Dose–response meta-analysis of silica and lung cancer

Abstract

Objective

To examine the association between occupational exposure to silica and lung cancer from a systematic review (and meta-analysis) of the epidemiologic literature, with special reference to the methodological quality of observational studies.

Methods

We searched Medline, Toxline, BIOSIS, and Embase (1966–December 2007) for original articles published in any language. Observational studies (cohort and case–control studies) were selected if they reported the result of dose–response analyses relating lung cancer to occupational exposure to silica after appropriate adjustment for smoking.

Results

Ten studies (4 cohort studies and 6 case–control studies) met the inclusion criteria of the meta-analysis, nine of which contributing to the main analysis (dose–response analysis, no lag time). We found increasing risk of lung cancer with increasing cumulative exposure to silica, with heterogeneity across studies however. Posthoc analyses identified a set of seven more homogeneous studies. Their meta-analysis resulted in a dose–response curve that was not different from that obtained in the main analysis.

Conclusion

Silica is a lung carcinogen. This increased risk is particularly apparent when the cumulative exposure to silica is well beyond that resulting from exposure to the recommended limit concentration for a prolonged period of time.

Appendices

Appendices

Appendix 1: statistical methods for meta-analysis

Let I = 1,…, I indexes independent studies and J = 1,…, n _i indexes exposure levels within studies. Let Y _ij  = log(RR _ij ) be the estimated log risk ratio corresponding to exposure level x _ij . The fixed-effects model is then written as

$$ Y_{ij} = f\left( {x_{ij} } \right) + \varepsilon_{ij} + e_{ij} ,\quad i = 1, \ldots ,I,\quad J = 1, \ldots ,n_{i} ,\quad {\text{model}}\;1 $$

where f is a smooth continuous function, describing the relationship between the exposure level and the log relative risk response. ε _ij  → N(0, s ² _ij ) are the sampling errors in Y _ij since the latter are estimated rather than observed. Estimated s ² _ij are given by individual studies. Finally, e _ij  → N(0, σ²) are the overall error terms. It is assumed that ε _ij and e _ij are independent.

For the mixed-effects model, a random effect term γ _i common to points of the same study is added. This yield

$$ Y_{ij} = f\left( {x_{ij} } \right) + \gamma_{i} + \varepsilon_{ij} + e_{ij} ,\quad i = 1, \ldots ,I,\quad J = 1, \ldots ,n_{i} , \quad {\text{model}}\;2 $$

where γ _i  → N(0,τ²) and are independent from ε _ij and e _ij . Testing heterogeneity corresponds them to performing the following:

$$ {\text{H}}_{0} :\tau^{ 2} = 0\;\;\;\;{\text{vs}} .\;\;\;\;{\text{H}}_{ 1} :\tau^{ 2} > 0. $$

The null hypothesis H₀ is rejected at level α if

$$ - 2\left\{ {{ \log }\left( {{\text{maximum}}\;{\text{likelihood}}\;{\text{model}}\; 1} \right) - { \log }\left( {{\text{maximum}}\;{\text{likelihood}}\;{\text{model}}\; 2} \right)} \right\} \ge \chi_{ 1,\alpha }^{2} , $$

where χ ²_1,α satisfies $P\left( {\chi_{1}^{2} > \chi_{1,\alpha }^{2} } \right) = \alpha.$ In both models, f is left completely unspecified providing flexibility. It is nonparametically estimated by a spline of order 3 [17]:

$$ f\left( x \right) = \beta_{01} \,x + \beta_{02} \,x^{2} + \beta_{03} \,x^{3} + \Upsigma_{1 \le I \le C - 1} \beta_{i3} \left( {x - k_{i} } \right)_{ + }^{3} , $$

where (x − k _i )₊ = max(x − k _i ,0) is the positive part and $\left\{ {k_{i} ,\;i = 1, \ldots ,C - 1} \right\}$ are knots. We set C = 3. The models parameters $\left\{ {\beta_{0 1} ,\beta_{0 2} ,\beta_{0 3} ,\beta_{ 1 3} ,\beta_{ 2 3,} \tau^{ 2} ,\sigma^{ 2} } \right\}$ are estimated by the algorithm given by Stram [19].

Appendix 2 Reasons for exclusion of observational studies with dose–response analysis of silica and lung cancer