In attempting to replicate the findings of Oghami and colleagues, ^{Reference Ohgami, Terao, Shiotsuki, Ishii and Iwata1} it was our aim to stay close to their methods thus allowing for comparison with our results. Using weighted least squares (WLS) regression in ecological studies is a recognised method. ^{Reference Nurminen2,Reference Morgenstern3} By incorporating previous criticism, we extended the WLS model of Oghami et al by implementing further covariates and tested for stability of the hypothesis. As stated originally, weighting by population per district (number of inhabitants per district), was chosen.

In order to clarify the uncertainty raised by Yang, we recalculated the lithium estimates (R² = 0.38; β = –0.24; t = – 2.33; P = 0.022) from the multivariate WLS model from Table 2: (a) without log-transformation of variables and (b) with additional weighting variables. Using non-transformed covariates, the estimates for lithium levels in the multivariate model were: R² = 0.35; β = –0.25; t = –2.71; P = 0.008. Weighting for the variance of suicide mortality produced a similar result for lithium levels (R² = 0.41; β = –0.35; t = –3.40; P = 0.001) and weighting for the variance of lithium levels even improved the estimates (R² = 0.76; β = –0.55; t = –7.17; P = 2.9×10^–10), which further supports our hypothesis.

Concerning the issue of ecological fallacy, we rephrase a part of our discussion: it is clear that our study design cannot prove cause and the results are not applicable to individual cases. Our statement that we provide conclusive evidence, that lithium concentrations in drinking water are inversely correlated with suicide rates, is far away from any ecological fallacy. It would have been unacceptable to state that drinking lithium-containing water will reduce an individual's risk for suicide. Such suggestions could only be justified after double-blind placebo-controlled randomised trials with evidence level 1 (Grade A recommendation) according to the Oxford Centre for Evidence-based Medicine (www.cebm.net). Such trials would be desirable after the presentation of our replicated ecological evidence which can be classified as level 2c evidence and thus only justify a Grade B recommendation.

A recalculation of the model by means of a multilevel Poisson model with repeated measures would indeed be interesting and would further challenge the hypothesis. As previously applied by us, ^{Reference Kapusta, Posch, Niederkrotenthaler, Fischer-Kern, Etzersdorfer and Sonneck4} a hierarchical Bayesian model incorporating the neighbourhood structure to estimate the effects of variables on suicide mortality wouldbe even moreappropriate andwillbe applied in the context of a future study, which will take additional variables into account.