Comment on 'The latency period of mesothelioma among a cohort of British asbestos workers (1978-2005)': the effect of left censoring.

Sir,

We read with extreme interest the article by Frost on mesothelioma latency period among asbestos workers (Frost, 2013). Despite the main aim of the study being to investigate ‘the determinants of mesothelioma latency among a cohort of asbestos workers, paying particular attention to indicators of intensity of asbestos exposure' (Frost, 2013), the reported lack of evidence of an association between duration of exposure and latency attracted some attention. Commenters argued that right censoring occurring in the underlying cohort could have biased an analysis restricted to cases (Consonni ; Mirabelli and Zugna, 2014).

We would like to highlight a different pitfall of Frost's analysis. She observed huge differences in median latency periods across categories of year of first exposure to asbestos. Indeed, the median latency for deaths among workers exposed to asbestos before 1940 was 48 years, whereas a median latency of only 11 years characterised cases exposed not earlier than 1980. This difference translated in a dramatic decrease of time ratios with increasing year of first exposure. However, it is surprising that the author interpreted these data without considering the limited follow-up window (1978–2005). On the one hand, all the cases exposed before 1940 entered the analysis with a latency of at least 38 years, as all deaths that occurred before 1978 were left censored. On the other hand, the maximum latency observable for subjects exposed after 1980 was just 25 years as events potentially occurring after 2005 were right censored. To describe how left and right censoring can affect the estimates presented by Frost, we conducted a simple simulation study. We assumed a true latency period constant across categories of the year of first exposure to asbestos based on a gamma distribution (shape parameter 11, scale parameter 3). This distribution has a median of 32 years, in line with the median mesothelioma latency reported for occupational mesothelioma and presented by Frost in the discussion section of her paper (Lanphear and Buncher, 1992). In our simulation, we considered six categories for the year of first exposure (as in Frost's article) and we assumed 300 mesothelioma deaths within each group. For pragmatic reasons, within each category we used the mid-point (i.e. 1935, 1945, 1955, 1965, 1975, and 1985) as the first year of exposure. Figure 1 presents the results from our simulation. On the basis of these assumptions, there is no difference among the categories of first year of exposure when the follow-up is complete and there are no censored cases (Panel A). However, in the presence of left and right censoring, a spurious strong association between time to mesothelioma death and year of first exposure to asbestos is observed (Panel B). This fact is the consequence of the differential loss to follow-up with respect to the exposure categories. In Figure 1, we show the estimates from a single simulation. Nonetheless, we performed a further analysis based on 10 000 repetitions and the findings were highly consistent with those presented in this letter (data not shown).

Figure 1

Simulation study of mesothelioma latency after occupational exposure to asbestos. Analysis of latency periods by categories of first year of exposure. Latency periods were simulated assuming a gamma distribution (shape parameter: 11; scale parameter: 3). Time ratios were estimated by fitting accelerated-time failure models based on a gamma distribution of the events.

It is remarkable that our estimates are not so far from those reported in Table 2 of Frost's manuscript and this fact suggests that a strong bias might affect her findings. Remarkably, a spurious association between the year of the first exposure and mesothelioma latency might bias all the multivariate time ratios presented in Table 3. Indeed, all the estimates for variables putatively correlated with the year of first exposure (e.g. main occupation, as the proportion of subjects employed in manufacturing and removal has changed over time) could be biased by the improper adjustment for a covariate spuriously associated with the outcome. Furthermore, left censoring could also directly bias the estimates for other time variables. Compared to the later cohorts, the group of workers exposed for the first time to asbestos before 1950 is likely to have a longer average duration of exposure as well as a spuriously longer average latency. This fact could contribute to explain the increase in time ratios observed across categories of duration at the univariate analysis (Table 2).

Noteworthy, as the information on asbestosis was available only from 1978, Frost restricted the follow-up window even though information on mesothelioma deaths was available from 1972. This choice determined both a loss of cases and an exacerbation of the bias due to left censoring. Remarkably, asbestosis was only weakly associated with the outcome; hence, this variable is not likely to induce substantial confounding. Thus, Frost should have considered the entire follow-up period to study the other variables. Estimates restricted to 1978 and 2005 and adjusted by asbestosis could have served as a sensitivity analysis.

We would invite Frost to perform a simple and quick reanalysis. She should (i) include only cases exposed for the first time between 1950 and 1969 to limit left and right censoring (she would still retain 56% of the cases); (ii) analyse the entire follow-up period (1972–2005) to limit left censoring and increase the number of cases; (iii) avoid adjustment for the year of first exposure. If confounding by the latter is a strong concern, Frost could conduct stratum-specific analysis. The number of deaths that occurred among subjects exposed for the first time between 1950 and 1959 (216 or more after the addition of the years from 1972 to 1977 to the follow-up), and 1960 and 1969 (145 or more) is large enough to fit regression models with a reasonable number of covariates. We believe that this supplemental analysis could add an important piece of knowledge.