The author regrets that, due to a misunderstanding between the author and the data provider, the incorrect data were used for malignant glioma and glioblastoma (multiforme). As a result, the 1985–2014 trends shown in Fig. 1 and results of the statistical analyses shown in Table 1 and Fig. 2 are incorrect. This had no significant impact on the results of study, the interpretation of the results, or on the conclusions in the paper, which remain unchanged; i.e. there is no evidence of a causal association between mobile phone use and the incidence of malignant glioma and glioblastoma (multiforme). The corrected results are shown in Figs. 1 and 2 and Table 1 below. The author would like to apologise for any inconvenience caused.