Statistical analysis

A random-effect dose–response meta-analysis was conducted with the method proposed by Greenland and Longnecker [14] and Orsini and Bellocco [15], which takes into account the correlation between the log RRs estimates across categories of selenium levels. The non-linear relationships by modelling selenium levels were also explored by using restricted cubic splines with three knots at fixed percentiles (25%, 50% and 75%) of selenium levels distribution [16]. The P-value for non-linearity was calculated by testing against the null hypothesis that the coefficient of the second spline transformation was equal to zero [17]. The required conditions are that the number of cases and person-years or participants and the RRs (95% CIs) with the variance estimates for at least three quantitative exposure categories are known. We will estimate the slopes (linear trends) by using variance-weighted least squares regression analysis although the number of cases and person-years or participants was not available [18,19]. The median level selenium for each specific category was assigned to each corresponding log RRs estimate. We used the midpoint between the upper and lower boundary if the median intake was not reported in the article. If the upper boundary of the highest category was not provided, we assumed that the boundary had the same amplitude as the adjacent category. Statistical heterogeneity across studies was assessed using the I² statistics [20], and I² values of 0, 25, 50 and 75% represent no, low, moderate and high heterogeneity respectively [21]. Sensitivity analysis [22] was performed to describe how robust the pooled estimator risk was to removal of each individual studies. Publication bias was evaluated using Begg's funnel plot [23] and Egger's regression asymmetry test [24]. All statistical analyses were tested by STATA version 10.0. Two-tailed P ≤ 0.05 was accepted as statistically significant. The P value <0.1 was considered as significant for between-study heterogeneity and publication bias.