spatial variation of natural radiation and childhood leukaemia incidence in great britain

STATISTICS IN MEDICINE, VOL. 14, 2487-2501 (1995)

SPATIAL VARIATION OF NATURAL RADIATION AND CHILDHOOD LEUKAEMIA INCIDENCE IN

GREAT BRITAIN

SYLVIA RICHARDSON, CHRISTINE MONFORT Institut National de la Sante et de la Recherche Medicale, Unite 170, Villeju$ France

MARTYN GREEN National Radiological Protection Board, Chilton, Didcot. U.K.

GERALD DRAPER Childhood Cancer Research Group, University of Oxford, Oxford, U.K.

AND

COLIN MUIRHEAD National Radiological Protection Board, Chilton, Didcot, U.K.

SUMMARY

This paper describes an analysis of the geographical variation of childhood leukaemia incidence in Great Britain over a 15 year period in relation to natural radiation (gamma and radon). Data at the level of the 459 district level local authorities in England, Wales and regional districts in Scotland are analysed in two complementary ways: first, by Poisson regressions with the inclusion of environmental covariates and a smooth spatial structure; secondly, by a hierarchical Bayesian model in which extra-Poisson variability is modelled explicitly in terms of spatial and non-spatial components. From this analysis, we deduce a strong indication that a main part of the variability is accounted for by a local neighbourhood ‘clustering’ structure. This structure is furthermore relatively stable over the 15 year period for the lymphocytic leukaemias which make up the majority of observed cases. We found no evidence of a positive association of childhood leukaemia incidence with outdoor or indoor gamma radiation levels. There is no consistent evidence of any association with radon levels. Indeed, in the Poisson regressions, a significant positive association was only observed for one 5-year period, a result which is not compatible with a stable environmental effect. Moreover, this positive association became clearly non-significant when over-dispersion relative to the Poisson distribution was taken into account.

1 . INTRODUCTION

The aetiology of childhood leukaemia is still largely unknown. ‘ q 2 Apart from genetic determi- nants, the only firmly established leukaemogenic agents are some chemotherapy treatments3 and ionizing radiation. Increased risks in populations exposed in childhood to doses in the range from about 0.01 up to 10 Gy have been reported notably in the cohort of A-bomb survivor^,^ following ante-natal exposure’ and radiotherapy treatment.6

Recent interest has also been focused on whether there is a role of factors such as parental occupational exposures, environmental exposure to electromagnetic fields and environmental

CCC 0277-47151951222487-15 0 1995 by John Wiley & Sons, Ltd.

2488 S. RICHARDSON ET AL.

radiation exposure, either natural or connected to the operation of nuclear power facilities.’ It is the potential role of natural radiation which is the subject of the present investigation. There have been some studies suggesting that there may be an increased risk of leukaemia in connection with terrestrial gamma radiation and radon;’-’’ only a few studies specifically addressed childhood leukaemia.’ ‘-14 There has been controversy over some of the results and the interpretation of these

Two types of design have been traditionally used in epidemiology to search for potential disease causing agents: individual level studies (in particular case-control or cohort studies) and so-called ecological studies where association is investigated at a group level, the group being most commonly defined by a geographical area. It is not our purpose to enter in to the debate of the relative merits of these two designs and the sources of bias of ecological studies (see Richardson,” Greenland and Robinsz6 for recent reviews). Let us just say that for some environmental factors like natural radiation, geographical studies offer a natural design in view of the constancy over time of the exposure and the existence of strong geographical contrasts, while there are substantial difficulties and large sources of measurement errors in the assessment of exposure at the level of the individual.

This paper describes an analysis of the geographical variation of childhood leukaemia incidence in Great Britain over a 15 year period in relation to natural radiation (gamma and radon). Potential geographical confounding by socio-economic factors is investigated. The analysis is performed in two complementary ways. First by Poisson regressions with the inclusion of environmental covariates and a smooth spatial structure expressed as a function of the geographical co-ordinates. Secondly, by a hierarchical Bayesian model in which extra-Poisson variability is explicitly modelled in terms of spatial and non-spatial component^.^^

As a result, we will have gone some way towards characterizing the structure of childhood leukaemia incidence as that particular geographical scale (the districts), and its stability over that 15-year period as well as assessing the potential influence of natural radiation and socio- economic factors.

2. DATA AND METHODS

2.1. Data

The leukaemia cases analysed come from the National Registry of Childhood Tumours which is a population-based registry of malignant disease in children aged under 15 which covers the whole of England, Scotland and Wales.

The present study concerns 6691 cases of leukaemia diagnosed between 1969 and 1983, which are further sub-classified (according to the scheme described in Birch and Marsden”) as lymphocytic and unspecified leukaemias (LL) (80.2 per cent) and acute non-lymphocytic leukaemia (ANLL) (165 per cent). As discussed in D r a ~ e r , ’ ~ unspecified leukaemias were grouped with lymphocytic leukaemias because it is believed that the great majority of these cases would in fact have been acute lymphoblastic leukaemias. This leaves a very small proportion of other specified leukaemias.

The address at diagnosis was postcoded and assigned to an enumeration district from which coarser geographical location can be easily derived. For our purpose, we shall only be concerned with the 459 district level local authorities. These include both cities and boroughs as well as districts but will hereafter be referred as districts. The reader is referred to Draperz9 for further details on the data base.

SPATIAL VARIATION OF NATURAL RADIATION AND CHILDHOOD LEUKAEMIA INCIDENCE 2489

The study period spans two national censuses in 1971 and 1981 and annual estimates of district population are available. The study period was subdivided into three five years intervals: 1969-1973; 1974-1978; 1979-1983. Expected number of cases per district were computed for each period using the relevant population base and the national incidence rate for the whole 1969-1983 period. These expected numbers were calculated separately for the three five year age groups: 0-4; 5-9; 10-14.

Using census information, a socio-economic score was calculated for each district by averaging three (standardized) socio-economic characteristics: the proportion of economically active males who are working; the proportion of households with car, and the proportion of households which are owner-occupied. The 1971 (respectively 1981) score was used for the 1969-1973 (respectively 1979-1983) period. For the intermediate 1974-1978 period, the score was taken to be the average of the 1971 and 1981 scores.

The National Radiological Protection Board (NRPB) has undertaken a national survey of the concentration of radon and the level of terrestrial gamma rays in homes." A survey of terrestrial gamma rays outdoors, based on the Ordnance Survey grid, has also been ~omple ted .~ ' These data have been reanalysed for the present study to provide information by district.

The sample selection for the national survey was undertaken with great care. It was extracted from the postcode address file maintained by the Post Office. The aim was a representative sample of the total housing stock weighted by population density which was not biased by circumstances such as social class, income, house type or geographical location. The target number of dwellings to be measured was 2000 dwellings or approximately 0.01 per cent of the housing stock. The reanalysis of the data from the national survey in dwellings to provide information by district was undertaken by reference to the post office address file. Some miscodings in the data file used previously have been corrected.23

The objective for the survey of terrestrial gamma radiation outdoors was to make at least one measurement in every 10 km square of the Ordnance Survey grid throughout Great Britain. Some 3100 meqsurements were made covering 90 per cent of the 2400 or so 10 km grid squares in Great Britain. When more than one measurement was made in a square, the average result was taken to represent it. The outdoor terrestrial gamma data were allotted to districts on the basis of the Ordnance Survey grid reference.

In view of the different sizes, both in population terms and geographical spread, of the districts, the number of measurements taken varied quite widely. The mean number of measures per district are around 5, 8 and 7 for indoor gamma, outdoor gamma and radon, respectively. These measurements were combined using arithmetic means for gamma dose rates and a geometric mean for indoor radon concentration as the latter distribution was skewed and approximately log-normal.

Finally, geographical co-ordinates were assigned to each district by recording the latitude and the longitude of its main town. A nearest neighbour structure for each district was created which can be summarized by a 459 x 459 contiguity matrix: W = ( Wij) where Wij is equal to 1 if districts i and j have a common border and Wij is equal to 0 otherwise.

2.2. Statistical methods

For each district (indexed by i), we denote by Oi the observed number of cases (known), by Ei the expected number of cases, and by Bi the relative risk (unknown).

Since the observed numbers of events are small, we make the hypothesis that the number of cases follows a Poisson distribution: Oi - Poisson (EiBi) . To study the influence of covariates Z i ( p x l), we have used two approaches.


2.2.1. Poisson regressions

We consider that Oi are independent Poisson variables, with mean EIOi I p, Ei] satisfying

log E[Oi I p, E i ] = log Ei + p’zi (1)

To take into account an overall smooth spatial structure of the incidence data, a polynomial with p a ( p x 1) vector of regression coefficients.

function of the co-ordinates of each area can be introduced:

logE[OiIp,y,Ei] = log& + p’z, + y’Ti (2)

where Ti = (lati, longi) characterizes a linear spatial trend. Poisson regressions were fitted using the glrn procedure of S-PLUS.32 Statistical significance

was assessed using analysis of deviance with an asymptotic chi-square distribution for the deviance difference. The indication of statistical significance has to be treated with caution as some of the observed number of cases are very small and there is some evidence of overdispersion. The overdispersion was explicitly taken into account by the hierarchical model described in the next section. This model was used to investigate further some of the significant associations with environmental covariates brought to light by the Poisson regressions.

2.2.2. Hierarchical Bayesian model

The use of the hierarchical Bayesian approach to account for spatially structured extra-Poisson variations was first introduced by Clayton and K a l d ~ r ~ ~ and further developed by Besag et al.34 and Clayton and c o - w o r k e r ~ . * ’ ~ ~ ~ Basically this approach provides a way to integrate, in the estimation of the unknown relative risks O i , local information consisting of the observed and expected number of cases in each area and prior information on the overall variability of the relative risks, their potential similarity in neighbouring areas and their connection with geo- graphically defined covariates.

Poisson fluctuation is modelled at a first level and a log-linear mixed model for Bi is specified at a second level, with area-specific random effects further decomposed into a component that models unstructured heterogeneity and a spatially structured component modelling local clustering.

The hierarchical model is thus formulated as:

1st level - local variability (within area):

Oi - Poisson(EiBi)

2nd level - structure between areas: log-linear mixed model

logei = p + ui + ui + ~ z , where Z i are the covariates and ui and ui are random effects representing, respectively, unstructured heterogeneity and spatial clustering. Note that ui and ui can be included separately or jointly and that the constraint Xui = Cui = 0 is used for identifiability.

The following distributional forms are adopted for the two random effects:

Heterogeneity:

[uil u j , j # i] - N(Ui, (Au)-’) where Ui = ui/N - 1 j # i

SPATIAL VARIATION OF NATURAL RADIATION AND CHILDHOOD LEUKAEMIA INCIDENCE 249 1

Clustering: [ui l uj, j # i ] - N(Ci, (niA,)-’) where Vi = C Wijuj/ni

j # i

and ni is the number of neighbours of area i. The parameters A, and A, control the amount of variability in ui and ui, respectively, and

consequently the variability of the relative risks. Note that these parameters are not comparable since Au characterizes a marginal variability whilst I , measures a local variability conditional on the neighbouring values of u.

In order to carry out a full Bayesian analysis, hyperprior distributions are specified for p, B, A, and A,. We assumed (improper) uniform priors for all these parameters. For I , and A” this implicitly allows the possibility of large geographical variations and in some cases might create a convergence problem. Another possibility would be to have chosen proper chi-square distributions for A,, and A,, as suggested in Clayton.36 The influence of the choice of hyperparameters with prior chi-square distributions has been considered by Bernardinelli3’ (this issue).

The estimation of this hierarchical model calls upon stochastic simulation techniques, in particular Gibbs sampling, which belongs to the family of Markov Chain Monte Carlo (MCMC) methods; see Gilks et for a general account of MCMC and M ~ l l i e ~ ~ for a review of their application in Bayesian disease mapping. The estimation of this model was developed in a Bayesian framework by D. Clayton and is implemented in the software BEAM (Bayesian Ecological Analysis Method).36 A sample of values of u j , ui, A,, A,, p and fl is produced which can be considered (after an initial warming up period) as values for the joint posterior distribution of the parameters conditional on the data. Analysis of this sample produces both point and interval estimates.

A summary of the variability of the random effects, allowing the assessment of their relative contribution to the overall variability of the Bi , is given by

It is advisable to try to check the convergence of the algorithm, that is, to assess whether the underlying Markov chain seems to have converged to its stationary distribution (the joint posterior distribution of the parameters conditional on the data). Several convergence diagnostics have been proposed, the most commonly used monitor the output of relevant parameters. We have used the approach proposed by Gelman and Rubin4’ which consists of running parallel algorithms with overdispersed starting values and testing whether the total variance between the different sequences is no larger than the variance within each sequence. The ratio l? of these two variance estimates gives a scale reduction factor ,/I? which should be reasonably close to 1 if the values produced by the algorithm are indeed close to a sample from the stationary distribution.

3. RESULTS

3.1. Poisson regressions

We first investigate leukaemia incidence (all leukaemias, LL and ANLL) in relation to natural radiation in the three time periods by univariate Poisson regressions (Table I). Note that the number of units is slightly different for each regression as the districts with missing data were not the same for radon, indoor or outdoor gamma radiation.

Overall we see that no coherent pattern of association between radiation exposure and leukaemia incidence emerges. There is weak evidence of a positive association with radon in the

S. RICHARDSON ET AL.

Table 1. Poisson regressions of childhood leukaemia incidence rates: change in deviance with inclusion (separately) of radon, indoor gamma, outdoor gamma, socio-economic score and

spatial trend

Diagnosis Period Radon Indoor Outdoor Socio- Spatial (1 d.f.) gamma gamma economic trend

(1 d.f.) (1 d.f.) score (2 d.f.) (1 d.f.)

N =402 N = 391 N = 394 N =459 N =459

All leukaemias 1969-73 0.05 0.0 1 0.56 12-08 ( + ) 4.75 1974-78 3.49 009 0.0 1 5.32 ( + ) 2.32 1979-83 0.28 4.79 ( - ) 2.20 2.97 4.39

Lymphocytic and 1969-73 0.73 0.10 1-47 6-75 ( + ) 2.08 unspecified 1974-78 4.19 ( + ) 0.09 0.00 6.31 ( + ) 2.42 leukaemias 1979-83 0.98 2.3 1 0.69 294 1.39

Acute non- 1969-73 2.03 0.6 1 2-5 1 1.83 4.2 1 lymphocytic 1974-78 0.02 0.25 0.35 0.60 0.94 leukaemias 1979-83 0.97 4.35 ( - ) 2.93 1.28 6.39

Using the chi-squared approximation to the distribution of scaled deviance in this table, the critical values at the 5 per cent significance level are 3.84 for 1 degree of freedom and 5.99 for 2 degrees of freedom. Changes in deviance significant at the 5 per cent level are in bold, accompanied by the sign in bracket of the regression coefficient (for univariate regressors)

middle period related solely to LL, but not for the other two periods, nor for ANLL. A significant negative association between all leukaemias, and in particular ANLL, and indoor gamma radiation is also found for the third period but not for the earlier periods. There is no evidence of association of leukaemia incidence with outdoor gamma radiation and hereafter we shall focus our analysis solely on radon and indoor gamma levels.

Regression results concerning the socio-economic score and a linear spatial trend are also presented in Table I for reference. As noted previou~ly,~~ there is evidence of a positive association of leukaemia incidence with the socio-economic score, an association which is only significant in the first two periods. Similar results arise for LL but not for ANLL. Overall leukaemia incidence is not well described by a linear spatial trend, the only exception being ANLL incidence in the third period, which is significantly negatively correlated with latitude.

To complement these first results, we next carry out a multivariate analysis. For the sake of completeness, results for the three periods are presented in Tables I1 and 111, though we are mostly interested with investigating further the associations shown in Table I for the last two periods.

(i) In the first period, deviance comparisons between the models in Table11 show that the geographical variation of leukaemia incidence, as well as that of LL, is essentially linked to the socio-economic score. Inclusion of a spatial trend term does not further decrease the deviance to a statistically significant extent.

(ii) In the middle period, by comparing model 4 and model 1 in Table 11, we see that for LL the inclusion in the regression of both the socio-economic score and a linear trend term leads to a significant decrease of deviance. There is evidence of confounding between the score and the spatial trend term as the score is negatively correlated both with latitude (r = - 038) and longitude (r = - 0.23) in that period. The contribution of radon to LL


Table 11. Poisson regressions of childhood leukaemia incidence rates in relation to radiation exposure: change in deviance with adjustment for socio-economic score and spatial trend

Radiation Diagnosis Period Model 1 Model 2 Model3 Model 4 exposure ( 1 d.f.) (2 d.f.) (3 d.f.) (4 d.f.)

Radon All leukaemias N = 402

Lymphocytic and unspecified leukaemias

Indoor gamma All leukaemias N = 391

Acute non-lymphocytic leukaemias

1969-73 1974-78 1979-83 1969-73 1974-78 1979-83

1969-73 1974-78 1979-83 1969-73 1974-78 1979-83

0.05 3.49 0.28 0.73 4-19 0.98

0.0 1 0.09 4.79 0.6 1 0.25 4.35

f 4.23 5.5 1 3.43 9.80 7.84 4.05

13.04 4.35 6-10 3.68 040 4.47

5.61

4.96 3.88

2.24

11-14

11.69

6.48 6.19 6.57 5.29 1.28 8.40

14.80 12.61 5.70 9.91

13.83 4.16

14-04 9.26 7.05 7.78 1.81 8.6 1

Model 1: radiation exposure (radon or indoor gamma) ( 1 d.f.) Model 2: radiation exposure + socio-economic score (2 d.f.) Model 3: radiation exposure + spatial trend (3 d.f.) Model 4 radiation exposure + socio-economic score + spatial trend (4 d.f.) Using the Chi-squared approximation to the distribution of scaled deviance in this table, the critical values at the 5 per cent significance level are 3.84 for 1 degree of freedom, 5.99 for 2 degrees of freedom, 7.81 for 3 degrees of freedom and 9.49 for 4 degrees of freedom

incidence is still significant after adjustment on the socio-economic score and the linear spatial trend in 1974-78 (TableIII). Moreover the contribution of radon to overall leukaemia incidence in this period is also significant after similar adjustments (Table 111). In view of these results, the same multivariate model was also estimated separately for the three age groups. The regression coefficients are overall of the same order of magnitude for the three age groups (except for LL and the 10-14 years old) but the association with radon appears stronger for the 5-9 years old and becomes borderline significant for LL. The small number of cases confers low power to the analyses per age group which will not be pursued further.

(iii) In the third period, the negative links found with indoor gamma radiation are partially explained by the socio-economic score or a simple spatial structure (Table 11). For all leukaemia incidence, the negative association with indoor gamma level becomes non- significant in the multivariate models (2) and (3), while for A N L L i t becomes non- significant in the multivariate model (3) (results not shown). The negative association is thus indirectly created by the geographical correlation of indoor gamma levels with the socio-economic score ( r = - 0.31), latitude ( r = 0.41) and longitude ( r = 0.31).

In conclusion, we see no evidence of geographical association of leukaemia incidence with either indoor or outdoor gamma levels.

As shown by the deviances given in Table 111, there is evidence of over-dispersion. We pursue our analysis of the structure of leukaemia incidence in the three periods in the framework of the Bayesian hierarchical model described in Section 2.2.2. The associations with radon and the socio-economic score arising in the Poisson regressions are also reanalysed in this framework.

Tab

le 1

11.

Pois

son

regr

essi

ons o

f ch

ildho

od le

ukae

mia

inci

denc

e ra

tes

by p

erio

d: r

egre

ssio

n co

effic

ient

s (SD

) and

t v

alue

s fo

r ra

don,

soc

io-e

cono

mic

sc

ore,

latit

ude

and

long

itude

Dia

gnos

is

Dev

ianc

e Pe

riod

A

ge g

roup

R

adon

So

cio-

econ

omic

scor

e L

atitu

de

Lon

gitu

de

(yea

rs)

Coe

ffic

ient

t

Coe

ffici

ent

t C

oeffi

cien

tt t

Coe

ffici

ent

t

All

leuk

aem

ias

1969

-73

0-14

1974

-78

0-4

5-9

10-1

4

0-14

1979

-83

0-14

Lym

phoc

ytic

and

1969

-73

0-14

un

spec

ified

leuk

aem

ias

1974

-78

0-4

5-9

10-1

4

0-14

1979

-83

0-14

- 0

.002

1 (0

.00

18)

0.00

26

0.00

37

(0.0

024)

04

035

(0.0

035)

0.

0033

(0

.00

1 5)

- o

m00

4 (0

.001

8)

- 0

.003

1

(0.0

022)

(0.0

022)

0.

0033

(0

.002

3)

0004

3 (0

.002

5)

0000

9 (0

0053

) 00

037

(0.0

01 6)

O.

OOO9

(0

0018

)

- 1

.16

0.02

75

(0.0

091)

1.

20

0.02

54

(0.0

130)

1.

57

- 0

.015

5 (0

.016

1)

0.99

0.

0039

(0

.018

9)

2.26

0.

0108

(0

.008

9)

- 0.

02

0.00

83

(000

97)

(0.0

102)

(0.0

141)

(0.0

1 78)

0.

17

0.00

99

(0.0

238)

2.

30

0.01

46

0.51

0.

0148

(0

.0 10

7)

- 1

.40

0-02

49

1.47

0.

031 1

1.75

- 0

.018

2

(0.0

100)

3-00

1.98

- 0

.96

0.2

1

1.21

0.86

2.44

2.19

- 1

.02

0.42

1.45

1.38

- 0

.012

1 - 0

.68

(0.0

1 77

) 0.

0515

2.

07

(0.0

248)

0.

0580

- 1

.75

(0.0

33 1

) 0.

0946

2.

52

(0.0

375)

0.

0300

1.

71

(0.0

176)

(0.0

189)

- 0

.000

7 - 0.

03

(0-0

199)

0.

0474

1.

75

(0.0

271)

- 0

.062

5 - 1

.70

(0.0

366)

01

040

2.20

(0

.047

1)

0.02

52

- 1

.27

(0.0

198

)

(0.0

206)

- 0

.024

6 - 1

.31

- 0

.006

3 - 0

.30

0.00

98

0.55

(0

.01 7

7)

(0.0

259)

(0.0

324)

- 0

.014

5 - 1

.60

-001

02

-0.3

1

- 0

.107

9 - 2

.67

(0.0

404)

- 0.0460

- 2

.54

(0.0

1 8 1)

- 0

.003

6 - 0

.19

(0.0

191)

(0,0

200)

(0.0

280)

(0.0

358)

(0.0

51 1)

(0.0

203)

- 0

.005

9 - 0

.29

- 0

.047

7 - 1

.70

- 0

.000

6 - 0

.01

-014

37

-28

1

- 0

.048

9 - 2

.41

- O

~OoO

4 - 0

.02

(0.0

2 10

)

459-

0 (3

97)

472.

5 (3

97)

4626

v,

(397

) 40

4.7

E (3

97)

458.

0 ~

(397

) P

429.

7 (3

97)

476.

6 (3

97)

469.

9 (3

97)

438.

0 (3

97)

389.

3 (3

97)

483.

6 (3

97)

455.

7 (3

97)

2 1 2: h

Y 1

t*

Coe

ffici

ents

sta

tistic

ally

sign

ifica

nt a

t th

e 5

per

cent

leve

l are

in b

old


Comparing the dispersion of SMR and bayesian estimates

0 .

N-

a I

r -

0 -

Figure 1.

3.2. Log-linear mixed model

All the results presented on the hierarchical Bayesian model correspond to runs of 20000 iterations of the Gibbs sampler. From these runs, parameter estimates were computed by averaging every 10th iteration. Convergence of the Gibbs sampler was investigated by comparing parallel runs of 20000 iterations with over-dispersed starting values for the hyperparameters. We typically obtained values around 1.2 for the scale reduction factor JR computed from the runs of SD, and SD,.. Even though,, R is reasonably close to 1, there is an indication that convergence could still be improved. We were nevertheless satisfied that the results presented would not be noticeably altered if a larger number of iterations was carried out.

At first the log-linear mixed model was fitted separately for the three periods without the inclusion of any covariates. The 'shrinkage' effect of considering a hierarchical model for the 8;s rather than estimating them directly by the corresponding SMRs is illustrated in Figure 1. Some extreme SMRs corresponding to areas with very few cases and a small population are shrunk towards as the Bayesian estimate takes account of local neighbouring values of Oi and of their overall distribution.

Characteristics of the heterogeneity and the clustering components for the three periods are given in Table IV. First of all, we see that a coherent picture of the structure of leukaemia and LL incidence over the three periods emerges. Both the clustering and the heterogeneity components contribute significantly to the overall variability of 0; and there is a stability of the estimates of SD, and SD,. over the three periods. Furthermore, the clustering component appears in each period to be larger than the heterogeneity component. This is true for the incidence of all leukaemias as well as that of LL.

To investigate in more detail the stability of the underlying structure over time, we estimated for each district and for each period the average U; and 6; of the values of ui and ui over the 2000 values extracted from the total run, and computed the cross-period correlations between the values of Ui (respectively V i ) for the two pairs of consecutive time periods (Tablev). For all leukaemias and LL, the cross-period correlations are very low for the heterogeneity component, reflecting that this component of over-Poisson dispersion has no spatial stability over time. On


Table IV. Bayesian hierarchical model: estimation of the relative contribution of the heterogeneity and clustering components to the overall variability of the relative risks. Posterior means with posterior standard

deviations in brackets

Period All leukaemias Lymphocytic and unspecified leukaemias

Heterogeneity Clustering Heterogeneity Clustering SD" SD" SD" SD"

without with without with without with without with covariates covariates* covariates covariates* covariates covariates* covariates covariates*

69-73 0.033 0.032 0.04 1 0.035 0.035 0034 0.042 0.034 (0.011) (0011) (0016) (0011) (0.017) (0.015) (0.018) (0.01 1)

74-78 0.035 0037 0054 0035 0.033 0.043 0.059 0.043 (0.021) (0.024) (0.035) (0.014) (0.013) (0.034) (0.037) (0.021)

79-83 0034 0.033 0.04 1 0.039 0.033 0.035 0.037 0.037 (0013) (0.012) (0.015) (0.016) (0.015) (0.015) (0.015) (0.014)

* Covariates: radon level and socio-economic score

Table V. Geographical correlations between successive periods of the estimated random effects corresponding to the heterogeneity or the clustering components

Periods All leukaemias Lymphocytic and unspecified leukaemias

Heterogeneity Clustering Heterogeneity Clustering without without without without

covariates covariates covariates covariates

69-73174-78 0.077 - 0.004 0.103 0.479 74-78179-83 0.084 0386 0.024 0.668

the other hand, for LL the local values of the clustering component show a certain amount of stability over time, indicating that the same districts keep high (or low) values of the clustering component over time.

Covariates, that is, radon levels and the socio-economic score, were introduced in the log-linear mixed model. Note that inclusion of covariate information results in estimates of the Pis which are a little more spread out (Figure 1). The previous estimates of SD, (heterogeneity) are not noticeably altered. The estimates of SD,. (clustering) are slightly diminished. Nevertheless, the same coherent pattern to the estimates is still apparent (Table IV). Some interesting results are revealed with respect to the covariates (Table VI). The effect of the hierarchical model is different for the two covariates. For the socio-economic score, there is a close similarity between the values of the regression coefficient estimates given in Tables 111 and VI. In particular, the score is again clearly linked to leukaemia and LL incidence in the first period, the link becoming weaker but still apparent for the other two periods. In contrast, the significant positive associations between radon levels and leukaemia incidence (all leukaemias and LL) which had been found in the second period (Table 111) are no longer present, with regression coefficient estimates being quite substan- tially lower. We add that this phenomenon occurs if either the heterogeneity or the clustering component is introduced alone into the log-linear mixed model (results not shown). Hence, the effect of radon in the second period is partially confounded with each type of random effects.


Table V1. Bayesian hierarchical model: estimation of the regression coefficients in the log-linear mixed model. Posterior means with posterior standard deviations (in brackets)

and their ratio

Period All leukaemias Lymphocytic and unspecified leukaemias

Radon Socio-economic Radon Socio-economic score score

69-73 - 0.0026 1.30 0.0288 3.35 - 0,0043 1.95 0.0268 2.85 (0.0020) (0.0086) (0.0022) (0.0094)

(0.0014) (0.0084) (0.00 1 7) (0.0094)

(0.00 1 7) (0.0090) (0~00 1 7) (0.0099)

74-78 0.0019 1.36 0.0120 1.33 0.0022 1.29 0.0182 1.94

79-83 - O.OOO1 0.06 0.0120 1.33 - 0.0008 047 (0.0149) 1.51

4. DISCUSSION

In this ecological study, we have endeavoured to assess the potential link between the geographical variations of childhood leukaemia incidence in the United Kingdom and those of natural radiation levels. Childhood leukaemia is a rare disease, and at the scale of our study, the districts, an average of five cases per district over 5-year period was observed. Consequently it is of paramount importance to take into account the Poisson variability of the observed number of cases.

Moreover, as in many geographical studies of rare disease incidence, there is clear evidence of extra-Poisson variability, arising in part from the heterogeneity in individual risk level within each area. After fitting standard Poisson regressions, we have explicitly modelled the over- dispersion in a hierarchical Bayesian framework which, as discussed by many authors, is well adapted to the analysis of disease risks on a small geographical S C ~ I ~ . ~ ~ * ~ ~ * ~ ~ ~ ~ ~

Estimation of the parameters of the hierarchical model necessitates the use of stochastic algorithms belonging to the class of MCMC methods. Improvements in the implementation of these algorithms, and in particular the development of procedures to assess convergence to the stationary distribution of the underlying Markov chain, is a subject of much recent re- ~ e a r c h . ~ ~ . ~ ’ . ~ ~ In our analysis, we chose to use improper uniform prior distributions for the heterogeneity and clustering parameters. This resulted in fairly slow convergence and the need to have long runs. The alternative choice of using proper chi-square distribution for these hyperparameters, and the subsequent sensitivity of the results to this choice deserves further investigation. The reader is referred to Bernardit~ell i~~ (this issue).

From this analysis, interesting results have arisen on the characteristics of the variability of the log relative risks. There is a strong indication that a main part of the variability is accounted for by a local neighbourhood ‘clustering’ structure. This structure is furthermore relatively stable over the 15-year period for the lymphocytic leukaemias which make up the majority of observed cases. Thus there is some evidence that local risk factors, relatively stable over time, are influencing the spatial structure of leukaemia incidence. These local risk factors might correspond to a complex combination of environmental and socio-demographic local characteristics and it would be interesting to be able to extend this analysis after 1983 to investigate the persistance of this local structure. Clustering of childhood cancer, and in particular leukaemias, at a much finer geographical scale has been the object of several s t ~ d i e s , ~ ~ , ~ ~ including investigations of a pos- sible infective basis.44


As in any ecological study, great care has to be taken not to over-interpret the results. Indeed there are many potential sources of bias which will concur to create a discrepancy between the results of an ecological study which analyses aggregated level data, and studies carried out at the level of the i n d i v i d ~ a l . ~ ~ Typically ecological studies suffer from the problem of between-group confounding (here a group is a geographical area), partly because data on confounders are often unavailable, partly because groups are likely to be more heterogeneous with respect to confounders than individuals with a group. Consequently, part or all of the observed variation in disease rates could be attributable to unmeasured confounders which are varying widely between the groups and which could be responsible, say, for a variation of the base line disease rate (in unexposed individuals) between the areas or for an effect modifier of the dose-response relation- ship between the areas. Hence, attention has recently been turned towards ecological designs which include a sub-sampling in each area in order to obtain a more accurate evaluation of exposure and c o n f o ~ n d e r s . ~ ~ , ~ ~

In our present study, we are in a relatively favourable situation to carry out an ecological analysis, as there are no major known risk factors of childhood leukaemia which could act as main confounders in the study of the potential association of childhood leukaemia with natural radiation exposure. This is a different case from a geographical study of lung cancer incidence and radon exposure, for example, where smoking would clearly be a major confounding factor. Let us add that in our study, the radiation exposure measurements were carried out by NRPB with great care, by using a representative sample of dwellings. Plummer and Clayton47 have recently developed design guidelines for ecological studies including wit hin-area subsampling. They indicate that in most instances, a sample size of twice the number of cases per area for evaluating the exposure would be sufficient to obtain reasonable precision when estimating the ecological regression coefficients. We note that the number of samples in each area recorded by the NRPB survey is not very far from this rough guideline.

To summarize our results, we found no evidence of a positive association of childhood leukaemia incidence with outdoor or indoor gamma radiation levels. With the exception of the study of Knox et a!.’ ’ in the United Kingdom, the results of which have been debated,23 no excess cancer risk has been demonstrated in high background radiation areas in other countries,48 in particular in China,49 in the United States5’ or in France.” We found a weak indication of an inverse association with indoor gamma levels. An inverse association of cancer mortality with background radiation had also been found in the United States, however this association became non-significant once altitude was introduced in the explanatory variable^.^' In our case, the negative correlation of indoor gamma levels with all leukaemia and ANLL found in the third period was weakened by the inclusion in the regression of the socio-economic score and/or a spatial trend term. This again indicates that this inverse association should not be interpreted directly.

The potential association of childhood leukaemia incidence with radon levels has been a subject of great interest since the reports of Lucie7 and Henshaw et a/.” Overall, we are inclined to conclude that, at the geographical level of our analysis (the districts) there is no consistent evidence of any association with radon levels. This conclusion is in agreement with that of Muirhead et aLZ3 which reported the first results of a district level analysis using essentially the same data base. Indeed, in the Poisson regressions, a significant positive association was only observed for one period. Not only was this result incompatible with a reasonably stable environmental effect as should be expected for effects of radon, but there was no prior reason to focus on that period (1974-78). Moreover, this positive association became clearly non-significant when Poisson over-dispersion was explicitly modelled. Of course, there is always the possibility that the inclusion of the random effects in the hierarchical model over-adjusts the potential


influence of a covariate, particularly if that covariate has a spatial structure,35 but the lack of coherence of the association between the periods is a strong argument in favour of the alternative explanation, that the positive association in the middle period is a chance finding or an indirect effect, perhaps related in some way to an inadequate adjustment for the influence of socio- economic factrs. We recall that in the middle period, the variables included in the socio-economic score were not measured, and that the score for this period was constructed as the average of the score of the first and third period.

Finally, our results confirm a link between the spatial variations of childhood leukaemia incidence and socio-economic indicators at a district level, as was pointed out previously in Draper.” These results are consistent with previous reports using different data base^.^^.^^ At a finer geographical scale an indication of excess risk of childhood leukaemia in electoral wards with higher socio-economic status was reported in Alexander et However, the strength of the link in the present study declines over the 15-year period. This might suggest that the characteristics chosen to make up the soci-economic score, which are the proportion of economically active males who are working, the proportion of households with car and the proportion of households which are owner-occupied, are less relevant in a recent period. Other measures of socio-economic level and demographic characteristics of the districts should be considered in future development of this analysis.

An updated survey of radon exposure in the United Kingdom has recently been completed by the NRPB. It will be interesting to review the results presented here in the light of these new exposure measurements and to extend the analysis over a longer time period. We feel strongly that the coherence of an association between disease incidence and a stable environmental risk factor is a key argument for interpretating the results of ecological studies.

ACKNOWLEDGEMENT

This research was partially supported by the European Commission under contract no FI3P- CT820064f.

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