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Natural environments and suicide mortality in the Netherlands: a cross-sectional, ecological study

Summary Background Natural outdoor environments, such as green spaces (ie, grass, forests, or parks), blue spaces (ie, visible bodies of fresh or salt water), and coastal proximity, have been increasingly shown to promote mental health. However, little is known about how and the extent to which these natural environments are associated with suicide mortality. Our aim was to investigate whether the availability of green space and blue space within people's living environments and living next to the coast are protective against suicide mortality. Methods In this cross-sectional, ecological study, we analysed officially confirmed deaths by suicide between 2005 and 2014 per municipality in the Netherlands. We calculated indexes to measure the proportion of green space and blue space per municipality and the coastal proximity of each municipality using a geographical information system. We fitted Bayesian hierarchical Poisson regressions to assess associations between suicide risk, green space, blue space, and coastal proximity, adjusted for risk and protective factors. Findings Municipalities with a large proportion of green space (relative risk 0·879, 95% credibility interval 0·779–0·991) or a moderate proportion of green space (0·919, 0·846–0·998) showed a reduced suicide risk compared with municipalities with less green space. Green space did not differ according to urbanicity in relation to suicide. Neither blue space nor coastal proximity was associated with suicide risk. The geographical variation in the residual relative suicide risk was substantial and the south of the Netherlands was at high risk. Interpretation Our findings support the notion that exposure to natural environments, particularly to greenery, might have a role in reducing suicide mortality. If confirmed by future studies on an individual level, the consideration of environmental exposures might enrich suicide prevention programmes. Funding European Research Council (grant agreement number 714993).


Regression model description
Statistical methods to determine the relationship between natural environmental exposures and suicide mortality are numerous, with Bayesian ecological regressions standing out, 1-3 particularly when studying risk and protective factors from a spatial standpoint. [4][5][6][7][8][9][10][11] Bayesian generalized linear models with random effects were fitted. For the data model, we assumed a Poisson distribution to model suicide counts as an outcome (Eq. 1) 3 . The relative suicide risk ( ) was modeled through a set of risk and protective factors ( ) in the process model, whereas areaspecific effects were further decomposed additively into a spatially structured ( ) and an unstructured ( ) component (Eq. 2). Such a model can smooth the relative (residual) suicide risk by sharing information across spatial units (i.e., municipalities). 2,12 The model is given by: ln( ) = 1 + 2 + … + + + refers to the number of suicides in municipality ( = 1, … ,398) and is the age-adjusted indirectly standardized expected number of suicide cases. refers to the relative risk of having a suicide in area . Besides adjusting for the covariates , a structured random effect was included to model spatial dependence among adjacent areas while an unstructured random effect incorporated area-specific heterogeneity. 13 Omitting spatial dependence among adjacent areas, where present, would have severely biased the estimation of the regression parameters. 2 Prior distributions for the unknown random parameters were assigned as follows. For the fixed effects, diffuse priors based on normal distributions with mean zero and different precisions including 0.01, 0.001, and 0.0001 were investigated. The structured random effect followed an intrinsic conditional autoregressive prior. Adjacency was operationalized as first-order queen contiguity where areas are considered neighbors when they share a common topological point or boundary. 5 Model robustness checks with an alternative neighbor specification, specifically the rook contiguity, was also carried out. 14,15 For the unstructured random effect a normal prior with an exchangeable structure was chosen. Due to a lack of prior knowledge, non-informative priors based on a logged gamma distribution were specified for both and . 12 To ease the prior specification, the structured effect was additionally scaled. 16 As Bayesian models can be sensitive to prior specifications, sensitivity tests are obligatory. 17 We tested a range of alternative log-gamma( ; ) priors with a shape of 0.7, 1, and 1.3 as well as a precision of 0.005, 0.0005, and 0.00005.
To obtain descriptive statistics of the marginal posterior distributions, Bayesian inference was carried out with the integrated nested Laplace approximation (INLA) approach. 18 21 and the deviance information criterion (DIC) 22 were used.
Both performance measures consider a penalty term adjusting for model complexity. Lower DIC and WAIC scores refer to a better model fit.

Descriptive statistics
Supplementary Table S1 reports descriptive statistics for the involved variables. Summary statistics and histograms were used to divide the environmental variables into three groups. Grouping the data is favorable by skewed distributions while permitting the analysis of dose-response relationships. Supplementary

Model diagnostics and sensitivity tests of the Bayesian regression
Non-spatial regressions were initially fitted. Residual independence was not confirmed across the models by Moran's I statistics (I: 0.146; p<0.001), supporting the application of spatially explicit models. In order to evaluate the sensitivity of different prior specifications, the fully adjusted model 2 was re-estimated with the aforementioned priors. In total, 27 models were fitted for this sensitivity study. For the spatially structured ( ) and unstructured ( ) components, different priors with different shape and precision were tested. For the fixed effects, different precisions were tested. The model fits are shown in Supplementary Table S2. As indicated by the WAIC and DIC scores, the models showed minor variations in the goodness-of-fit with different prior specifications.
The best fitting model (i.e., lowest WAIC score) was used in the paper.
Supplementary  Figure S3 shows the posterior densities of each fixed effect for the 9 best performing models in Table S2 with different alternative priors. The alternative priors showed very close agreement.
Supplementary Figure S3: Posterior densities of the 9 best performing models (the first value refers to hyperparameter a, the second to b, and the third to k) Supplementary Figure S4 shows the posterior means along with the 95% CIs for the first 9 models.
No significant differences were obtained. Supplementary Figure S5 plots the posterior marginal distribution of tau and sigma for the best fitting model, which is also used in the paper.
Supplementary Figure S4: Posterior means and 95% CIs for the first 9 best performing models (the first value refers to hyperparameter a, the second to b, and the third to k) Supplementary Figure S5: Posterior marginal distribution of tau and sigma for the best fitting model adjacency). As indicated by the descriptive statistics of the neighborhood matrices (Table S6), both specifications are similar. Therefore, it was not surprising that switching between the queen and the rook case did not translate into substantial differences in the posterior distributions. We followed the majority of studies and utilized queen contiguity as adjacency definition. 5,6,12 Supplementary The residual relative suicide risk of the fully adjusted model is shown in Figure S7