaffected by climatic conditions. Both these factslead one to suspect that there is a genuine causativerelationship between the weather and sicknessabsence. The object of this investigation is todevelop a model to illustrate this relationship inorder to obtain some idea of its precise form.Any effect of weather on the weekly incidence of

sickness absence can be assumed to take one ofthree forms:

(i) a steady long-term cumulative effect wherebythe more adverse weather conditions in wintereventually affect the health and absence behaviourof employees;

(ii) a more short-term effect whereby deviationsof weather conditions about the seasonal norm mayinfluence the sickness absence frequency in thesame or subsequent weeks;

(iii) the spread of infectious disease, wherebyone week's sickness absence frequency is determinedto some extent by the amount of infection broughtover from previous weeks. Though waves ofinfection are influenced by weather conditions (e.g.,they are more frequent in winter), their occurrenceis largely unpredictable and they must be consideredseparately from (i) and (ii).The regression model described below is designed

to assess the importance of the effects of types (ii)and (iii) after the elimination of the broad seasonaltrends indicative of effects of type (i). This model isillustrated by sickness absence data from oneorganization.

LITERATURELittle research has been carried out on the effect

of the weather on absenteeism. However, severalattempts have been made to discover the relationshipbetween meteorological factors and various indicesof mortality and morbidity, in most cases forparticular types of disease.

MORTALITY STUDIESYoung (1924), Russell (1926), and Wright and

Wright (1945) are three early studies of the effect of

climate on weekly or monthly numbers of deathsdue to respiratory disease. Their analyses based onsimple correlational techniques showed that lowertemperatures were associated with higher mortalityrates. More recently, Boyd (1960) looked at theassociation between various measures of climateand air pollution and deaths from respiratory andheart disease in London and East Anglia duringeight winters. Temperature and humidity two weeksbefore death had strongest correlations with weeklymortality whereas pollution was of secondaryimportance. The effect of fog appeared only duringperiods of low temperature and then for respiratorydisease only.One serious flaw in all these studies is the failure

to take into account the infectious nature of respira-tory disease. For instance, during an influenzaepidemic the weekly deaths from respiratory diseaserelate more directly to the amount of infection inprevious weeks than to the actual weather conditions,one measure of this infection being the previousweek's numbers of deaths. Thus, the autocorrelationpresent in such time series of respiratory deathsmust be taken into account before one can commenton the effect of weather conditions. One furtherfault in the methods of Wright and Wright andBoyd is the failure to eliminate broad seasonaltrends (e.g., by using deviations from a movingaverage or some parametric trend) before investi-gating correlations between disease and meteorologi-cal factors. Spicer (1959) draws attention to the needto use such deviations, sometimes called residuals,and this approach has been adopted in the regressionmodel described below.

MORBIDrrY STUDIEsHolland, Spicer, and Wilson (1961) used two

measures of the monthly occurrence of disease-admissions to the Emergency Bed Service of aLondon hospital and admissions to the sick quartersin three Royal Air Force stations. The climaticfactors considered were average temperature,absolute humidity, rainfall, barometric pressure,sun, and pollution (smoke), and analysis of covari-ance was used to eliminate broad seasonal and

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RELATION OF SICKNESS ABSENCE TO METEOROLOGICAL FACTORS

annual trends. For the London hospital there wasno significant relationship between non-respiratorydisease and the weather. However, for respiratoryillness, temperature and air pollution both had asignificant effect in adults only. For the RAFstations, the effect of temperature on respiratoryillness was evident.Davey and Reid (1972) studied the relationship

between air temperature and outbreaks of influenzausing a straightforward descriptive approach whichperhaps makes it difficult to generalize from theirconclusions.The effect of climate on the incidence of polio-

myelitis has provoked a considerable amount ofresearch, much of which is critically summarized inLawrence (1962). The incidence of poliomyelitis washigher in summer but the factor or combination offactors (climatic or other) which caused this summerpeak was not immediately obvious. There aremultitudinous variables with seasonal cycles andtheir close association makes distinction betweenthem difficult. Furthermore, Lawrence points outthat the variations in meteorological conditionsover short periods and over quite small areas cannotbe adequately illustrated in standard meteorologicaldata.

Spicer (1959) and Wise (1966) illustrate the typeof methods most appropriate for estimating theeffect of climate on disease. They both use the samedata consisting of the monthly numbers of polio-myelitis inceptions during 1947-56 with the corres-ponding averages for temperature and relativehumidity. Spicer used an analysis of covariancemodel to remove annual and seasonal trends, thusobtaining multiple regression coefficients of log(poliomyelitis incidence) on the climatic variablesin the same and the preceding two months. All sixcoefficients were bigger than their standard errors(positive for temperature and negative for relativehumidity) with temperature in the preceding monthmaking the greatest contribution, and Spicer thusinferred that warm, dry weather does play a part inthe spread of the disease.Wise first points out that the main factor deter-

mining one month's poliomyelitis rate is the previousmonth's incidence of the disease. He thus elaborateson Spicer's model by introducing the previousmonth's poliomyelitis as an extra covariate. He alsoallows the regression coefficients for temperatureand relative humidity to have different values fordifferent calendar months; the consequent peakeffects are shown to occur in late summer and earlyspring. He concludes that the temperatures in July-September have a direct influence on poliomyelitisoccurrence through to October and perhaps even

December. Wise's analysis thus provided greaterinsight into the behavioural pattern of the disease.

DATA AND METHODSSICKNESS ABSENCEOne limitation in many investigations of the

relationship between weather and disease is that thedata about the disease characteristic are oftencollected over large areas (e.g., national or regionalfigures) with the result that local variations inmeteorological conditions or disease incidencecannot be taken into account. Such a macroscopicapproach can result in failure to discover the truenature of such a relationship. A similar failure canoccur if data are grouped according to quite lengthytime intervals (e.g., a month or more). Fortunately,sickness absence is a sufficiently common phenome-non for one to be able to adopt a more detailedapproach, the records of a single factory being idealfor this purpose. In this case, one site of a largecontinuous process industry in south-east Englandhas been chosen.The population under study is defined as the

1,057 male manual workers who were in employ-ment from 1960 to 1964. The numbers of spells ofsickness absence starting in each week of this five-year period have been accumulated from the recordsof individual employees. Sickness absence includesall spells of absence due to medical incapacity (andthus accompanied by a doctor's certificate) whichlasted for one shift or more. Self-certification ofshort spells was introduced in 1965 and the subse-quent change in absence behaviour means that theperiod of observation is before then. Diagnosticinformation has enabled the weekly numbers ofspells to be categorized into upper respiratorydisease, bronchitis, and non-respiratory illness.The estimated seasonal trend in the total weekly

spells of sickness absence is shown as a continuousline in Figure 1. This curve has been obtained byusing harmonic analysis and the details of thisapproach are given by Pocock (1972). The dottedline in Figure 1 is a simple harmonic of period oneyear and can be seen to provide a good fit to theseasonal trend except for the peak at New Year, thedrop in absence before Christmas, and the slightdrop during August.

It is essential to allow for the effects of non-climatic factors on sickness absence before studyingits association with the weather, and these exceptionsindicate that one such factor is the occurrence ofannual and public holidays. At the factory annualholidays were spread throughout the summer butthe peak holiday period was from mid-July to mid-August and the relevant six weeks of each year have

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THE WEATHERThe nearest weather station to the factory was

10 miles away, which should be near enough tomake any differences in weather between the twoplaces negligible. The following meteorologicalinformation was available for every day from 1959to 1964:

(1) the maximum temperature (MAX TEMP) for thet t t 24-hour period starting at 9 a.m. on the day,New Auaust Christmas to an accuracy of °F;Year Bank 'Holiday week (2) the minimum temperature (MIN TEMP) for the

,,I, , , 24-hour period starting at 9 a.m. the previouso 0 20 30 40 50 day, to an accuracy of 1°F;Week number (3) the rainfall (RAIN) recorded in I-0ths of anEstimated seasonal trend in weekly spells (1960-64). inch for the 24 hours starting at 9 a.m. on the

day;excluded from analysis. The effect of Easter (4) the hours of sunshine (suN) recorded to anWhitsun on sickness absence is short-lived so accuracy of _th of an hour for the whole day.,he exclusion of one week (Thursday to Wednes- It would have been desirable to obtain details ofwas assumed to be adequate in each case. The barometric pressure and relative humidity but these; of Christmas and New Year is more long- were not available. However, the high correlationsand it is necessary to exclude a three-week between meteorological factors, as shown by BoydId starting the week before Christmas. (1960), make it difficult to distinguish between thee occurrence of an influenza epidemic causes effects of some variables, and thus the inclusion ofan extreme rise in sickness absence frequency more might merely confuse the conclusions from.t might be appropriate to exclude the relevant the analysis. The weekly averages of the fours. However, in 1960-64the only severe epidemic measurements, MAX TEMP, MIN TEMP, RAIN, and suN,rred during the Christmas period and the are the meteorological variables used in the model.Iem is thus avoided. The weather back as far as eight weeks beforeere was ths avoidence absence is used so that a few week's data from 1959ere was no evidence of any long-term trends in

wr eddess absence over this period, the annual were needed.xers of spells being fairly stable. To illustrate seasonal variations in meteorologicalfactors the monthly averages of mean temperature,. weekly intervals are taken from Thursday to total rainfall, and total hours of sun for the above-nesday since this enables the correction for .

wWrto be restricted to one week only. As shift mentioned weather station for 1921-50 are showners aoberestrinvoedioonweeken weekorking An f in Figure 2; although these years do not includeers are involved in weekend working and form the period of the survey, the use of 30-year averagesone third of the total work force, there is no give a ore rve ese of the seas..sdiidn pon fo th wek so thtiti gives a more reliable estimate of the seasonal)us dividingtmoit fornv heweek,ndvsion thatit trends. For mean temperature and hours of sun theto take the most convenient division, smooth trends obtained should be adequatelye period 1960-64 contains a total of 261 weeks represented by harmonic curves. For rainfall theiding one day from 1959 and excluding one seasonal curve is more irregular but the large1964 so that the week starts on Thursday). standard deviations about this mean curve, not

ever, the exclusion of holidays reduced the shown here but present in all British rainfall data,ber of weeks in the regression analysis to 186. make the effect of the trend itself of lesser impor-average spells per week of sickness absence tance. Thus, it is assumed that the elimination ofIg this period was 22* 9 with standard deviation trend in the four meteorological variables mentioned

above can be adequately obtained by use of theidampen the greater variationsencountered in appropriate harmonic curves of period one year.-r absence frequencies a square-root transfor-mn has been applied to all weekly numbers of THE REGRESSION MODELs. The theoretical basis for this is that if weekly' The objective here is to describe a method forice frequency is a Poisson random variable analysing variations in weekly sickness absence

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frequency over a number of years N with a totanumber of weeks K.Suppose there are J types of absence (e.g

diagnostic groups) and define YV, as the square-rocof the number of spells of type j starting in weekfor j = 1,...., J and i = I ..., K. These J typeare not necessarily exclusive or exhaustive.Suppose there are H meteorological factors wit

their weekly averages Wih for h = 1., H ani= 1,....,K.Now consider absence of a particular type k an

the combination of factors which determine itweekly values Yik. There are five such factors:

(i) a broad seasonal trend, characterized byharmonic of period one year such that Yik ha

expected value aO, + b1, cos - + a0I befor

modification for the effects of (ii) - (v) below, wherea,, bo, and a,, are constants.

(ii) deviations of weather conditions about theseasonal norm for week i and the S preceding weeks.Since the seasonal trends for these H factors areassumed to be harmonic, such deviations can bedefined as

Wi-s,h-bsh cos (-K + 1sh) } for s = 0.....S and h = 1, ...., H where {bsh} and { sh} areconstants;

(iii) deviations of previous weeks' sicknessabsence frequencies about the seasonal norm.Considering up to T preceding weeks and assumingseasonal trends to be harmonic, such deviationscan be defined as

Yi-tj-a,tj cos (2N-+ at) } for t = 1 ....

T and j = 1, ........., J where {atj} and {a,j} areconstants;The effect of such deviations on Yik can be attributedto the carry-over of infections from one week to thenext;

(iv) other unknown factors which are assumedto be sufficiently unsystematic to be treated asrandom variations;

(v) the occurrence of holidays. This factor hasbeen eliminated by excluding the relevant weeksfrom the data and it is therefore not includedhenceforth.Under the assumption that the effects of (i) to

-c (iv) are additive, the following linear regressionmodel is obtained:

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ESTIMATION PROCEDURELeast squares is the method to be used for

estimation of the regression coefficients, but thefitting of the full regression model is liable to giverise to a large number of non-significant estimates.Thus, the method of stepwise regression, as described

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by Efroymson (1960), is adopted, introducingvariables into the regression model one by one untilthere exist no further variables with coefficientssignificantly different from zero. One modificationto Efroymson's method is that the two harmonicterms are included as 'forced variables', i.e., thecoefficients a and b are included as the first twosteps in the regression and cannot be excluded. Thisis essential as the model is based on the investi-gation of variations about the seasonal trend.

RESULTSThe regression model is now applied to the data

described earlier. The period covered is 1960-64 sothat N = 5 years and K = 261 weeks.The following four types of absence are considered

(so that J = 4): j = 1 represents all spells ofsickness absence, j = 2 spells due to upper respira-tory disease, j = 3 spells of bronchitis, and j = 4spells diagnosed as non-respiratory.

It seems reasonable to suppose that the detectionof any possible relationship between absencefrequencies in adjacent weeks may be assisted by theuse of diagnostic information. Furthermore, thelack of seasonal trends in all non-respiratory absencemakes it sensible to combine all such absence intoone type. k is set equal to 1 so that the model isapplied with total weekly spells as the dependentvariable.

Also, T = 2, so that the effect of absence up totwo weeks previously is considered. The exclusionof all weeks which contain holiday period absence as

either dependent or independent variables means

that the number of weeks for analysis is reduced to166.

Meteorological data are as described earlier so

that H = 4 and h = 1, 2, 3, and 4 respectively forMAX TEMP, MIN TEMP, RAIN, and SUN. S = 8, so that

the effect of weather up to eight weeks previously isconsidered.A first analysis showed that the absence fre-

quencies two weeks previously did not have signifi-cant coefficients. Consequently, analysis was re-

peated with T = 1, thus enabling the number ofweeks to be increased to 186.The results of this second analysis are summarized

in Table I. Variables are listed in the order in whichthey entered the model with their estimated regres-sion coefficients and standard errors in the finalmodel.

Thus, it can be seen that the previous week'supper respiratory absence and the mean maximumtemperature two weeks previously are both signifi-cant (at the 1 % level) in determining one week'stotal frequency of absence, after elimination of

TABLE ITOTAL SPELLS: THE MODEL OBTAINED BY

STEP-WISE REGRESSION

EstimatedRegression Standard

Variable Coefficient Error

(constant) (5 * 335)

Cos(21KN ) 0*220 0*118

Sin (2i) -0 156 0 084

Y..1,2 (Upper resp. 0-239* 0-058absence 1 weekprevious)

Wi-2,1 (Max. temp. -0 * 0227* 0*00812 weeksprevious)

*P < 0-01

seasonal trends. Furthermore, no other variablewas significant at the 5% level. In particular, it isinteresting that respiratory absence in the previousweek takes precedence over total absence forinclusion in the model.The following analysis of variance table is

obtained from the model with the four independentvariables presented in Table I.

Degrees of Sum of MeanFreedom Squares Square F-Ratio

Regression .. 4 50*03 12*51 46-58

Residual .. 181 48*60 0*268

Thus, 51 % of the variation of Yi1 can be explainedby the regression.The residual mean square is 0i 268, close to the

value 1/4 to be expected if all non-random variationis contained in the regression. This is evidence thatthe model adequately explains weekly variationsin sickness absence.

It is unsatisfactory at this stage to assume thatthe mean maximum temperature only affectsabsence two weeks before the event. As shown byWise (1966), it is sensible to consider a weightedsum of the mean maximum temperatures over aperiod of several weeks before absence, this beingdone by introducing the relevant variables into theregression model.

Thus, MAX TEMP 0, 1, and 3 weeks before absenceare included in a new expanded regression modelresulting in the regression coefficients listed inTable I.The magnitudes of the regression coefficients for

mean maximum temperature 0, 1, and 3 weeksbefore absence are all less than half their respective

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TABLE IIRESULTS OF ENLARGED REGRESSION MODEL

EstimatedRegression Standard

Variable Coefficient Error

(constant) (5 *208)

Cos (2-rN) 0-241 0140

Sin (2Ni) -0*140 0*097

Yi-1.2 0-241 0-060Wi-3.1 00004 0-010Wi-2,1 -0-025 0.011Wi-_a -0-003 0-012Wt. I 0 003 0-011

standard errors, indicating that the inverse relation-ship between maximum temperature and totalabsence exists only when considering the temperature2 weeks before absence.The equivalent regression model using mean

minimum temperature instead of mean maximumtemperature resulted in a slightly smaller regressionsum of squares, indicating a preference for maximumtemperature in the model.So far the effects of weather and previous absence

on weekly total absence have been assumed to bethe same for all times of year. To check on thevalidity of this assumption the 186 weeks aredivided into three times of year as follows:

Time of Year No. of Weeks

January-March (winter) 55April-June (spring) 55

Late August-December (autumn) 76

It would have been ideal to break the year intofour seasons but the annual holidays make analysisof summer absenteeism impracticable. To ensurewhole numbers of weeks for 'winter' and 'spring'the dividing point varied slightly between years.

Separate regressions have been performed for thethree times of year, attention being restricted to thoseindependent variables found significant in theoverall regression model above. That is, Cos

K,ISin K, Yi-1,2 and Wi-2,1 are the fourK K

independent variables. The results of these threeregressions are shown in Table III.

YI-1,2 is the square root of the number of spellsof upper respiratory disease for the week beforethe one under consideration. From its three regres-sion coefficients for the three 'seasons' it can beseen that the effect of previous upper respiratoryabsence on weekly total absence is most marked in

TABLE IIIRESULTS OF SEPARATE REGRESSIONS OF TOTAL WEEKLY

ABSENCE FOR WINTER, SPRING AND AUTUMN

Winter Spring Autumn

Regression Regression RegressionVariable Coefficient SE Coefficient SE Coefficient SE

(constant) (4 871) (5*009) (4*495)

Cos 2nNr -0-111 0-651 -0-415 0-573 0-821 0-364K

Sin 2nNi -0-027 0-826 0 437 0 407 -0-683 0 547

Yi-1.2 0 - 396t 0-089 0 045 0 111 0 152 0*112

W,2.1 -0-023* 0-010 -0-024 0-018 -0-015 0-019

*P<0.05tP<0*01

the winter months. However, the inverse relation-ship between weekly total absence frequency andtemperature two weeks previously is more consistentfor all times of year, though significance is achievedonly in winter.

In order to check the validity of a regressionmodel an analysis of the residuals (i.e., differencesbetween observed and expected weekly spells) iscustomary. No systematic deviations were foundexcept for the winters of 1963 and 1964. For theformer, 9 out of 11 residuals were positive, whereasthe latter had all 11 residuals negative. The winterof 1963 was extremely severe and it could be thatthe effect of long periods of very cold weather had amore serious effect on sickness absence than themodel estimated. The lower than expected absencerates in early 1964 might be due to the fear ofredundancies present at that time, though thiscould not be detected in the absence rate for thewhole year.Pocock (1972) showed that non-random variation

in weekly sickness absence frequency is marked onlyfor upper respiratory disease and bronchitis.Therefore it is reasonable to assume that therelationships discovered in this investigation arepredominantly due to respiratory illness. Further-more, since upper respiratory disease occurs morefrequently than bronchitis, this last commentapplies mainly to the former absence category.However, both non-respiratory illness and bron-

chitis can be studied separately. First, using thenotation defined above, the correlation coefficientfor Yi4 and YI-1,2 over the 186 weeks used in theabove model has a value 0 182 (P < 0 05). This isevidence that one week's frequency of non-respira-tory absence may be affected by the incidence ofupper respiratory disease in the previous week,

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indicating that bouts of respiratory infection maylead to a worsening in the general health of apopulation.Suppose Y,3, i.e., weekly frequency of bronchitis,

is the dependent variable in the regression equationand the model is applied to the 55 winter weeks of1960-64. Then, after the removal of seasonal trends,W1.1,1 is the only significant variable in the step-wise regression, it being significant at the 1% level.Thus, the incidence of absence due to bronchitis ismost closely related to the temperature in theprevious week. Boyd (1960) showed that mortalitydue to bronchitis was most affected by temperaturetwo weeks before death. However, these two resultsare not conflicting since absence is a more minormanifestation of the disease process which onemight expect to be more immediately affected bymeteorological factors.

DISCUSSIONTromp (1964) gives a general description of the

methods of bio-meteorological analysis. He citestwo main approaches: the 'empirical method'where one is attempting to define the form of theweather-disease relationship and the experimentalapproach where one is concerned with validatingmore specific theories or hypotheses. The formernecessarily precedes the latter since one must havesome idea of the problem before one can produceelaborate theories.The approach adopted in this investigation has

been 'empirical', This enables one to suggest therelationship between the weather and variousaspects of sickness absence, but one is not able toexplain these relationships without further experi-mental research. However, the results of this studyshould be a guide as to the direction which futureresearch could take.Tromp gives two general ways in which the

weather might affect the occurrence of disease:(i) a physiological effect, whereby the resistance

of the body to disease is lowered;(ii) a social effect, whereby the changed social

behaviour (e.g., crowding in rooms) increases thespread of infection.When looking at sickness absence one must

remember that it is not merely a measure of diseasebut also of the motivation to go to work, and thisintroduces a third possible way in which the weathermight play a part:

(iii) a motivational effect, whereby weatherconditions affect the employee's 'will to work'.

This study has shown that the weekly frequencyof absence is related to two factors after the elimina-tion of seasonal trends:

(i) the previous week's frequency of absencedue to upper respiratory disease, this effect beingstrongest in winter;

(ii) the mean maximum temperature two weeksbefore, which seemed to have a slight effect in allseasons, was again most marked in winter.

Overall, (i) was more important than (ii), whichimplies that the spread of respiratory infection playsa dominant role in determining weekly sicknessabsence frequency. There is no evidence that weatherconditions in the current week affected the weeklyabsence frequency, and therefore the postulatedmotivational effect mentioned above would appearto be of minor importance, variations in weeklyabsence frequency being largely due to variations inthe incidence of disease. This negative finding is ofsome interest in view of the widely accepted viewthat personal motivation, and job satisfaction inparticular, plays an important part in the genesis ofa short spell of sickness absence (Office of HealthEconomics, 1971).

This investigation is essentially dealing withweekly fluctuations in the total incidence of sicknessabsence, and the model is therefore not designedfor the detailed study of epidemics of particulardiseases. Nevertheless, an outbreak of influenza on alarge scale might be thought to build up sufficientimmunity in the community actually to cause theincidence of respiratory illness (and therefore allillness) to fall below average in the aftermath of suchan epidemic. Evidence in support of this can befound in the national weekly claims for sicknessbenefit for 1969-70 (published by the Departmentof Health and Social Security, 1971). The influenzaoutbreak in December/January was followed bybelow average sickness not only in the week imme-diately after the epidemic but for the whole ofFebruary and March. It is possible, therefore, thatthe model might be somewhat inadequate in suchan extreme situation. However, in most years (andcertainly during the period used in the results) anepidemic either does not occur or is much lesssevere. For example, in the population of 1,057men, never more than 40 went off sick with respira-tory disease in any one week and, therefore, therewould appear to be little chance of widespreadimmunity arising.One interesting future project would be to

investigate whether the spread of respiratoryinfection illustrated in this study occurred primarilyin the work or in the home environment. This couldperhaps be achieved by the study of space-timeclustering in the incidence of respiratory absencewith two space factors, the employee's location atwork and his location at home.

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As regards the effect of temperature on sicknessabsence, it might be thought that the difference intemperature between one week and the next is moreimportant than the actual level. For instance, asharp fall in temperature might lead to increasedsickness absence, whereas people might becomeaccustomed to a continuing cold spell. However, ifsuch a relationship did occur it would have beendetected in the estimation of the regression equationshown in Table II.

SUMMARY

A regression model is developed for investigatingthe effect of weather and respiratory infection on theincidence of sickness absence in an industrialpopulation. After elimination of broad seasonaltrends, the number of spells of upper respiratorydisease in the previous week and the temperaturetwo weeks previously are found to be the mostimportant factors determining sickness absence inany one week.

I am very grateful to Professor P. Armitage and Dr.P. J. Taylor for their invaluable advice throughout thisinvestigation. I would also like to thank the Companyfor permission to use their sickness absence records.

REFERENCESBOYD, J. T. (1960). Climate, air pollution and mortality.

Brit. J. prev. soc. Med., 14, 123.DAVEY, M. L., and REm, D. (1972). Relationship of air

temperature to outbreaks of influenza. Brit. J. prev.soc. Med., 26, 28.

DEPARTMENT oF HEALTH AND SOCIAL SEcuRTrY (1971).Digest of Statistics Analysing Certificates of Incapacity,June 1967-May 1968.

EFROymsON, M. A. (1960). Multiple regression analysisIn Mathematical Methods for Digital Computers,pp. 191-203, edited by A. Ralston and H. S. Wilf.Wiley, New York,

HOLLAND, W. W., SPIcER, C. C., and WILSON, J. M. G.(1961). Influence of the weather on respiratory andheart disease. Lancet, 2, 338.

LAWRENCE, E. N. (1962). Importance of meteorologicalfactors to the incidence of poliomyelitis. Brit. J. prev.soc. Med., 16, 46.

OmCE OF HEALTH ECONOMIcS (1971). Off Sick. Publi-cation No. 36. Office of Health Economics, London.

POCOCK, S. J. (1972). Statistical Studies of SicknessAbsence with special reference to Temporal Variation,ch. 4. Ph.D. thesis, London University.

RUSSELL, W. T. (1926). The relative influence of fog andlow temperature on the mortality from respiratorydisease. Lancet, 2, 1128.

SPicER, C. C. (1959). Influence of some meteorologicalfactors in the incidence of poliomyelitis. Brit. J. prev.soc. Med., 13, 139.

TROMP, S. W. (1964). Weather, climate and man. Ch. 16,p. 283 of Adaptation to the Environment, Section 4 ofHandbook of Physiology, edited by D. B. Dill. Ameri-can Physiological Society, Washington.

WISE, M. E. (1966). Poliomyelitis and weather during10 years in England and Wales. Int. J. Biomet., 10, 77.

WiuGHiT, G. P., and WiuGHrr, H. P. (1945). Etiologicalfactors in broncho-pneumonia amongst infants inLondon. J. Hyg. (Lond.), 44, 15.

YOUNG, M. (1924). The influence of weather conditionson the mortality from bronchitis and pneumonia inchildren. J. Hyg. (Lond.), 23,151.

Author's present address: StatisticalLaboratory, State University ofNew York at Buffalo, Amherst, New York 14226, U.S.A.

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RELATIONSHIP BETWEEN SICKNESS ABSENCE AND METEOROLOGICAL ... · relationship between the weather and sickness absence. The object of this investigation is to develop a model to illustrate