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Lithium concentrations in drinking water

Published online by Cambridge University Press:  02 January 2018

Min Yang*
Affiliation:
Division of Psychiatry, School of Community Health Sciences, University of Nottingham, Nottingham NG7 2TU, UK. Email: min.yang@nottingham.ac.uk
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Abstract

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Copyright
Copyright © Royal College of Psychiatrists, 2011 

Kapusta et al claim that they provide conclusive evidence that lithium concentrations in drinking water are inversely correlated with suicide rates. This claim is apparently based on the estimate of a negative association between the average level of lithium in drinking water and average district suicide mortality at a marginally significant level (P = 0.022) of an ecological study, males and females combined, in 99 Austrian districts. However, this claim can be challenged as there are limitations of the ecological model used to analyse the study.

First, it is well know that suicide mortality is associated with social demographic factors such as gender, age, area poverty and economic issues. Reference Platt, Boyle, Crombie, Feng and Exeter1 Such factors are largely variable across regions and hence constitute major heterogeneity in health outcomes such as suicide rate. Failing to take into account those risk factors will most likely lead to biased results. The authors were aware of this deficiency, but could not properly compensate for it for two reasons: (a) an ecological regression model with only 99 data-points can only include a few covariates; and (b) their model was incapable of incorporating variables at levels lower than district.

Second, weighted least square (WLS) regression analysis was used in the study to examine the possible association between lithium level in drinking water and district suicide mortality. The authors were careful to perform sensitivity analyses to examine the impact of extreme values on the outcome, and log-transformed many independent variables, as WLS is known to be sensitive both to extreme values and to distribution of variables. However, one most important aspect about the WLS analysis which seems not to be articulated in the paper is that in the model estimate of WLS analysis much depends on the choice of weighting variable. A different weighting would produce different estimates, in particular standard error of estimates. It is not clear what weighting variable the authors used in their analysis. Was it population size of district or variance of suicide mortality or something else? Was sensitivity analysis carried out on different weighting variables? Would the significant finding still be present if different weighting variables were used? What would be a better weight for this data-set? There seems a black box of uncertainty in interpreting the results.

Third, it is well known that ecological analysis is subject to the ecological fallacy, namely, association from the ecological model at area level may overestimate the population association that would be established by individual-level analysis. Reference Robinson2 Although not every ecological analysis necessarily presents such drawbacks, this study has not shown justification for not having such a problem. A negative correlation between suicide standardised mortality rate (SMR) and some area poverty measures such as unemployment rate and population density were not supported by individual-level analysis. Reference Lin3

Finally, since both district data on lithium concentrations and suicide mortality are available for up to 5 years for the period 2005–2009, the study could have obtained findings with more statistical power than the current findings if multilevel Poisson models for repeated measures within region were used for analysing SMR data. Reference Rasbash, Steele, Browne and Goldstein4 To organise data as years (i = 1–5) nested within district (j = 99), such a model will have many more data-points (maximum 495) so that important variables such as age and gender in some type of aggregated form, such as percentage of female and percentage of old people per district, could be included in the analysis without overfitting the model. In addition, the increasing trend of suicide mortality over time and variability of the SMR between districts and over time can be disentangled in the model. Although this model still cannot provide evidence on causal relationships based on aggregated data, it can overcome some limitations in the method used in the study. The core finding of this study as currently presented cannot be supported unless further analyses by means of more advanced multilevel models also yield the same finding.

References

1 Platt, S, Boyle, P, Crombie, I, Feng, Z, Exeter, D. The Epidemiology of Suicide in Scotland 1989–2004: An Examination of Temporal Trends and Risk Factors at National and Local Levels. Scottish Government, 2007 (http://www.scotland.gov.uk/Publications/2007/03/01145422/0).Google Scholar
2 Robinson, WS. Ecological correlations and the behavior of individuals. Am Sociol Rev 1950; 15: 351–7.Google Scholar
3 Lin, S. Unemployment and suicide: panel data analyses. Soc Sci J 2007; 43: 727–32.Google Scholar
4 Rasbash, J, Steele, F, Browne, WJ, Goldstein, H. A User's Guide to MLwiN (Version 2.10): 117–28. Institute of Education, University of London, 2000.Google Scholar
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