On behalf of myself and the co-authors, I would like to thank Dr Ulm for his comments on our article about a pooled analysis of exposure-response for lung cancer in ten silica exposed cohorts . We agree with Dr Ulm that based on the spline curve in Figure 1 that there appears to be a threshold at about 4 units (log cumulative exposure, mg/m3-days), before which there is no increase in risk. This implies, as Dr Ulm states, that there would be little or no increase in lung cancer risk at cumulative exposures below 55 mg/ m3-days, or below an average exposure of 0.005 mg/m3 over a 45 year working lifetime (taking into account a 15 year lag). We note, however, that in the U.S. the permissible level of exposure to quartz (100% quartz) is 0.10 mg/m3, 20 times higher than the suggested threshold in this model. We have conducted further analyses of possible thresholds using several different models with either cumulative or average exposure, as any presumed threshold might be model-dependent. In each model we used an iterative procedure to evaluate a large variety of possible thresholds until finding the one with the largest log-likelihood. For the model using the log of cumulative exposure with a 15 year lag, the best threshold was at 4.8 log mg/m3-days (similar to the spline model); the threshold model fit the data better than a model with no threshold (model likelihood 23.4 vs 18.8). A model using the log of average exposure found the best threshold at an average exposure of 0.011 mg/m3, which again was a slight improvement over the model with the log of average exposure with no threshold (model log likelihood 22.6 vs. 20.0). A model with cumulative exposure alone did not show any improvement by using a threshold, nor did the piece-wise linear model presented in the paper. Models with untransformed cumulative (or average) exposure, however, tended to display more heterogeneity between studies, probably due to the extreme skewness of some of the exposure data, and may therefore be less preferable.
Kyle Steenland and James A. Deddens, NIOSH R13, Department of Health and Human Services, Robert A. Taft Laboratories, 4676 Columbia Parkway, Cincinnati, OH 45226, USA