Overcoming Standardization: Revealing Hidden Age Patterns of Suicide with Spatiotemporal Models

(2) Joint Research Unit UMH-FISABIO (StatSalut); (3) Department of Social Psychology; A. L\'opez-Qu\'ilez (1); Center of Operations Research. Miguel Hern\'andez University; J. Mart\'in-Pozuelo (1); M. Marco (3) ((1) Department of Statistics; Operations Research. University of Valencia; University of Valencia.); X. Barber (2)

REVIEW 4 major objections 6 minor 31 references

Overcoming Standardization: Revealing Hidden Age Patterns of Suicide with Spatiotemporal Models

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that indirect standardization hides a post-2020 rise in suicide-related emergency calls among younger people, which an age-structured Bayesian spatiotemporal model reveals.

desk verdict A competent, extensive age-space-time CAR model comparison applied to suicide calls; the youth post-2020 finding is plausible but needs uncertainty intervals and a frank handling of the calls-as-proxy assumption. read the letter →

arxiv 2507.12033 v1 pith:HZ7BQW6G submitted 2025-07-16 stat.ME

J. Martín-Pozuelo (1) , A. López-Quílez (1) , X. Barber (2) , M. Marco (3) ((1) Department of Statistics , Operations Research. University of Valencia , (2) Joint Research Unit UMH-FISABIO (StatSalut) , Center of Operations Research. Miguel Hernández University , (3) Department of Social Psychology

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University of Valencia.)

This is my paper · ORCID

classification stat.ME MSC 62P1062M3062F15

keywords indirectstandardizationdiseasemappingage-structuredhierarchicalBayesianmodelsspatiotemporalinteractionsINLAsuicide-relatedemergencycallsproportionalityassumptionWAIC

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Indirect standardization, the default way to filter out age when mapping disease risk, assumes that age effects are the same in every place and every year; the paper shows this assumption breaks down for suicide-related emergency calls in the Valencian Community between 2017 and 2023. The authors replace the standardized analysis with age-structured hierarchical Bayesian models that include spatial, temporal, and age random effects plus space-time, space-age, and time-age interactions. Fitting 520 such models, they find that adding age effects improves fit substantially, and the best model reveals a rising temporal trend, a nonlinear age pattern, and a post-2020 increase in risk concentrated among younger age groups. If this is right, conventional standardized estimates would have hidden exactly the age-specific shift that matters for prevention policy.

What carries the argument

The load-bearing object is the age-structured hierarchical Bayesian spatiotemporal model with log-linear predictor, where the risk $\Theta_{ijk}$ in area $i$, year $j$, and age group $k$ is decomposed into an intercept, spatial $\phi$, temporal $\delta$, and age $\gamma$ main effects, plus additive pairwise interactions $\zeta^1$ (space-time), $\zeta^2$ (space-age), and $\zeta^3$ (time-age). The interaction terms are built by Kronecker products of the precision matrices of the corresponding main effects, following the Type I-IV typology of Knorr-Held (2000), with identifiability constraints from Goicoa et al. (2018). This machinery lets the age pattern vary across space and time rather than forcing a common multiplicative age schedule, which is exactly the assumption that indirect standardization imposes and that the paper argues biases conventional estimates. INLA makes fitting 520 candidate models computationally feasible, and WAIC selects the final model.

What would settle it

Re-run the best model on suicide mortality records for the same region and years: if the post-2020 increase in younger age groups disappears or reverses while the model structure is unchanged, the paper's central pattern is an artifact of emergency-call reporting rather than a property of suicide risk.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the proportionality assumption behind indirect standardization, $E(O_{ijk}/N_{ijk}) = \theta_{ij} q_k$, is violated in this setting, and that a hierarchical Bayesian model with age in the linear predictor captures what standardization misses. The best-fitting model takes $\log(\Theta_{ijk}) = \alpha + \phi_i + \delta_j + \gamma_k + \zeta^1_{ij} + \zeta^2_{ik} + \zeta^3_{jk}$, with a Leroux conditional autoregressive spatial effect, an unstructured time effect, a first-order random walk age effect, and Type II space-time, Type I space-age, and Type IV time-age interactions. Its posterior shows a temporal trend that rises from 2017 through 2022 and then stabilizes, a nonlinear age profile with elevated contributions from the 15-55 age range and declines in the oldest groups, and a time-age interaction in which the youngest groups shift from below-average to above-average contribution around 2021 while middle and older age groups move the opposite way. The paper reads this as evidence that the age-specific post-2020 increase would have been invisible under indirect standardization.

Load-bearing premise

The load-bearing premise is that emergency calls related to suicide measure suicide risk the same way across age groups, regions, and years; if help-seeking or call behavior changed over time or differed by age, the estimated age-time patterns would describe reporting rather than risk.

Editorial extensions

If this is right

If the proportionality assumption is violated, indirect standardization can misreport both the level and the direction of spatiotemporal risk trends, so age-disaggregated modeling should replace it in disease mapping.
The post-2020 increase in suicide-related emergency calls is not uniform across age: younger groups carry the increase, so prevention resources directed only at historically high-risk older groups would miss the emerging pattern.
Adding age effects improves model fit by thousands of WAIC units relative to models without age, meaning age is not a nuisance to standardize out but an informative dimension of risk.
The time-age interaction shows a reversal around 2020-2021, with younger groups increasing and older groups decreasing, a divergence that a summary standardized rate would smooth away.
The computational approach scales to large space-time-age datasets because INLA avoids expensive MCMC simulation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same modeling template could be applied to suicide mortality or to other rare outcomes such as substance abuse or gender-based violence, where age patterns plausibly vary by place and time; the authors gesture at these applications but do not test them.
A direct comparison of municipality rankings from standardized ratios versus posterior risk from the full model would quantify how often policy prioritization changes when the proportionality assumption is dropped.
The post-2020 youth increase is an observational pattern in emergency-call data; without adjusting for changes in help-seeking or reporting behavior, it should not be read as direct evidence about the pandemic's causal effect on suicide risk.
Repeating the analysis separately by sex or by call outcome, such as attempt versus ideation, would show whether the time-age pattern is driven by a particular subgroup or severity category.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is a solid, workmanlike application of age-space-time CAR models to suicide-related emergency calls in the Valencian Community. The methodology itself is not new—Knorr-Held (2000) interactions, Goicoa et al. (2016) CAR, INLA—and the "overcoming standardization" pitch has been made before by Congdon and Perez-Panades. What is new is the specific empirical application and the systematic comparison of 520 model specifications, which is a real piece of effort and genuinely useful as a template for model selection in this subfield.

The good stuff: the model comparison is thorough, with identifiability constraints handled correctly following Goicoa et al. (2018). The prior sensitivity check (Table 4, PC vs non-informative) is honest and shows the main results are not driven by prior choice. The data description and the exploratory proportionality check via the Wakefield-style plots are transparent. I believe the analysis is internally coherent.

The soft spots are concentrated in the inference from the best model. First, the central empirical claim—a post-2020 increase in the time-age effect concentrated in younger groups—is presented with posterior means only, no credible intervals. Figure 5 is visually striking, but without intervals or a formal comparison (e.g., is the 2020-2021 shift in the 10-25 groups distinguishable from noise?), the claim is under-supported. Second, and more fundamental, suicide-related emergency calls are a proxy for risk, not risk itself. The authors themselves cite work showing calls are influenced by neighborhood and social factors; if help-seeking or willingness to call changed differentially by age after 2020, the time-age interaction would capture reporting behavior, not suicide risk. The paper should acknowledge this directly and, ideally, cross-check against mortality data (e.g., INE). Third, WAIC-based selection among 520 models with no holdout validation is common in this literature, but it means the "best" model's superiority on fit does not translate directly into predictive or explanatory validity. The Loess-based proportionality test is exploratory; fine as motivation, but it is not a formal test.

None of these are fatal. The empirical pattern is plausible and worth taking seriously. The paper deserves a serious referee. I would send it to review, and I'd ask for the uncertainty quantification and a frank discussion of the proxy issue before accepting. I would not cite it myself, but I'd bring it to the reading group if we were doing disease-mapping or small-area health work.

Referee Report

4 major / 6 minor

Summary. The paper argues that indirect standardization in disease mapping relies on a proportionality assumption that is often violated, and proposes age-structured hierarchical Bayesian spatiotemporal models as an alternative. Using suicide-related emergency calls in the Valencian Community for 2017–2023, the authors fit 520 model variants with INLA, including space-time, space-age, and time-age interactions, and select the best model by WAIC. The best model (Model 8) has an unstructured time effect, an RW1 age effect, and Type II, I, and IV interactions; it reportedly reveals a rising temporal trend, a nonlinear age pattern, and a post-2020 increase in the time-age effect for younger age groups. The methodological claim is that such age-specific temporal patterns would be missed under indirect standardization.

Significance. If the empirical results were supported by uncertainty quantification and validation, the paper would make a useful applied contribution by demonstrating the practical consequences of the proportionality assumption and by providing a transparent comparison of 520 interaction structures. The manuscript has notable strengths: the supplementary table reports all 520 WAIC values, the identifiability constraints for the interaction models are explicitly tabulated, and prior sensitivity is examined with non-informative priors. However, the central empirical claims—especially the youth-specific post-2020 increase—are currently based on posterior means of random effects without credible intervals, and the outcome variable (emergency calls) is treated as a direct proxy for suicide risk without discussion of ascertainment. These gaps make the headline findings not yet convincing.

major comments (4)

[Section 4, Figures 2 and 5, Table 4] The plotted posterior means of exp(δ), exp(γ), and exp(ζ3) in Figures 2 and 5 are presented without credible intervals, and Table 4 reports posterior intervals only for hyperparameters. Because the abstract's claims of a rising temporal trend and stronger risk increases among younger individuals are statements about these random effects, the absence of uncertainty bands means the reader cannot judge whether the 2020–2023 increase in the time-age interaction for ages 10–35 is distinguishable from noise. I request pointwise credible intervals or posterior probability statements for the differences that define the conclusion.
[Section 4, data description] The outcome is suicide-related emergency calls, not verified suicide deaths or attempts. The paper explicitly uses these calls as a proxy for suicide risk but does not discuss ascertainment bias: if younger people became more likely to call after 2020 (e.g., due to awareness campaigns) or if call rates are influenced by neighborhood and social factors (as cited from Marco et al. 2024), the estimated time-age interaction would reflect reporting behavior rather than underlying risk. This is load-bearing for the empirical conclusion and should be addressed, ideally by validating against mortality data or by discussing the direction and possible magnitude of the bias.
[Section 3.2 and Table 3] Model selection relies solely on WAIC over the 520 fitted models, with no hold-out validation or cross-validation checks. The WAIC improvement of Model 8 over Model 7 is only 174.87 units on a scale where differences between some models exceed 1,000 units; without validation, the superiority of Model 8 and the robustness of its interaction structure are not established. A small simulation study, a temporal hold-out, or bootstrap-based model selection would strengthen the claim.
[Section 2 and Figure 1] The proportionality assumption is tested only through Loess-smoothed scatterplots for a selected set of municipality-years, which is a subjective graphical procedure. Since the motivation for the modeling approach rests on the claim that proportionality is violated in these data, I recommend a formal statistical test or a quantitative summary of the deviations across all S×T units.

minor comments (6)

[Section 3, after Eq. (3)] The age effect is defined as γ = (γ1, . . . , γT)′ but should be indexed by K age groups, not T time periods.
[Section 4, paragraph on Figure 7] 'the reduction in the reduction of the suicide-related emergency calls rate' appears to be a typo and should read 'a reduction in the suicide-related emergency calls rate'.
[References] The text cites 'Morris, 2017' and 'Wakefield et al., 2017', but the reference list contains Morris (2001) and Wakefield et al. (2001); the citations and the reference list need to be reconciled.
[Figure numbering] The text refers to 'Figure 7 shows the spatio-temporal effect' immediately after Figure 2, but Figure 7 in the supplementary material is the full space-age effect; the in-text figure cross-references are inconsistent.
[Abstract and Section 4] The abstract states the temporal trend rises over 2017–2022, while the text of Section 4 describes a stabilization between 2022 and 2023; please reconcile these statements.
[Section 2] The statement that indirect standardization assumes 'age-specific risks are homogeneous across regions and time periods' is imprecise; the assumption in Eq. (2) is that the age-specific rates qk are common up to a multiplicative spatiotemporal risk θij, so proportionality, not homogeneity, is the issue.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the empirical age-time findings are estimated from data rather than derived from model inputs, and self-citations are not load-bearing.

full rationale

The paper's central claims, namely a rising temporal trend, a nonlinear age pattern, and stronger risk increases among younger age groups after 2020, are posterior summaries of random effects estimated from the suicide-call data. They are not quantities derived from the model assumptions or from the standardization offsets. The only self-referential construction is the internal standardization of expected counts Eijk, which is standard practice: the age effect gamma_k is estimated relative to that baseline, and the time-age interaction zeta3_jk is a separate random effect whose posterior pattern is data-driven. No equation in the paper sets the claimed result equal to an input or to a fitted parameter renamed as a prediction. The self-citations to prior Marco et al. studies are used only to motivate the relevance of suicide-related emergency calls and are not load-bearing for the WAIC-based model comparison or for the specific age-time pattern. The paper is therefore self-contained with respect to its empirical findings; concerns about uncertainty intervals or the call-data proxy for suicide risk are correctness and validity issues, not circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central empirical claims rely on standard disease-mapping assumptions (Poisson counts, CAR priors, RW1/independent effects, Knorr-Held interactions) and on the untested premise that emergency calls are a faithful proxy for suicide risk. No new physical or conceptual entities are introduced. Two prior hyperparameters are chosen by hand; sensitivity analysis shows only small posterior shifts.

free parameters (2)

PC prior scale for standard deviation hyperparameters = P(sigma > 1) = 0.01
Chosen by the authors for all random effect standard deviations; a sensitivity run with uniform priors shows minor shifts, largest in sigma_delta (0.37 vs 0.33).
PC prior for Leroux mixing parameter lambda = P(lambda < 0.5) = 0.5
Default prior for the spatial CAR mixing parameter; posterior mean 0.42-0.45 under both priors.

assumptions (5)

domain assumption Suicide-related emergency call counts follow a Poisson distribution given the latent relative risk.
Section 3, equation for Oijk|Thetaijk; standard in disease mapping but unverifiable from the paper.
domain assumption The spatial effect follows a Leroux conditional autoregressive prior.
Section 3, phi prior; a modeling choice that can affect spatial smoothing.
domain assumption The time and age effects are either independent or first-order random walks.
Section 3, delta and gamma priors; the 520 models compare these choices.
domain assumption Knorr-Held interaction types and sum-to-zero constraints guarantee identifiability of the linear predictor.
Section 3.1, Table 2; identifiability of the chosen Model 8 depends on these constraints.
domain assumption The Wakefield et al. graphical test (Loess scatterplot of stratum rates against reference rates) is a valid indicator that indirect standardization is biased.
Section 2 and Figure 1; the test is exploratory and not quantitative.

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Cite this review

Pith. "Pith review of Overcoming Standardization: Revealing Hidden Age Patterns of Suicide with Spatiotemporal Models." pith.science (2026). https://pith.science/paper/HZ7BQW6G

@misc{pith2026250712033,
  author       = {Pith},
  title        = {Pith review of: Overcoming Standardization: Revealing Hidden Age Patterns of Suicide with Spatiotemporal Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HZ7BQW6G}},
  note         = {Machine review of arXiv:2507.12033}
}

read the original abstract

Indirect standardization is widely used in disease mapping to control for confounding, but relies on restrictive assumptions that may bias estimates if violated. Using data on suicide-related emergency calls, this study highlights such limitations and proposes age-structured hierarchical Bayesian models as an alternative. These models incorporate space-time, space-age, and time-age interactions, allowing for more accurate estimation without strong assumptions. The results show improved model fit, especially when including age effects. The best model reveals a rising temporal trend (2017--2022), a nonlinear age pattern, and stronger risk increases among younger individuals compared to older ones.

Figures

Figures reproduced from arXiv: 2507.12033 by the authors.

**Figure 1.** Rates by regional stratum Oijk/Nijk against the risk of stratum qj of some municipalities-year Numerous municipalities have been found where this hypothesis is not verified, indicating how restrictive it can be, especially with data disaggregated in space, time, and age. The property described by equation (2) should be verified for all indices i and j. However, the relationship between observed rates and stratum ris… view at source ↗

**Figure 2.** Posterior mean of the main random effects: spatial effect across the Valencian Community ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Posterior mean of the spatio-temporal effect ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Posterior mean of the spatial-age interaction effect ( [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Posterior mean of the time–age interaction effect ( [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: Posterior mean of the spatio-temporal effect ( [PITH_FULL_IMAGE:figures/full_fig_p024_6.png]

**Figure 7.** Figure 7: Posterior mean of the spatial-age effect ( [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

and Rue, H

Abdul-Fattah, E., Van-Niekerk, J. and Rue, H. (2023). INLA ^+ : approximate Bayesian inference for non-sparse models using HPC. Statistics and Computing , 35(17), 1--23

work page 2023

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work page 1974

[3] [3]

and Mart\'inez-Beneito, M

Botella, P. and Mart\'inez-Beneito, M. A. (2015). A unifying modeling framework for highly multivariate disease mapping. Statistics in Medicine , 34(9), 1548--1559

work page 2015

[4] [4]

J., Perdomo-Jurado, Y

Ca\ non-Ayala, M. J., Perdomo-Jurado, Y. E. and Caro-Delgado, A. G. (2024). Spatiotemporal analysis of suicide attempts in Colombia from 2018 to 2020. Cadernos de Sa\'ude P\'ublica , 40(8), 1--16

work page 2024

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Congdon, P. (2006). A model for geographical variation in health and total life expectancy. Demographic Research , 14(9), 157--178

work page 2006

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and Rea\ no, C

Gayosa, E. and Rea\ no, C. (2024). Spatio-temporal Modelling of Measles Risk in the Provinces of Central Luzon, CALABARZON, and MIMAROPA Linking the Impact of Climate-based Factors. Philippine Journal of Science , 153(6A), 2079--2086

work page 2024

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Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. and Rubin, D. B. (2013). Bayesian Data Analysis. 3rd Ed. Chapman & Hall / CRC , New York

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