RR876. Mesothelioma mortality in Great Britain. The revised risk and twostage clonal expansion models


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1 Health and Safety Executive Mesothelioma mortality in Great Britain The revised risk and twostage clonal expansion models Prepared by the Health and Safety Laboratory for the Health and Safety Executive 211 RR876 Research Report
2 Health and Safety Executive Mesothelioma mortality in Great Britain The revised risk and twostage clonal expansion models Emma Tan & Nick Warren Harpur Hill Buxton Derbyshire SK17 9JN Asbestos is a known carcinogen that is the cause of the majority of mesothelioma cases worldwide. Various models have been used to describe the increase and likely future pattern of mesothelioma rates seen in many western countries a legacy of past heavy industrial asbestos use. Following on from previous work (Tan and Warren, 29), we analysed female mesothelioma mortality using the same risk model that was assumed for males. We also analysed mesothelioma mortality in males in Great Britain using two alternative risk models; the first is based on asbestos import data where the population is categorised into low and high exposure groups, with the calculation of risk based on the cumulative lung burden of the individual; the second is a twostage clonal expansion model (TSCE), a biologicallybased carcinogenesis model that assumes that the development of a malignant cell is the result of two critical and irreversible events, with asbestos lung burden as the measure of dose that enters the doseresponse component of the TSCE model. We use Markov Chain Monte Carlo within a Bayesian framework to fit the models presented in this report. Though considerably uncertain, peak mortality in females is predicted to occur over a decade later than in males, but with a substantially lower annual number of deaths. The updated models provide a reasonable basis for making relatively shortterm projections of mesothelioma mortality in Britain. However, longerterm predictions comprise additional uncertainty not captured within the prediction intervals for the annual mortality rates. Taking this into account, 21 deaths in 216 represents our current best estimate of the upper limit for the male projections. This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including any opinions and/or conclusions expressed, are those of the authors alone and do not necessarily reflect HSE policy. HSE Books
3 Crown copyright 211 First published 211 You may reuse this information (not including logos) free of charge in any format or medium, under the terms of the Open Government Licence. To view the licence visit write to the Information Policy Team, The National Archives, Kew, London TW9 4DU, or Some images and illustrations may not be owned by the Crown so cannot be reproduced without permission of the copyright owner. Enquiries should be sent to ACKNOWLEDGEMENTS: The authors would like to thank Andrew Darnton and John Hodgson (CSEAD Epidemiology, HSE) for their valuable contribution to this report. ii
4 EXECUTIVE SUMMARY Aims This report presents Bayesian statistical analyses of mesothelioma mortality in Great Britain between the years 1968 and 27. This report updates previous work carried out in HSE Research Report RR728. The aims of the statistical analysis were: To fit the previous statistical model to female mortality data; To consider alternative approaches to modelling mesothelioma mortality; To investigate whether the risk of mesothelioma increases indefinitely with time since first exposure to asbestos; To allow for varying asbestos exposure profiles for different subgroups of the population; To fit the alternative models to male mortality data; To produce and subsequently compare updated estimated annual mesothelioma deaths to 25 with confidence and prediction intervals in order to determine whether the previous projections were specific to the previous model. Main Findings Males: Two alternative approaches have been developed that share a common exposure framework based upon asbestos imports data, the revised risk model and the twostage clonal expansion (TSCE) model. Using the optimal revised risk and TSCE models considered in this report, mesothelioma mortality is predicted to peak at around 186 deaths in 212 and 178 deaths in 21 respectively. The estimated number of background cases in 27 using the revised risk and the TSCE model were 19 and 9 cases respectively. Within the framework of the TSCE model, the cumulative hazard at age 89 for males who were exposed from age 25 for 5 years (the largest exposure category) was highest amongst the 193 to 194 birth cohort. The updated models provide a reasonable basis for making relatively shortterm projections of mesothelioma mortality in Britain, including the extent and timing of the peak number of deaths. However, longerterm predictions comprise two additional sources of uncertainty which are not captured within the prediction intervals for the annual number of deaths: 1) whether the form of the model is valid for more recent and future exposure contexts; and 2) if the model is valid in such iii
5 contexts, the uncertainty arising from the particular choice of exposure model or model parameters; Given these uncertainties, a range spanning the lowest and highest confidence bands of the Tan and Warren (29) model, the optimal revised risk and the TSCE model is likely to give a better reflection of the true uncertainty in the projections than the range based on any one of the three models. On this basis, the upper limit from Tan and Warren (29), that is, 21 cases in 216 is represents our current best estimate of the upper limit for the male projections. Females: There was a sharp increase in the implied exposure amongst females around the year 1948 with a rapid decline following; the implied exposure subsequently increased to a global peak around 1965, however there was greater uncertainty in the exposure levels after 198. The background rate was estimated at approximately 1.3 cases per million, suggesting that there are a small number of cases (about 3 per year) that are not caused by exposure to asbestos. Although there was considerable uncertainty regarding current and recent exposure levels, a consistent finding was that the peak year of mortality is predicted to occur over a decade later in females than in males, with a lower number of peak deaths for females than males.. Recommendations Make comparisons of the projections with the latest mortality data as it becomes available in order to further assess the fit and the adequacy of the existing models. The models might also be refitted to obtain updated model parameters and model projections. Investigate the effects of asbestos exposure on malignant transformation rates within the twostage clonal expansion modelling framework. Investigate what evidence exists for the determination of stock removal parameters. iv
6 CONTENTS 1 INTRODUCTION Asbestos Mesothelioma Deaths and Asbestos Imports Data FEMALES The Model Models fitted Statistical Methodology Results Discussion REVISED RISK MODEL Representation of exposure Risk function Statistical Methodology Results Discussion TWOSTAGE CLONAL EXPANSION MODEL Background Representation of exposure The Model Statistical Methodology Results Hazard function MALE PROJECTIONS 34 6 DISCUSSION 45 7 CONCLUSIONS 46 APPENDIX REFERENCES v
7
8 1 INTRODUCTION Mesothelioma is a rapidly fatal form of cancer that is almost always caused by exposure to asbestos. The majority of those who develop mesothelioma have had occupations with significant exposure to asbestos fibres (Rake et al., 29). Mesothelioma has a long latency period; symptoms usually emerge between 15 and 6 years after exposure to asbestos. Projections of the future burden of mortality in Great Britain have been published by the Health and Safety Executive and have been widely used both within HSE and externally. Hodgson et al. (25) developed a statistical model based on the doseresponse model for mesothelioma (Heath Effects Institute, 1991), where an individual s exposure to asbestos is assumed to be dependent on calendar year and the age of the individual in that calendar year. Using this model, mesothelioma mortality in Great Britain amongst males aged under 9 was predicted to reach a peak at around 1,65 to 2,1 deaths per year some time between 211 and 215, followed by a rapid decline. Tan and Warren (29) presented a more refined statistical analysis of mesothelioma mortality amongst males in Great Britain based on Markov Chain Monte Carlo (MCMC) methods using a modified form of the model formulated by Hodgson et al. (25). The use of MCMC allowed the calculation of credible intervals for model parameters and prediction intervals for mesothelioma mortality to be made. Mortality amongst all males was predicted to peak at around 2,4 deaths in the year 216, with a rapid decline following. The recommendation in Tan and Warren (29) to carry out further investigations of fitting the model used for males to data for females, in particular whether to assume common parameter values for males and females in some cases, has been considered and the results presented in Section 2. Although the Tan and Warren (29) model fits the data well, it is not clear whether the model form is valid for more recent and future exposures. In particular, the fact that the model does not fit well when deriving exposure from imports and the relatively high impact of exposure at higher ages gives us cause to have some doubts about the model, as well as to question whether the risk should eventually level off with time since exposure. In Section 3, we attempt to address these issues by moving to a more empirically based exposure index; a statistical analysis of mesothelioma mortality in Great Britain from 1968 to 27 is presented, using a revised risk model based on asbestos import data in which the male population is classified into low and high exposure categories. Those in the high exposure category are then subclassified according to age and duration of exposure, with the calculation of the risk based on the cumulative lung burden of the individual. The analyses carried out by Hodgson et al. (25) and Tan and Warren (29) have been based on statistical models where it was assumed that the increase in subsequent mesothelioma risk caused by each period of asbestos exposure is proportional to the asbestos exposure during that period, and to a power of time since exposure. Section 4 presents a statistical analysis of mesothelioma mortality within the framework of the twostage clonal expansion (TSCE) model (Moolgavkar and Knudson, 1981), a carcinogenesis model which takes into account biological considerations. The TSCE model allows us to incorporate information about exposure patterns to toxic carcinogens in mesothelioma risk assessment and has previously been used to model the effects of asbestos on lung cancer risk (Richardson, 29) and the effects of tobacco smoke on lung cancer mortality (Hazelton et al., 25). 1
9 1.1 ASBESTOS Asbestos is a mineral that is extremely flexible, durable and nonflammable at high temperatures. It first became popular in Great Britain in the late 18s due to its highly desirable properties and was widely used in the rail and shipyard industries, and later in the building industry which represented the biggest use of asbestos. Asbestos use was at its highest around the 194s to the 197s when thousands of asbestoscontaining products were made. Although the majority of asbestos fibres may lie intact in buildings for several years or decades, those that are disturbed may become airborne and pose a risk when inhaled and retained in the lungs. Asbestos is classed as a category 1 carcinogen and inhalation of fibres may lead to serious diseases such as lung cancer and mesothelioma. There are three main types of asbestos fibres that have been commercially used in Great Britain: crocidolite (blue), amosite (brown) and chrysotile (white). Chrysotile is the most common and abundant form of asbestos with shorter fibre lengths than amosite and crocidolite. Several studies have shown that chrysotile has a half life in the lungs of around 15 days and does not pose as great a risk of cancer as crocidolite and amosite, which have longer fibre lengths and a longer half life of several decades, thus remaining in the lungs for a much longer period (Berry, 1999) Observed males Observed females 14 Number of deaths Year Figure 1 Male and female mesothelioma deaths (aged 2 to 89) from 1968 to MESOTHELIOMA DEATHS AND ASBESTOS IMPORTS DATA The number of deaths due to mesothelioma in Great Britain (where mesothelioma was mentioned on the death certificate) is published annually by the Health and Safety Executive. In both males and females, 99% of all these deaths have been amongst those between the ages of 2 and 89. The data used in this report are based on deaths of males aged between 2 and 89 between the years 1968 and 27. Figure 1 shows the observed deaths amongst males and females aged 2 to 89 between the years 1968 and 27. The population data that was used in the analyses were the ONS midyear population estimates for 1968 to 27 and GAD population projections for 28 to 25. 2
10 The UK imports data for crocidolite, amosite and chrysotile from 188 to 27 were obtained from reports and submitted evidence from the Advisory Committee on Asbestos. From 1978 to 1995, data were obtained from the Asbestos Information Council with the exception of years 1984 to 1989 which were obtained from Eurostat. Crocidolite and amosite imports were formally banned in the UK in the mid198s; very little crocidolite was imported after 197 whereas amosite continued to be imported and widely used until about 198. Chrysotile imports and use declined during the 198s and a total ban on asbestos came into effect in Linear interpolation was used to estimate imports for individual years where data were unavailable. Figure 2 shows the annual UK asbestos imports from 188 to Annual UK asbestos imports (tonnes) Annual UK asbestos imports (tonnes) x Year x Amosite Crocidolite Chrysotile Year Figure 2 Annual UK asbestos imports 3
11 2 FEMALES Initial exploration of fitting the Tan and Warren (29) model to data for females showed that the smaller number of deaths in comparison to males led to greater uncertainty in the estimated model parameters. A simple substitution of the estimated parameters obtained for males did not result in a satisfactory estimation of female deaths, suggesting that some of the parameter values may not be common to both males and females and that a set of separate parameter estimates are required to make reliable inferences on female mortality and model parameters. This led to the recommendation in research report RR728 to carry out further work on female mesothelioma mortality data. The number of mesothelioma deaths amongst females is much lower than amongst males so assuming a common background rate of mesotheliomas not caused by asbestos across both genders implies that background cases account for a higher proportion of female deaths. The data on females are thus important in their own right as they potentially allow more reliable estimation of background rates to be made. 2.1 THE MODEL The model for males that was used in Tan and Warren (29) has been used to model female deaths between the ages of 2 and 89 however, as the diagnostic trend parameter was found to be insignificant when analysing male data, the diagnostic trend component has been omitted from the female model. The female model takes the following form: λ A,T = where A 1 89 [ W 27 A l D T l I (l + 1 L) k l=1.5 l/h ]P A,T (M A=2 T=1968 B A,T ) A 1 + B A,T [ W A l D T l (l + 1 L) k A=2 T=1968 l=1.5 l/h ]P A,T (1) λ A,T is the number of deaths at age A in year T ; W A is the overall agespecific exposure potential at age A; D T is the overall population exposure in year T ; L is the lag period in years between exposure and its contribution to the risk of mesothelioma and is fixed at 1 years; H is the halflife in years for asbestos clearance from the lungs; k is the power of time representing the increase in risk with time since exposure; P A,T is the personyears at risk for age A in year T ; M is the total observed mesothelioma deaths from 1968 to 27; I is an indicator variable where I = if l < L 1 and I = 1 otherwise; l indexes years lagged from the risk year; B A,T is the number of background cases for age A at year T. 4
12 The agespecific exposure potential, W A, allowed the exposure of a female to differ by age. Nine parameters were assigned to W A, representing the exposure weighting for the age groups (in years) to 4, 5 to 15, 16 to 19, 2 to 29, 3 to 39, 4 to 49, 5 to 59, 6 to 64 and 65+, with the age group 2 to 29 years chosen as the baseline category. The overall population exposure, D T, represents the average effective carcinogenic dose in the breathing zone of females aged 2 to 89 years and is included as a unitfree parameter vector in the model. In this framework it is the shape of the exposure profile D T over time, rather than the scale in any given year (which is set arbitrarily) that determines future mesothelioma risk. D T was defined by growth and decline rates for years in multiples of 1 before and after the maximum exposure year, Peakyear (at which the gradient of the exposure curve is zero). The growth rates for intermediate years were determined by linear interpolation. The growth rates at Peakyear 65 (D 1 ), Peakyear 55 (D 2 ), Peakyear 45 (D 3 ), Peakyear 35 (D 4 ), Peakyear 25 (D 5 ), Peakyear 15 (D 6 ), Peakyear 5 (D 7 ), Peakyear + 5 (D 8 ) and Peakyear + 15 (D 9 ) were included as parameters in the model. The proportion of the peak exposure in 2, Prop, was also included as a parameter; this value was fixed at 4% for males in Tan and Warren (29). Exposures for years between Peakyear + 15 and 2 were calculated by linear interpolation. The background rate (Rate) is represented by the number of background cases per million in the female population. The age distribution of the background cases in each year is assumed to be (A L) k b where k b is the power of time representing the increase in risk with age. The proportion (A L) k b of background cases at age A in each year is therefore assumed to be P. (A L) k b A 2.2 MODELS FITTED In the female model, the power of time k b associated with background cases has been allowed to differ from the power of time k associated with asbestos exposure; both k and k b have been estimated. As it was found for males by Tan and Warren (29) that there was no optimal value of the clearance halflife H, H has been fixed at 1,, years for females. Although the change in exposure index at Peakyear 65, Peakyear 55 and Peakyear 45 were fixed in Tan and Warren (29), they have been estimated at a common value for females for the following reasons: (i) allowing the parameters to vary potentially allows us to infer asbestos exposure from mortality data as opposed to fixing the parameters based upon little knowledge of exposure during that period, (ii) preliminary analysis suggested that assuming a common value provided almost an equally good fit as assuming three distinct values, and (iii) fewer estimated parameters result in a more parsimonious model. The effects of changing assumptions about exposure post198 were also explored. In particular, the assumptions used for males that the exposure levels were 4% of the peak level in 2, 2% in 21 and.75% in 25 were changed to allow for the fact that the differential between the past peak exposure and recent/future exposures is likely to be lower for females. Historically, a lower proportion of females would have worked in high risk occupations compared to males, thus resulting in a lower peak level of exposure at a population level. In more recent years (around 2 onwards), the exposure levels of males are likely to have reduced to similar levels as females, as the levels of exposure begin to level off to a background/threshold level. To assess this we fitted two different models: Model F1: the exposure in 2 as a proportion of the peak, Prop, was fixed at 2%; Model F2: Prop was estimated. 5
13 In both cases the exposure in 21 and 25 were set at Prop/2 and Prop/4 respectively, and exposures for other years calculated by linear interpolation. 2.3 STATISTICAL METHODOLOGY Preliminary analyses were carried out by fitting the model using the fminsearch function in Matlab (The Mathworks, Inc., 29) by minimising the model deviance, a measure of how well the model fits the observed data. The Poisson deviance can be expressed as L Y A,T deviance = 2 Y A,T log (Y A,T FˆA,T) (2) A,T where Y A,T are the observations and FˆA,T are the fitted values. Although fminsearch allows the data to be fitted quickly and easily, a disadvantage is that confidence intervals are not provided. fminsearch has thus been used to provide initial point estimates of the parameters, which in turn have been used as approximate starting values for the MetropolisHastings algorithm (Hastings, 197), a Markov Chain Monte Carlo (MCMC) technique. This allowed not only model parameters to be estimated, but also allowed credible intervals to be easily obtained using formal statistical methods. FˆA,T Markov Chain Monte Carlo From a Bayesian perspective, the parameters of a statistical model are considered random quantities. Bayesian inference can usually be summarised by random draws from the posterior distributions of the model parameters. Let Lik(Y θ) be the likelihood function of the data Y, θ be the vector of model parameters and φ(θ) be the prior distribution of the parameters, which represents the prior information we have on θ. The posterior distribution π(θ) of θ is π(θ) Lik(Y θ)φ(θ). (3) Assuming that the observations follow a Poisson distribution, the likelihood function is ˆ λ Y A,T ˆ A,T e λ Lik(Y θ) = A,T Y A,T! A,T (4) which is the product of the individual likelihood contributions for each observation over all ages and years of death. Unfortunately, evaluation of the posterior distribution is normally extremely difficult and numerical techniques, particularly MCMC, are required. MCMC techniques require simulation to generate random samples from a complex posterior distribution. A large number of random draws from the posterior distribution is generated. After a burnin period (where an initial portion of samples are discarded to minimise the effect of initial values on posterior inference), the empirical distribution should eventually closely approximate the true shape of the posterior distribution. The MCMC chain is thinned in order to reduce autocorrelation. The process of thinning records samples periodically and discards the remaining samples. Point estimates and credible intervals are then calculated. 6
14 In the MetropolisHastings algorithm, given θ t at time point t, the next state θ t+1 in the chain is chosen by sampling a candidate point θ from a proposal distribution q( θ t ). The candidate point θ is then accepted with probability p where π(θ )q(θ t θ ) p = min 1,. π(θ t )q(θ θ t ) If the candidate point is accepted, the next state θ t+1 = θ. If the point is rejected, the chain does not move, i.e. θ t+1 = θ t. The process is then repeated for state θ t at every time point t to obtain a sequence of values θ 1,θ 2,... The approximate distributions at each step in the simulation converge to the target distribution of interest, π(θ). As θ is a vector of model parameters, each component will be individually updated for convenience. Further details on the choice of the prior and proposal distributions can be found in Appendix RESULTS Models F1 and F2 were fitted to the dataset using the MetropolisHastings algorithm. The results from fitting Models F1 and F2 are displayed in Tables 1 and 2 respectively. The posterior medians of k in both models were larger than the posterior medians of k b, at around 2.7 and 2.4 respectively, suggesting that the power of time may be greater for the risk associated with asbestos exposure than with background cases. However, there was not a significant difference between the values k and k b, with the posterior medians of k lying within the 9% credible intervals of k b, and vice versa. The background rate was estimated to be around 1.3 cases per million in both models, corresponding to around 3 cases in 27 amongst females aged 2 to 89. The background rate amongst males estimated by Tan and Warren (29) was 1.8 cases per million, corresponding to around 23 cases in 27 amongst males aged 2 to 89. However, assuming an equal proportion of male and female background cases, the female data potentially allow a more reliable estimate of background rate due to the much lower number of allcause female cases. The posterior medians of the agespecific exposure potential parameters were highest for females between the ages of 3 and 39, indicating a higher exposure contribution from the 3 to 39 age group (where the exposure contribution encapsulates both the exposure levels and proportion of females exposed associated with that age group). The lowest were for females aged below 2 and above 5 years. However, due to the lag period, there was high uncertainty in the estimates of the relative exposure potential for females aged 6 and above. Figures 3A to 3D show plots of the fitted and observed deaths in F1 for females aged 2 to 89 by year of birth, age and year of death. Figures 4 and 5 shows the observed and fitted deaths (with associated prediction intervals) for females aged 2 to 89 and estimated exposure profiles (with associated credible intervals) for F1 and F2 respectively. The posterior median of the peak year of mortality ranged from 225 (Model F1; 444 deaths) to 227 (Model F2; 477 deaths). Credible intervals for the peak level of mortality were calculated, however due to the high levels of uncertainty in the exposure levels for females from 198 onwards in F2, the upper bounds for the prediction intervals for the peak number of deaths increased for several decades after the expected peak year of mortality, whereas the upper bounds under F1 decreased. Similarly, the lower bounds for the prediction intervals under F2 decreased to much lower levels than that in F1. These patterns have been observed due to the fact that Prop has been estimated in F2 (introducing a degree of uncertainty), but artificially fixed in F1. 7
15 The estimated exposure curve in both models indicated a local peak of exposure just prior to 195, and a global peak around Between 1965 and 198, the estimated exposure levels decreased rapidly. There was great uncertainty in the exposure levels after 198 in F2, as any effects of exposure on the risk of mesothelioma from then onwards may not be observed for several decades. For F1 however, Prop has been fixed at.2; this explains the apparent lack of uncertainty in the exposure profile from the year 2 onwards. The posterior median for the deviance was lowest in F1 at (9% C.I. [263.7,29.]), indicating that a better fit was achieved using F1. A plot of the deviance residuals by age group and birth cohort can be found in Figure A1 in Appendix A. Over 9% of the residuals lie within the range [2,2] and no obvious patterns can be seen, suggesting an adequate fit of the model to the data. Table 1 MetropolisHastings: Posterior median and 9% credible intervals for Model F1 Posterior median (9% credible interval) k 2.63 (2.41,2.9) Background rate 1.31 (1.5,1.58) k b 2.41 (2.4,2.77) % of peak exposure in 2 2 (fixed) Maximum exposure year 1965 Halflife (years) 1 (fixed) Change in exposure index (% per year) in... Relative exposure potential by age group 19 (D(1)) 191 (D(2)) 192 (D(3)) 193 (D(4)) 194 (D(5)) 195 (D(6)) 196 (D(7)) (D(8)) 198 (D(9)) (91.4,145.4) (91.4,145.4) (91.4,145.4) (4.5,191.5) (39.6,184.8) (71.,26.3) 74.3 (42.7,12.5) (by definition) (31.2,3.77) 5.2 (22.1,33.4) to 4 5 to to 19 2 to 29 3 to 39 4 to 49 5 to 59 6 to (.,.2).1 (.,.3).6 (.,.23) 1. (baseline) 1.2 (.93,1.44).71 (.25,1.15).3 (.,.12).9 (.1,.42).27 (.2,1.17) Projections of future mesothelioma deaths in females aged 289 Peak level 444 (38,527) Peak year 225 (223,227) Deviance (263.7,29.) Degrees of freedom 26 8
16 Table 2 MetropolisHastings: Posterior median and 9% credible intervals for Model F2 Posterior median (9% credible interval) k 2.67 (2.42,2.95) Background rate 1.34 (1.3,1.64) k b 2.45 (2.7,2.8) % of peak exposure in 2 41 (4,93) Maximum exposure year 1965 Halflife (years) 1 (fixed) Change in exposure index (% per year) in... Relative exposure potential by age group 19 (D(1)) 191 (D(2)) 192 (D(3)) 193 (D(4)) 194 (D(5)) 195 (D(6)) 196 (D(7)) (D(8)) 198 (D(9)) 98.3 (43.1,175.) 98.3 (43.1,175.) 98.3 (43.1,175.) 1.2 (9.9,188.1) 98.4 (49.1,169.8) (64.8,3.2) 61.1 (41.3,91.2) (by definition) (32.6,.94) 1.2 (31.8,37.5) to 4 5 to to 19 2 to 29 3 to 39 4 to 49 5 to 59 6 to (.,.2).1 (.,.3).7 (.,.26) 1. (baseline) 1.17 (.92,1.42).62 (.17,1.12).3 (.,.13).1 (.1,.39).29 (.2,1.29) Projections of future mesothelioma deaths in males aged 289 Peak level 477 (371,) Peak year 227 (224,) Deviance (265.8,294.2) Degrees of freedom 26 9
17 A 3 B Fitted 9% credible interval Observed Number of deaths Number of deaths Fitted 9% credible interval Observed Year of birth Age (years) 1 C 5 x 1 D Exposure index Fitted deaths Fitted 9% credible interval Observed Exposure index Number of deaths Number of deaths Year Year of birth Figure 3 Model F1: (A) Observed and fitted deaths by year of birth. (B) Observed and fitted deaths by age. (C) Observed and fitted deaths by year of death, with derived exposure index. (D) Observed and fitted deaths for birth cohorts.
18 6 5 Fitted 9% prediction interval Observed Number of deaths Year Exposure index x Year Figure 4 Model F1 (Top) Observed deaths with 5th percentile curve and 9% prediction interval (Bottom) Estimated exposure profile with 95% (red), 9% (green) and 5% (yellow) C.I. 11
19 9 8 7 Fitted 9% prediction interval Observed Number of deaths Year x Exposure index Year Figure 5 Model F2 (Top) Observed deaths with 5th percentile curve and 9% prediction interval (Bottom) Estimated exposure profile with 95% (red), 9% (green) and 5% (yellow) C.I. 12
20 2.5 DISCUSSION This section has presented a statistical analysis of female mesothelioma mortality using a model based on that formulated by Tan and Warren (29), with some additional modifications and assumptions. One of the modifications is that a distinction has been made between the power of time associated with asbestosrelated risk and that associated with background risk. The reason for this is that the underlying factors or processes that contribute to risk may differ between the two; both powers of time have been estimated in the female analysis. The effect of these causes over time may differ from the effects attributed to occupational exposure; it is thus appropriate to allow for a distinction between the two power parameters. Although a difference was seen, it is not significant. Another modification that has been made in the female analysis relates to the proportions of the peak level of exposure in 2, 21 and 25. In the male analysis, these proportions have been fixed at 4%, 2% and.75% respectively. Historically however, a smaller proportion of females have had occupations in industries involving asbestos. It is therefore expected that the average exposure levels of females during periods of high industrial asbestos use were lower than that of males. Two different models have been fitted to the female data; one where the proportions of the peak level of exposure in 2, 21 and 25 have been fixed at 2%, 1% and 5% respectively, and one where the proportions have been estimated. The final modification that has been made is the assumption of a common estimated parameter for the change in exposure index in Peakyear 65, Peakyear 55 and Peakyear 45. These values had previously been fixed in the male analysis carried out by Tan and Warren (29). As there is a latency period of several decades between exposure to asbestos and the onset of mesothelioma, the majority of those who were exposed to high occupational levels of asbestos during the high exposure years around the 196s are expected to die of mesothelioma within the next few decades. As with the male projections, the annual number of female deaths is expected to continue increasing until reaching a peak within the next few years, eventually decreasing due to the post197 decrease in levels of exposure, however this only holds for F1. A much wider range of projections are consistent with F2 due to the very high level of uncertainty in the estimate of exposure in 2 (41% of the peak, 9% C.I. [4,93]). In F1 this value was fixed at 2% on the basis that both occupational and environmental exposures are likely to be substantially lower than those of the 196s. A consistent finding of both models is that the year of the peak number of deaths is predicted to be over a decade later in women than men. The number of annual female deaths have historically been much smaller than the number of male deaths. Long range forecasts of both male and female deaths are highly uncertain, however it is likely that the numbers will eventually converge once the effect of occupational exposures especially those of the past that have predominated in men  cease to have a large impact on the population. The fact that these uncertainty ranges of the long term predictions for men and women overlap implies that such a scenario is consistent with these models. A comparison of the male projections (Tan and Warren, 29) and female projections (based on F1) can be seen in Figure 6, which shows a convergence to less than 4 deaths annually by 25. Additionally the background cases make up a much larger proportion of total cases in females, thus the female data arguably provide a more reliable estimate of confidence intervals for male and female background cases. 13
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