Fig. 5. Modified funnel plots for chewing tobacco and five head and neck cancer outcomes.

These modified funnel plots show the residuals of the reported mean relative risk (RR) relative to 0, the null value, on the x-axis and the residuals of the standard deviation, as estimated from both the reported standard deviation and gamma, relative to 0 on the y-axis. Each funnel plot corresponds to a different model for esophageal cancer (panel a), lip and oral cavity cancer (panel b), nasopharyngeal cancer (panel c), other pharynx cancer (panel d), and laryngeal cancer (panel e) and their corresponding association with chewing tobacco. The light blue vertical interval corresponds to the 95% uncertainty interval incorporating between-study heterogeneity; the dark blue vertical interval corresponds to the 95% uncertainty interval without between-study heterogeneity; the dots are each included observation; the red Xs are outliered observations; the grey dotted line reflects the null log(RR); the blue line is the mean log(RR) for chewing tobacco and the outcome of interest; the red line is the burden of proof function at the 5^th quantile for these harmful risk-outcome associations.