A parallel analysis of individual and ecological data on residential radon and lung cancer in south-west England

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1 J. R. Statist. Soc. A 2001) 164, Part 1, pp. 193±203 A parallel analysis of individual and ecological data on residential radon and lung cancer in south-west England Sarah Darby, Harz Deo and Richard Doll Imperial Cancer Research Fund, Oxford, UK and Elise Whitley University of Bristol, UK [Received February Revised July 2000] Summary. Parallel individual and ecological analyses of data on residential radon have been performed using information on cases of lung cancer and population controls from a recent study in south-west England. For the individual analysis the overall results indicated that the relative risk of lung cancer at 100 Bq m 73 compared with at 0 Bq m 73 was % con dence interval 0.99, 1.27)) after adjusting for age, sex, smoking, county of residence and social class. In the ecological analysis substantial bias in the estimated effect of radon was present for one of the two counties involved unless an additional variable, urban±rural status, was included in the model, although this variable was not an important confounder in the individual level analysis. Most of the methods that have been recommended for overcoming the limitations of ecological studies would not in practice have proved useful in identifying this variable as an appreciable source of bias. Keywords: Ecologic study; Lung cancer; Radon 1. Introduction Studies of miners of uranium and other igneous rocks provide substantial evidence that a high concentration of the natural radioactive gas radon-222 is associated with an increased risk of lung cancer National Research Council, 1999). These observations are supported by experimental studies, and radon has been classed as a human carcinogen by the International Agency for Research on Cancer 1988). Exposure to radon also occurs environmentally, particularly from indoor air in houses, and in the UK and in many other countries radon is the largest source of exposure to ionizing radiation of the general population. The miners' studies have been used to derive estimates of the risks associated with radon exposure. When these are applied to risks from residential exposures they suggest that radon may be the second most important cause of lung cancer after cigarette smoking in the general population and may, in conjunction with smoking, cause of the order of 2000 deaths each year in the UK alone. There is, however, considerable uncertainty in applying risks derived from occupational studies to residential exposures and, to formulate appropriate policies for indoor radon, direct estimates of the risk associated with residential exposures are desirable. Address for correspondence: Sarah Darby, Clinical Trial Service Unit and Epidemiological Studies Unit, University of Oxford, Nuf eld Department of Clinical Medicine, Harkness Building, Radcliffe In rmary, Oxford, OX2 6HE, UK. sarah.darby@ctsu.ox.ac.uk & 2001 Royal Statistical Society 0964±1998/01/164193

2 194 S. Darby, H. Deo, R. Doll and E. Whitley Fig. 1. Summary relative risks based on meta-analysis of published data from case±control studies of indoor radon &) Lubin and Boice, 1997), pooled analysis of cohort studies of miners occupationally exposed to radon &) Lubin et al., 1995) and Cohen's ecological study across 1601 US counties Cohen, 1995): the negative slope from Cohen's study is approximately 10 times its standard error gure reproduced from National Research Council 1999)) To provide such direct estimates several case±control studies of residential radon and lung cancer have been carried out. The results of these are in good agreement with the miners' studies Fig. 1). In contrast, an ecological study of residential radon and lung cancer, carried out across 1601 US counties, showed a strong negative association between residential radon and lung cancer Cohen 1995); see Fig. 1). Although it seems likely that the negative trend in the Cohen study is due to ecological bias, the results of this study have received substantial attention, particularly from scientists who are interested in hormesis, i.e. the theory that small doses of radiation condition the cells of an individual to reduce the subsequent risk of cancer. To give further insight into the reasons why individual and ecological studies of residential radon may give di erent results, we present information from the recent case±control study of lung cancer in south-west England Darby et al., 1998)including parallel analyses using individual and ecological data on residential radon concentrations. The methodology used follows closely that of a recent analysis of data from the Swedish nation-wide case±control study of residential radon Lagarde and Pershagen, 1999). 2. Materials and methods Cases of lung cancer were obtained prospectively from individuals referred, during a 4-year period, to one of the ve centres in the counties of Cornwall and Devon where lung cancers are investigated. Individuals were included in the study if their nal diagnosis was lung cancer, they were less than 75 years old, were of white ethnicity, were current residents of Cornwall or Devon, had lived in one of the two counties for at least 20 years out of the 30- year period ending 5 years previously and consented to participate. Initially, the sampling frame for the population controls comprised the Family Health Services Authority lists for the whole of the counties of Devon and Cornwall. However, during the study, access to the Devon list was withdrawn and so for Devon the electoral roll was used for the remainder of the study. Controls were randomly sampled with frequency matching to the numbers of

3 Residential Radon and Lung Cancer 195 individuals referred for investigation of suspected lung cancer by age, sex and county of current residence, and they were subject to the same inclusion criteria as the cases. Cases and controls were both interviewed by research assistants to obtain details of their residential histories, smoking habits and other risk factors. For all subjects, the radon concentration in the current residence was measured by using passive etched track radon detectors Hardcastle et al., 1996). Wherever possible, measurements were also made at the subjects' previous residences in the study area during the previous 35 years. On average, the subjects had lived in residences where no measurement could be made for approximately 15% of the period of interest. The radon concentrations for these periods were estimated by using area mean radon concentrations. A total of 982 cases of lung cancer and 1486 population controls were included. The original study also included hospital controls, but matching on residential area within each county was involved in their selection, and they have been excluded from the present analysis as their geographical distribution within each county does not represent the distribution of the population. Further details of the study design are given elsewhere Darby et al., 1998). Individual time-weighted average radon concentrations had previously been computed for all study subjects, using as weights the proportion of time that the individual had lived at each address Darby et al., 1998). Counties are subdivided into administrative districts, and district-speci c mean radon concentrations were derived from the individual data for the population controls and were computed as exp x 0:5s 2 )where x is the mean and s 2 the variance of the logarithms of the individual values i.e. assuming that the individual values followed a log-normal distribution). As in the analysis of the Swedish study, to avoid complicating the comparison between ecological and individual level risk estimates for radon, covariates other than radon were not in general aggregated. Therefore, in most analyses, adjustments for age, sex, smoking and social class were based on individual data. Previously de ned categories were used for these variables 5-year age groups; seven categories of smoker Ð lifelong non-smoker, current cigarette smoker of fewer than 15, 15±24 or 25 or more cigarettes per day, ex-smoker of fewer than 10 or 10 or more years and others current pipe or cigar smokers who did not smoke cigarettes and occasional smokers); three categories of social classði and II, III manual or non-manual, and IV and V O ce of Population Censuses and Surveys, 1980); see Darby et al. 1998)), and county and district a liation were based on current residence. Additional analyses compared individual and aggregate level adjustments for smoking. For these analyses, district-speci c mean smoking levels were calculated as the average number of cigarettes smoked per day among the population controls. In this calculation an appropriate allowance was made for current cigarette smokers who also smoked pipe tobacco Darby et al., 1998)and, on the basis of the relative risks of lung cancer among ex-smokers compared with current cigarette smokers, ex-smokers were scored as having a consumption of two cigarettes per day. The results presented assume that the e ects of smoking are the same in men and women. When the analyses were repeated allowing for an interaction between sex and smoking similar results were obtained. Relative risks are maximum likelihood values of the log-odds ratio, based on unconditional logistic regression Breslow and Day, 1980)with adjustment for age, sex and other factors, and were calculated using the Stata statistical package StataCorp, 1999). No information was available from within the study on lung cancer incidence in Devon relative to Cornwall as the number of population controls in each of the two counties was xed by the design of the study. Therefore, either separate analyses were carried out for the two counties or an adjustment was made for county. Con dence intervals CIs)are based on the estimated standard error. To calculate the relative risk of lung cancer for one district relative to the

4 196 S. Darby, H. Deo, R. Doll and E. Whitley whole county, a logistic model was tted with categorical variables for age, sex and district with one level of each variable as the base-line in the usual way. The tted relative risks were then multiplied by a factor 1= p i RR i, where RR i is the tted relative risk for district i and p i is the proportion of the population controls living in district i. Correlation coe cients were calculated using the Pearson method. 3. Results Relative risks RR of lung cancer for the districts of Cornwall and Devon, ranked in decreasing order within each county, are shown in Table 1 together with the mean radon concentration and the range of individual radon concentrations in each district. In Cornwall, there was a clear tendency for districts with higher mean radon concentrations to have higher lung cancer rates and the correlation between the relative risk of lung cancer and the district mean radon concentration was 0.71 p ˆ 0:11), although there was little overall evidence of heterogeneity in lung cancer incidence between the Cornish districts 2 5 ˆ 3:76; p ˆ 0:58). In Table 1. District-speci c lung cancer relative risks and radon concentrations in Devon and Cornwall from the south-west England case±control study of residential radon District Relative risk of lung cancer{ Radon concentration Bq m 73 )z Mean Range Cases of lung cancer Numbers of subjects Population controls Cornwall Penwith , 291)41 43 Kerrier , 1082)53 60 Restormel , 367)49 57 Carrick , 579)60 74 Caradon , 418)43 67 North Cornwall , 413)35 57 All Cornwall , 1082)281} 358 Correlation}} 0.71 Devon Exeter , 185) Plymouth , 183) Torbay , 101) Teignbridge , 545) West Devon , 544)26 49 East Devon , 287) Mid-Devon , 526)38 81 South Hams , 429)39 87 North Devon , 634)37 85 Torridge , 202)21 56 All Devon , 634)701} 1128 Correlation}} {Adjusted for age and sex using individual level data. The number of controls in Devon relative to the number in Cornwall was determined by the study design. Therefore, estimations were carried out separately for Cornwall and Devon. Separate data from the South and West Cancer Intelligence Unit show that the age- and sex-standardized annual registration rate for lung cancer during 1990±1996 was 74 per % CI 71, 77)) for Cornwall and 69 per % CI 67, 71)) for Devon. zfrom population controls: values shown are observed values with no correction for measurement error. The number of subjects is given in the right-hand column. }Mean radon concentrations for cases were 105 Bq m 3 in Cornwall and 37 Bq m 3 in Devon. }}Correlation between the relative risk of lung cancer and district mean radon concentration.

5 Residential Radon and Lung Cancer 197 Table 2. Comparison of individual and district level estimates of relative risk RR for lung cancer at 100 Bq m 3 residential radon concentration compared with 0 Bq m 3 and 95% CIs for different covariate adjustments in the south-west England case±control study of residential radon Additional covariates included{ Levels of definition for radon concentration: District mean Individual RR 95% CI RR 95% CI Cornwall onlyz None , 2.38) , 1.23) Smoking district) , 2.36) , 1.23) Smoking individual) , 2.51) , 1.32) Smoking individual), social class , 2.45) , 1.33) Devon only None , 0.82) , 1.04) Smoking district) , 1.17) , 1.06) Smoking individual) , 1.47) , 1.24) Smoking individual), social class , 1.75) , 1.26) Urban±rural , 2.55) , 1.11) Urban±rural, smoking district) , 5.09) , 1.12) Urban±rural, smoking individual) , 4.37) , 1.31) Urban±rural, smoking individual), social class , 4.34) , 1.31) {Adjustment for age and sex using individual level data throughout: the adjustment for social class, when included, is at an individual level. zno districts in Cornwall are classi ed as urban. Therefore, the adjustment for urban±rural status does not a ect the results for Cornwall. contrast with Cornwall, there was considerable evidence of heterogeneity in lung cancer incidence between the Devon districts 2 9 ˆ 25:21; p ˆ 0:003). However, there was no tendency in Devon for the districts with the higher mean radon concentrations to have higher lung cancer rates, and the correlation between the relative risk for lung cancer and the mean radon concentration was 0:35 p ˆ 0:31). In both counties the range of individual radon concentrations within each district was more than an order of magnitude and was much greater than the range of the district mean concentrations. The apparently di erent relationships in Devon and Cornwall between lung cancer risk and district-speci c mean radon concentration were con rmed by logistic regression. After adjustment for age and sex, an increase in the district-speci c mean radon level from 0 to 100 Bq m 3 was associated with RR ˆ 1:46 95% CI 0.89, 2.38)) in Cornwall, whereas in Devon a similar increase in the district mean radon level was associated with RR ˆ 0:36 95% CI 0.16, 0.82)) Table 2, middle columns). Adjustment for smoking reduced RR slightly in Cornwall and increased it somewhat in Devon. Within each county, the point estimate of the relative risk was similar, regardless of whether smoking was considered at the district or at the individual level. However, individual adjustment led to wider CIs than district mean adjustment. Adjustment for social class, which is the only other covariate that was included in the original analysis of the case±control study Darby et al., 1998), had a small e ect in Cornwall and led to some further increase in the estimate for Devon. However, even after adjustment for both smoking and social class at an individual level, the data still suggested a positive e ect in Cornwall and a negative e ect in Devon see Table 2). Additional information on the extent to which correlations between radon concentrations

6 198 S. Darby, H. Deo, R. Doll and E. Whitley Fig. 2. District-speci c radon±smoking correlations versus district mean radon levels in becquerels per cubic metre) for a) Cornwall and b) Devon: in b), urban districts ~) are indicated separately from rural districts *) and smoking habits might be biasing the ecological regressions was obtained by examining the correlation between the number of cigarettes smoked per day by an individual and the individual's radon concentration. The overall correlation between smoking and radon concentration based on all individuals in the study was 0:02. Separate correlations were also calculated for each district and these are plotted against the district-speci c mean radon levels in Fig. 2. For Cornwall all the correlations were close to 0 Fig. 2 a)). Therefore, the use of the simple district mean radon concentrations in the ecological regression should not cause any bias, as was apparent from Table 2 RR ˆ 1:44 with either district or individual adjustment for smoking). For Devon, seven of the correlations were close to 0, but for East and West Devon and Exeter values were higher, at 0.32, 0.20 and 0.18 Fig. 2 b)). Correspondingly, the relative risks di ered, taking value 0.45 when an adjustment was made using district mean smoking levels and 0.56 when using individual information see Table 2). This point is discussed in detail by Lubin 1998)who showed for a simpli ed example that, when smoking and radon are correlated within districts, then to obtain an unbiased estimate of the e ect of radon in the ecological regression it is necessary to give di erent weights to individuals with di erent smoking habits in the calculation of the district mean radon concentrations. Some indication of the cause of the qualitative di erence between the results for Devon and Cornwall when radon is aggregated at the district-speci c mean level is apparent from Table 1. The three districts in Devon with the highest lung cancer rates correspond to the three large conurbations of Exeter, Plymouth and Torbay. These districts have population densities that are at least an order of magnitude greater than any of the other districts in either Devon or Cornwall, on the basis of data from the 1991 census. Excluding these districts from the calculation of the correlation between the relative risk of lung cancer and districtspeci c mean radon concentration in Table 1 changes the value for Devon from 0:35 to When an explanatory variable indicating urban±rural status is introduced into the logistic regression in Table 2 then, even without adjustment for smoking, the negative trend in lung cancer risk with increasing district mean radon concentration in Devon largely disappears RR ˆ 0:93 at 100 Bq m 3 ), whereas the inclusion of smoking as an additional adjustment variable in the ecological regression leads to estimates for Devon that are in good agreement with those for Cornwall see Table 2). Adjustment for smoking had a larger e ect after the inclusion of urban±rural status than before. The reason for this is apparent from Fig. 2 b). Among the urban districts the district-speci c radon±smoking correlations and the district-speci c mean radon levels are almost linearly related.

7 Residential Radon and Lung Cancer 199 The same series of logistic regression models but with radon level de ned on an individual basis were also tted to the data see Table 2, right-hand columns). For Cornwall, the lung cancer risk tended to increase with increasing radon concentration and there was some negative confounding with smoking which was not removed when adjustment was carried out only at the district mean level. For Devon, the lung cancer risk tended to decrease with increasing radon concentration unless an adjustment for smoking was carried out at an individual level. Adjustment for social class led to small increases in the regression coe cient in both counties, and adjustment for urban±rural status had only a small e ect. The full results of an individual analysis of the data from this study have been presented elsewhere Darby et al., 1998). The coe cients based on individual radon concentrations given in Table 2 can be considered as overall values that are approximately equal to a variance-weighted combination of within-district values based on individual radon concentrations in a model that includes an adjustment for district)and between-district values based on district mean radon concentrations) Table 3). If the within- and between-district values di er, and in particular if the between-district values are subject to bias from the use of aggregated data, then the overall value may also be biased. For the present data, the relative width of the CIs indicates that the variance of the between-district estimates is very much larger than that of the within-district estimates see Table 3). Therefore, the overall values are very close to the within-district values and are only in uenced to a minor degree by the between-district values, even when the between-district and within-district values di er substantially, as in the Devon data before the inclusion of covariates other than age and sex. When data for the two counties were analysed together, the inclusion of urban±rural status as a covariate as well as smoking and social class increased the between-district estimate to Table 3. Comparisons of within-district, between-district and overall estimates of relative risk RR for lung cancer at 100 Bq m 3 residential radon concentration compared with 0 Bq m 3 and 95% CIs for different covariate adjustments in the south-west England case±control study of residential radon Additional covariates included Levels of effect estimation: Within district{ Between districtz Overall} RR 95% CI RR 95% CI RR 95% CI Cornwall only}}* None , 1.21) , 2.38) , 1.23) Smoking individual), social class , 1.32) , 2.45) , 1.33) Devon only}} None , 1.11) , 0.82) , 1.04) Smoking individual), social class , 1.31) , 1.75) , 1.26) Urban±rural, smoking individual), social class , 1.31) , 4.34) , 1.31) Cornwall and Devon combined** None , 1.13) , 1.51) , 1.13) Smoking individual), social class , 1.27) , 1.82) , 1.27) Urban±rural, smoking individual), social class , 1.27) , 2.23) , 1.28) {Analysis using individual radon concentrations with adjustment for district. zanalysis using district mean radon concentrations. }Analysis using individual radon concentrations without adjustment for district. }}Adjustment for age and sex using individual level data throughout. *No districts in Cornwall are classi ed as urban. **Adjustment for age, sex and county using individual level data throughout.

8 200 S. Darby, H. Deo, R. Doll and E. Whitley a value that was somewhat higher than the within-district estimate. In contrast, the withindistrict estimate was una ected by the inclusion of urban±rural status and the overall estimate was only minimally altered Table 3). After tting the nal model shown in Table 3 i.e. adjusting for age, sex, urban±rural status, smoking, social class and county of residence) a categorical variable indicating district was also included in the logistic regression. There was no evidence of remaining heterogeneity in the district-speci c lung cancer rates using either district mean radon levels p ˆ 0:96)or individual radon concentrations p ˆ 0:96). 4. Discussion In the present example, two parallel analyses have been carried out in which the only di erence is that one includes radon measured at the individual level, whereas in the other the individual radon values have been aggregated at the district mean level. Therefore it is possible to compare individual and ecological estimates of the e ect of radon, and also to obtain an ecological estimate of the e ect of radon that is free from the limitations that often apply in ecological studies, such as crude or misspeci ed exposure levels and confounders. The results illustrate the fact that important confounders may di er in individual and ecological studies of the same population. When radon was included at the individual level, the addition of urban±rural status changed the estimated increase in risk associated with 100 Bq m 3 by less than 10%, from 12% to 13%. In the original analysis of the case±control study Darby et al., 1998), which included hospital as well as population controls, the inclusion of urban±rural status had even less e ect, changing the estimated increase from 8.0% to 8.1%.)In contrast, when radon was aggregated at the district mean level, including urban± rural status changed the estimated radon e ect by a factor close to 3, from 12% to 35% Table 3), and its inclusion was necessary to produce qualitatively similar estimates in Devon and Cornwall. This large e ect is partly because it acted as a confounder directly, and partly because including it increased the e ect of adjusting for smoking Table 2). In both individual and ecological analyses the estimated urban±rural e ect was substantial and statistically signi cant individual analysis Ð RR ˆ 1:33, 95% CI 1.06, 1.67), p ˆ 0:01; ecological analysisðrr ˆ 1:30, 95% CI 1.04, 1.62), p ˆ 0:02). It is likely to be due in part to an e ect of air pollution and in part to di erences in the past smoking histories of urban and rural residents that are not accounted for even when an individual adjustment for smoking was made in seven categories, including two categories of ex-smokers, based on personal interviews with the subjects. When the e ect of radon was estimated at the between-district level, its CI was much wider than when it was estimated within districts or overall, and the true CI may be even wider than that given in Table 3, where no allowance has been made for spatial autocorrelation. A wide CI is to be expected given the much narrower range of radon concentrations at the district mean level than at the individual level Table 1). However, a direct comparison of the ranges is misleading as the individual radon values are subject to measurement error. Residential radon concentrations are log-normally distributed and the coe cient of variation of repeated measurements made on di erent occasions in the same house is around 50%. Thus the ranges of the true i.e. the mean over repeated measurements)radon concentrations for the houses in the present study are likely to be less than the ranges shown in Table 1, and an approximate calculation shows that the di erence is around a factor of 2. A detailed analysis of the individual data in this study taking into account uncertainties due to measurement error and to the estimation of radon concentrations in houses where no measurements could be made has been carried out Darby et al., 1998). In this analysis the estimated radon e ect was

9 Residential Radon and Lung Cancer 201 around 50% greater than the estimate derived from an analysis in which such uncertainties were ignored, and its CI was also increased by around 65%. After adjusting for urban±rural status, smoking and social class, the estimated e ect of radon using between-district information was larger than the estimate using only withindistrict information Table 3). A small part of this di erence is attributable to measurement error biasing the within-district estimate downwards. The remaining di erence is small compared with the CIs involved and will re ect both chance and any other unidenti ed covariates causing bias in one estimate but not in the other. As a consequence of the eligibility criteria for the south-west England case±control study, the present data include only long-term residents of Cornwall and Devon. Lung cancer registration rates for 1990±1996 were therefore used to obtain lung cancer rates for the whole population of the districts of Devon and Cornwall, directly standardized for age and sex to the combined population of the two counties. For Cornwall the correlation between these values and the district mean radon levels in Table 1 was 0.62, whereas for Devon it was 0:26. These values are similar to the values obtained from the study data Table 1), suggesting that the confounders found to be operating at the district level in the present analysis may also apply to the population of Devon and Cornwall as a whole. Two other ecological studies of the e ect of radon on lung cancer in Britain have been published. The rst found a negative association after adjusting for population density and regional variations in smoking, diet and social class, based on the counties of England and Wales Haynes, 1988). Adjusting for population density seems likely to have accounted for any urban±rural e ect in this analysis. However, regional variation in smoking was based on regional variation in household cigarette expenditure 20 years previously, and such a crude ecological measure may have left considerable confounding due to smoking. It is also possible that other confounders that are di erent from those operating at the district level are operating at the county level. This has been demonstrated by Muirhead et al. 1991)who carried out an ecological regression of radon and leukaemia rates at both district and county level. With data aggregated at the county level there was a positive coe cient for radon, whereas for data aggregated at the district level within counties the coe cient was negative. The second ecological study of lung cancer in Britain was based on cancer registration data for 1989±1992 for the postcode districts of Devon and Cornwall Etherington et al., 1996). It found a non-signi cant negative correlation between lung cancer and radon for both males and females after adjusting for age and social deprivation using the Carstairs index Carstairs and Morris, 1991; Carstairs, 1995). When the present ecological analysis was repeated with district-speci c Carstairs index, age and sex as adjustment variables, there was still a strong negative association with radon level for Devon, indicating that at the district level the Carstairs index does not remove the biases that are associated with smoking and urban±rural status. Worldwide, at least 18 ecological studies of radon and lung cancer have been carried out. The ndings vary widely, from the negative and statistically signi cant association of Cohen 1995)to positive and statistically signi cant associations. The studies have been reviewed by Stidley and Samet 1993)and National Research Council 1999), who concluded that their shortcomings render them uninformative on the lung cancer risk that is associated with indoor radon exposure. There has also been much discussion of Cohen's study and the likely explanation for the negative e ect that it reports Gilbert, 1994; Greenland and Robins, 1994a; Lubin, 1998; Smith et al., 1998). As cigarette smoking is the major risk factor for lung cancer, this discussion focuses on smoking as the cause of the bias. However, both in the present study and in the similar study using data from the Swedish nation-wide study of residential radon and lung cancer Lagarde and Pershagen, 1999), the main ecological bias

10 202 S. Darby, H. Deo, R. Doll and E. Whitley was not fully accounted for by an adjustment for smoking, even using individual data and the same categorization that had been considered su cient in the analysis of the case±control studies seven categories of smoker in the south-west England study see Section 2 for a de nition of categories), and ve categories never smoker, ex-smoker, current smoker of fewer than 10 or 10 or more cigarettes per day and unknown, based on postal questionnaires completed either by the subjects themselves or by their next of kin)in the Swedish study Pershagen et al., 1994)). In both studies additional variables were necessary for the results of the ecological analysis to be similar to those of the individual analysis. These were urban± rural status in the south-west England study and latitude in the Swedish study. These additional variables may in part be surrogate measures for some aspects of the study subjects' smoking history that are not accounted for by the smoking categories derived from the questionnaire data. However, the precise role of smoking in these variables is not well understood. Neither these variables nor any underlying variables for which they are surrogates had been identi ed as important a priori. Therefore, the methods that have been generally recommended for overcoming the limitations of ecological studies, namely Monte Carlo simulations to assess sensitivity to di erent sources of bias Stidley and Samet, 1994)or controlling for more than just a single summary of the covariate distribution Greenland and Robins, 1994a), would not in practice have been adequate in these examples to eliminate the ecological bias. For the present examples, aggregate studies, in which individual level data are obtained from samples of individuals within each group Prentice and Sheppard, 1995; Sheppard et al., 2000)would in principle have provided information on the extent of any bias due to district-speci c radon±smoking correlations. In addition, an examination of the individual level association within a few of the geographical units that are most in uential in the ecological regression, as suggested by Connor and Gillings 1984), might in principle have identi ed the urban±rural e ect. However, in this example, collecting su cient appropriate data to implement either the method suggested by Prentice and Sheppard or that suggested by Connor and Gillings with adequate power would have been complex and expensive. In practice, ecological studies are often based on very crude data and, as a result, tend to have substantial limitations in addition to any biases caused by the use of aggregated data or unrecognized confounders operating at the level of the geographical unit employed. However, as has been pointed out by Greenland and Robins 1994b), when there is disagreement between ecological and individual level associations it does not automatically follow that it is the ecological result that is wrong. Individual studies are also subject to many biases and it is at least logically possible that the true e ect under study is closer to the ecological association than to the individual level association. Investigators who have data at the individual level rarely carry out supplementary analyses incorporating aggregated measures of the explanatory variables as well as the individual values. This was recommended by Cox 1968)and, although it is not often used in epidemiology, may be of use in revealing confounders in individual level analyses that had not previously been suspected. Acknowledgements The south-west England case±control study of residential radon and lung cancer was carried out in the Imperial Cancer Research Fund ICRF)Cancer Epidemiology Unit with funding from the ICRF, the National Radiological Protection Board NRPB), the Department of Health, the Department of the Environment, Transport and the Regions, and the European Commission. Radon measurements were carried out by the NRPB. We acknowledge the role of many other ICRF and NRPB sta in the data collection and preparation. We thank

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