The predictions using the two methods are shown in figure 4. The age and calendar year model predicted 6779 cases for the period 2004–60—which is only 1% higher than the total predicted by the age/cohort model (6690 cases). The predicted pattern of annual counts varies between the two models, where the age/year model peaks earlier and at a higher level than the age/cohort model. The age/year model was based on an extra year of data for 2003, and in this year the observed number of mesotheliomas was high (n
174) compared with an average of 141 between 2000 and 2002. From a sensitivity analysis for the age/year model, we found that the inclusion of data for 2003 increased the total predicted number of cases for 2004–60 by only 7%.
There are some problems with the use of a birth‐cohort and age effects model. One is that it is assumed that the two effects are independent. That is, the mesothelioma rate for a birth cohort/age combination is the product of a birth cohort effect and an age effect. Assuming that most mesotheliomas are caused by occupational asbestos exposure, then for the more recent birth cohorts, the observed rates through age groups younger than 50 years have occurred as a result not just of increasing age but also as a result of increasing cumulative exposure. This would amount to an interaction between birth cohort and age which has not been taken into account. A second problem is that it is assumed that the age effect, as a power of (age − 20) up to 80–84 years, applies for all birth cohorts. For the more recent birth cohorts, who could only have been exposed during the early years of their working life, it may be questioned whether the increase in mesothelioma rate with age will continue to age 80 years or whether the flattening off will occur at younger ages. In the latter event then the predicted numbers in more remote future years, say after 2025, would be less than given. This disadvantage could be overcome by incorporating a term representing clearance of fibres from the lung over time but it was not possible to do this with the age/cohort model because the time of asbestos exposure is unspecified.
The age/year model overcomes the above problems. The model is specified in terms of potential exposure effects for both age and calendar year, and so the consequent interactions between age and birth cohort are built in. Furthermore, because the period of exposure is specified, a term representing clearance of fibres from the lungs can be included.
There is a close relation between the age/cohort model and the age/year model: the age/cohort model is an age/year model with exposure restricted to a specific age, hence the calendar dose function D(t) is effectively a function of birth cohort. The age/year model relaxes this restriction by allowing asbestos exposure throughout life, which will allow for more realistic predictions following the decline in asbestos exposure in the last quarter of the 20th century. We would expect the age/cohort model to perform well if asbestos exposure was mainly in young men, and then the age/cohort model would be roughly equivalent to the age/year model. However, our empirical estimates of the dose potentials from the age/year model are consistent with other evidence that there was exposure to asbestos across the working life.
The age/year model can be viewed as a re‐implementation of the mesothelioma model by Hodgson et al
Minor variations from the model formulation by Hodgson et al6
included: (a) the clearance time for asbestos included a lag, as suggested by Berry;14
(b) for incidence data, the latency period was assumed to be five years, rather than 10 years; (c) the rate function was defined using an integral form, rather than a discrete summation, in order to improve accuracy; and (d) the dose response functions were assumed to be spline functions. Our implementation allowed for joint estimation of all five model parameters and bootstrap estimation of the predictions. The implementation by Hodgson et al
included at least 14 model parameters,6
with unusual patterns for the relative exposure potential for age groups and for the change in exposure index relative to a peak year. Moreover, their implementation estimated the diagnostic trend and the power of time since first exposure. We argue that these parameters are not jointly identifiable and that a more parsimonious model is required. We chose to fix the rate of lung clearance6
and fix the power of time since first exposure, based on data from an Australian cohort study.14
As a further potential limitation, we have assumed that birth cohorts born from 1970 are at negligible risk of mesothelioma. There is currently little information on the mesothelioma rate in those born after 1970 but mesotheliomas could occur in this group as a result of exposure to amphibole asbestos during demolition or maintenance after the new use of amphibole was phased out in the 1980s. Also there was some use of chrysotile asbestos until 2003, and not all mesotheliomas are caused by asbestos exposure. Hodgson and colleagues assumed that the number of mesotheliomas would decline to 2% of the peak year;6
we did not follow this assumption, so that our predictions may be biased as low, and the actual number of cases in the future may be, on average, marginally higher than we predict. However, the magnitude of the level of uncertainty relating to our middle predictions is probably considerably more than this potential bias.
Relation of fitted models to amphibole asbestos use
Under the assumption that most mesotheliomas are caused by occupational asbestos exposure, and that amphibole asbestos is responsible for the majority, then the figures on asbestos consumption in Australia are relevant. Leigh and Driscoll gave data on asbestos production, asbestos imports and asbestos exports.7
Unfortunately the asbestos exports could not be broken down by asbestos type and between 1950 and 1969 the exports could have included both crocidolite and chrysotile. Under the assumptions that none of the small production of amosite was exported, and that no imported asbestos was later exported, a range of possible crocidolite exports was calculated, and hence a range of total amphibole use in Australia (table 1). The ranges of amphibole use were relatively narrow. Some mesotheliomas in Australia are in former miners and millers at Wittenoom and were caused by crocidolite that was subsequently exported, but less than 0.5% of mesotheliomas in New South Wales are in former Wittenoom workers and residents (Alison Reid, personal communication).
Table 1Approximate amphibole asbestos consumption (tonnes) in Australia (derived from Leigh and Driscoll under the assumptions described in the text7)
The major use of amphibole asbestos was in the three decades from 1950 to 1979, and the net amphibole use shown in the last column of table 1 shows a similar pattern to the dose potential by calendar period (fig 4) in the age/period model. Since there were no new uses of crocidolite after 1970 and amosite was phased out during the early 1980s, then occupational exposure to amphibole asbestos, except for exposure during demolition or repair work, would not have occurred in those born after 1970. The major amphibole consumption in 1950–79 corresponds to occupational exposure, particularly to birth cohorts from 1920 (who could have been exposed during this time when aged 30–60 years) to 1950 (who could have been exposed when aged 15–30 years). Those born earlier would be expected to have experienced less exposure because they would have been 35 years or older during the period of peak use, and those born later could not have been exposed much after age 25 years. This pattern is similar to the birth cohort effects in figure 1.
Importance of including knowledge on asbestos use
In making projections on future numbers of mesotheliomas it is important to incorporate knowledge of asbestos use into the modelling, and to model the time relation of mesothelioma incidence with increasing time since exposure as accurately as possible. The update of predictions of mortality from pleural mesothelioma in the Netherlands gave the peak number and the total during 2000–28 as only a little more than half of the figures predicted only four years earlier.2,4
This marked change in prediction occurred because of five extra years of data but also the known decrease in asbestos use after 1984 and a ban in 1993 were taken into account in the later modelling.
For the former workers at the Wittenoom crocidolite mine and mill in Western Australia predictions were made up to 2020 based on observed numbers up to 1986.9,10
Models of the mesothelioma death rate used included an increase in rate as a power of time since exposure, moderated by a factor representing elimination of crocidolite fibres over time since exposure, with rates of elimination from zero to 15% per year considered—assuming no elimination predicted more than twice as many mesotheliomas by 2020 than an elimination rate of 15% per year.10
The number of mesotheliomas that occurred in 1987–2000 was compared with these earlier predictions and found to be similar to predictions, based on observed numbers up to 1986, when an elimination model was used, whereas failure to allow for elimination gave a much higher prediction than was observed.15
This result provides evidence that models of mesothelioma incidence that take account of a gradual elimination of crocidolite from the lungs after exposure are more realistic. There is strong evidence from other sources that such elimination does occur and that for crocidolite the rate of elimination is in the range of 10–15% a year.14
The rate of clearance depends on asbestos type, being more rapid for chrysotile than amphibole asbestos. There is also evidence that fibre length is important. Longer chrysotile fibres (>10 μm) are cleared more slowly than the shorter fibres.16,17
Projections of the number of mesotheliomas in factory workers in London from 1972 were made based on observed numbers to 1972,8
and later compared with observed numbers for the period 1973–80.18
In this period 40 mesotheliomas were observed compared with predictions in the range of 45–59. No allowance for clearance of fibres from the lungs had been made in the predictions.
Peto et al
fitted an age‐cohort model for mesothelioma mortality in Britain from 1968–91 and projected a peak in men in about 2020 of between 2700 and 3300.1
The later projection of Hodgson et al
using mesothelioma mortality to 2001 and an age and calendar year model predicted a peak of between 1950 and 2450 deaths in males between 2011 and 2015.6
Price fitted an age‐cohort model to incidence data from the Surveillance, Epidemiology, and End Results (SEER) programme in the USA for 1973–92 and predicted a peak incidence in men of about 2300 before 2000.3
Using 1973–2000 incidence data it was noted that the peak was approximately 2000.5
A direct comparison between the two reports was noted to be not meaningful because of changes in the SEER data, but when the earlier modelling was repeated with the revised database it was found that predictions based on using only the data to 1992 gave higher predictions than using all the data up to 2000.5
Weill et al
noted that the usage of amphibole asbestos in the US reached its peak in the 1960s and that the differing pattern of mesothelioma incidence, with a later peak in Europe, may be related to a later amphibole use, particularly crocidolite.19
In Australia, new uses of crocidolite were phased out by 1970 and of amosite not until 1983. Consequently the peak time for mesothelioma incidence may be expected to be about 15 years later than in the USA and the predictions in this paper are consistent with that. In the UK the use of amphibole asbestos was phased out towards the end of the 1970s,1,6
and the predicted peak between 2011 and 2015 is also in line with our predictions. For the US, UK and Australia the peak time of mesothelioma incidence or mortality is about 35 years after discontinuation of amphibole asbestos.
All predictions depend on an assumed relation between incidence and time since exposure. Epidemiological data have shown that this relation is time to a power of about 3.5, and more recently the importance of moderating the increase by the inclusion of a term representing gradual clearance of amphibole asbestos from the lungs has been recognised. Nevertheless the relation after long periods since the cessation of exposure is not well determined, and is a source of uncertainty in the predictions.