{"id":"90880870-0872-4005-9034-94bb3adfd98c","arxiv_id":"2607.26210","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Using stratified Cox-type recurrent-event models, the paper finds sex, region, and deprivation effects on pediatric mental-health ED visits shifted across pre-, during-, and post-COVID periods in Alberta.","lead":"This paper applies a stepwise recurrent-event modeling framework to Alberta pediatric mental-health emergency department visits, comparing patterns before, during, and after COVID-19. It offers health planners and statisticians a workflow for zero-truncated, privacy-limited administrative count data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Independent censoring is the load-bearing assumption: because age = calendar time − birthdate, cohort effects violate it and confound period comparisons; the authors acknowledge this in the Discussion and only promise IPCW as future work. A cohort-effect simulation should be run to quantify bias.","rationale":"After reading the manuscript in good faith, I find the paper's strongest contribution is a well-organized, data-driven modeling pipeline for zero-truncated recurrent events with coarsened birthdates. The estimation equations are coherent and the stepwise flowchart is sensible. However, the most load-bearing assumption is the independent-censoring condition in §2.2.2. The paper itself acknowledges it may be violated and cites evidence of birth-cohort differences. Because the analysis uses age as the time scale and compares calendar periods, any cohort effect is absorbed into the period-specific estimates, directly threatening the headline comparisons. The reader's verdict already captures this as CONDITIONAL, and the proposed additional checks (data/code release, formal inference for period differences) are reasonable. My concern does not change the verdict; it refines the justification. I agree with the reader's weakest-assumption identification.","tokens_in":11985,"tokens_out":7488,"duration_ms":79239,"concrete_test":"Run a simulation study calibrated to the observed data (82,481 subjects, age 0–17, three periods with the stated cutoffs, left truncation and zero truncation). Generate birthdates and counting processes from an intensity model with a birth-cohort effect on the baseline rate (e.g., 2–5% annual increase in baseline intensity by birth year, a magnitude consistent with Xiong et al.'s generational differences), while keeping the true period effects fixed. Apply the paper's nonparametric estimator (Eq. 3) and the stratified Cox estimator (Eqs. 5–10) without adjusting for cohort. Measure the bias in estimated period-specific log-rate and coefficient functions. If the bias exceeds the width of the paper's displayed 95% pointwise CIs, the independent-censoring assumption is the load-bearing flaw and the period comparisons in Figs. 3–5 cannot be taken at face value.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that MHED visit frequencies and covariate effects evolved across the three COVID-19 periods—depends on the independent-censoring assumption stated in §2.2.2: birthdate B_i independent of the counting process N_i(·). On the age time scale, calendar period and birth cohort are collinear: age = calendar time − birthdate. If birth cohort affects the event rate, then within any period and age group the observed subjects are a mixture of cohorts, and the period-specific rate estimates are confounded. The authors themselves note in the Discussion that this assumption 'may be more restrictive' and cite Xiong et al. [18], which reported generational differences in MHED visit patterns. They propose IPCW only as future work and provide no sensitivity analysis. A violation of this magnitude would not simply change the magnitude of a coefficient—it would alter the qualitative comparison between periods, which is the main scientific output. Thus the framework's validity as a 'practical approach' is conditional on an assumption the authors have reason to believe is false.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a stepwise statistical framework for pediatric mental health-related emergency department (MHED) visits in Alberta, 2010–2025. The data are treated as zero-truncated recurrent events on the age scale. The framework proceeds from a nonparametric marginal rate estimator (with multiple imputation for coarsened birthdates and census-based denominators) to Poisson and history-stratified Cox-type models with age-varying coefficients, with all models stratified by three COVID-19 pandemic periods. The application to 82,481 subjects and 161,026 visits yields estimated rate functions, coefficient curves, and cumulative baseline intensities. The paper claims that the framework provides insights into how visit frequencies and covariate effects evolved across the pre-, during-, and post-pandemic periods and how previous MHED visits influence subsequent visits.","tokens_in":12242,"tokens_out":5475,"duration_ms":54209,"significance":"If the results are valid, the framework offers a practical way to analyze recurrent healthcare utilization data that feature zero truncation and coarsened birthdates, a setting common in administrative databases. The manuscript is transparent about its data sources, and the use of census denominators to account for subjects with no MHED visits is a genuine strength. The multiple-imputation approach for missing birthdates is also sensible. However, the methodological novelty is limited because the core estimating equations are adapted from the authors' earlier work; the new contribution is mainly the workflow and its application. The central scientific claim about changes across pandemic periods rests on an assumption that the authors themselves describe as possibly violated, and it is not supported by formal tests or simulation evidence. Reproducibility is also limited by the empty Code Availability section.","major_comments":[{"comment":"The independent-censoring assumption (birthdate B_i independent of N_i) is load-bearing because the age time scale is defined as calendar time minus birthdate, so birth cohort and calendar period are collinear. The authors acknowledge in the Discussion that this assumption 'may be more restrictive' and cite Xiong et al. [18] for generational differences in MHED visit patterns, but no sensitivity analysis or simulation is provided; IPCW is only promised as future work. If birth cohort affects the event rate, the period-specific estimates in Eqs. (2)–(3) and the stratified comparisons in Models (4) and (7) could be qualitatively biased. I recommend adding a simulation or sensitivity analysis that introduces a cohort effect and quantifies the resulting bias in the period comparisons.","section":"§2.2.2 and Discussion"},{"comment":"The central claim that covariate effects 'evolved' across the three pandemic periods is supported only by visual inspection of pointwise 95% confidence intervals. There is no formal test for differences between periods, no joint confidence bands, and no adjustment for the many age-grid comparisons. Some statements are stronger than the displayed intervals warrant; for example, the text notes 'substantial overlap' between age-varying and age-constant confidence intervals yet concludes that the results 'support the use of age-varying regression coefficients,' and several 'higher/lower risk' claims are based on overlapping pointwise intervals. Formal sup-norm tests or simultaneous confidence bands are needed, or the claims should be explicitly reframed as descriptive.","section":"§3.3 and Abstract"},{"comment":"No simulation study is reported for any of the proposed estimators. The estimating equations involve multiple imputation of birthdates, census-based denominators, and conditional probabilities for history-based strata, but the finite-sample bias, variance, and coverage of the resulting estimators are unexamined. Given that the methodology is adapted from prior work and this paper presents it as a practical framework, a simulation study under realistic zero-truncated, coarsened-birthdate settings is necessary to assess whether the proposed workflow reliably recovers the true rate functions and coefficients.","section":"§2.2.2–§2.2.4"},{"comment":"The sentence following Eq. (1) states that 'the summation over O can be equivalently restricted to O1' because Y_i^{(c)}(·|B_i)dN_i(·)=0 for subjects outside the MHED cohort. This is true for the numerator, but the denominator in Eq. (1) contains no dN_i term and must include the full target population O. If the restriction were applied to the denominator, the zero-truncation correction would be lost. This needs to be clarified, especially because the denominator is the mechanism that uses census information.","section":"Equation (1), §2.2.2"}],"minor_comments":[{"comment":"The text refers to 'Approach A' in Section 2.2.3 and 'Procedure A' in Section 2.2.4; these names are not defined and appear inconsistent. Please harmonize.","section":"§2.2.3–§2.2.4"},{"comment":"There are typographical spacing issues: 'TheAndersen-Gill model' and 'Prentice-Williams-Peterson models' should have spaces after 'The' and 'Prentice'.","section":"Introduction"},{"comment":"The table header reads 'T able 1'; the extra space should be removed.","section":"Table 1"},{"comment":"The sentence 'Set the pre-determined constant τ_L to 9 units...' is missing a subject; it should be 'We set...'. Also, the definition of age units (years vs. two-month units) should be stated more explicitly in the main text.","section":"§3.3"},{"comment":"The manuscript states that analyses were conducted in R and C++ via Rcpp, but the Code Availability section is empty. Since the data are not public, providing the analysis code is important for reproducibility.","section":"Code Availability"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is built largely on the authors' earlier methods, and the incremental contribution is the stepwise workflow and its application to MHED data. The main risk is the acknowledged independent-censoring assumption, which is not mitigated by sensitivity analysis or simulation. I would require a simulation study and either formal tests or careful descriptive language before publication. The issue in Eq. (1) regarding the denominator should also be resolved unless it is clearly a typo."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a competent applied paper: it applies the authors' own recurrent-event methodology to a large administrative dataset to describe how pediatric mental health–related ED visits in Alberta evolved across three COVID-19 periods. The data analysis is new, the stepwise modeling framework is clearly laid out, and the handling of zero truncation, coarsened birthdates, and history-based stratification is sensible. The estimating equations are coherent, and the authors are transparent about the data and coding limitations. This is not a methodological breakthrough; it is a well-executed application with a reusable workflow.\n\nSoft spots, in order of importance.\n\nFirst, the independent-censoring assumption in Section 2.2.2 is load-bearing. On the age time scale, calendar period and birth cohort are collinear: age = calendar time − birthdate. If birth cohort affects the event rate, the period-specific estimates are confounded. The authors acknowledge in the Discussion that this assumption 'may be more restrictive' and cite their own prior work reporting generational differences. That is a real problem for the headline conclusion that patterns changed across pandemic periods. A sensitivity analysis or simulation under plausible cohort effects would strengthen the paper substantially; promising IPCW for future work is not enough.\n\nSecond, there is no simulation study, and neither code nor data are available. That limits independent verification. I understand privacy constraints, but a simulation with synthetic data would help.\n\nThird, the claim in Section 3.3 that 'the results support the use of age-varying regression coefficients' is not supported by the displayed pointwise confidence intervals, which mostly overlap the age-constant estimates. The authors themselves note the overlap, then draw the stronger conclusion anyway. That should be toned down.\n\nMinor: there is no formal test for differences across pandemic periods, only pointwise intervals. The paper should state this plainly rather than imply formal comparisons.\n\nWho is this for? Health-services researchers and statisticians working with zero-truncated recurrent administrative data with coarsened follow-up. The framework is a useful template, but the empirical conclusions should be read conditionally. I would send this to peer review rather than desk-reject; the topic is important and the methods are sound conditional on the acknowledged assumption. I would, however, ask for a simulation or sensitivity analysis, code release, and a revision of the overclaim before publication.","headline":"Competent applied extension of the authors' own recurrent-event methods to a timely public-health question; the main caveats are a potentially violated censoring assumption the authors themselves flag, and some interpretive overreach relative to the paper's own confidence intervals.","tokens_in":12737,"tokens_out":2477,"would_cite":true,"duration_ms":23887,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62N01","62P10"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper develops a stepwise statistical framework for analyzing pediatric mental health–related emergency department (MHED) visits as zero-truncated recurrent event data, where each child is observed only if they had at least one visit, a","keywords":["conditional intensity function","health administrative data","stratified regression analysis","zero-truncated recurrent events","patient mental health","COVID-19 pandemic","time-varying coefficients"],"falsifier":"A sensitivity analysis that adds birth-cohort terms or uses inverse probability of censoring weighting and checks whether the estimated period-specific rate curves and sex-effect crossover ages change materially; if they do, the independent-censoring assumption does not hold.","tokens_in":11860,"feed_emoji":"🧠","tokens_out":4980,"duration_ms":51610,"temperature":0.7,"pith_summary":"The paper claims that a carefully staged modeling approach can recover how pediatric mental health–related emergency department visits changed across the COVID-19 pandemic periods, despite two data limitations: children with no visits are missing from the records, and exact birthdates are unavailable. Starting with nonparametric rate estimates to guide model choice, the analysis moves to Cox-type intensity models with time-varying coefficients, first stratified by pandemic period and then by whether the child has already had a visit. Applying this to 82,481 children with 161,026 visits, the framework yields period-specific visit rates and risk-factor effects, showing, for example, that annual visit counts rose during the pandemic while visits per person fell, and that the age at which female risk exceeds male risk dropped from about 11 to about 10 years. A sympathetic reader would care because the approach offers a practical template for extracting reliable conclusions from imperfect administrative health records.","feed_headline":"COVID reshaped pediatric mental-health ED visits, model shows","feed_subtitle":"Stepwise framework tracks how the pandemic changed children's mental-health ED visits.","key_machinery":"The key machinery is the adaptation of Cox-type recurrent-event regression to zero-truncated, coarsened data. Because exact birthdates are masked, the method generates plausible birthdates from the intervals implied by integer ages at visits, assuming a uniform distribution, and averages estimates over replicates. Because non-visitors are absent from the data, population census counts supply the at-risk denominators. The final model uses age as the time scale, stratifies by pandemic period and a history indicator (first visit vs. subsequent visits), and lets regression coefficients vary with age via local linear kernel smoothing.","core_discovery":"The central claim is that a stepwise statistical learning framework—nonparametric marginal rate estimation followed by Cox-type regression models stratified by pandemic period and event history—can characterize how pediatric MHED visit patterns evolved across the pre-, during-, and post-COVID periods. The analysis finds that the pandemic period saw higher annual visit counts but fewer visits per person, a larger female share of visits, and a shift in the sex-effect crossover age from roughly 11 years before the pandemic to roughly 10 years during and after it. The history-stratified model further shows that after a first visit, the risk of subsequent visits is substantially higher and has di","pith_inferences":["If the independent-censoring assumption fails—because birth cohort is associated with visit patterns—the period-specific rate and covariate estimates could be biased; an inverse probability of censoring weighting extension would test and correct this.","The prespecified cutoffs (WHO pandemic declaration and school-mask lifting) treat the period boundaries as known; treating them as unknown change-points could alter which differences are attributed to the pandemic versus background trends.","The same framework could be applied to condition-specific MHED visits (e.g., self-harm, mood disorders) or to other regions with similar administrative data, potentially revealing whether the observed sex and deprivation patterns are generalizable.","The shift in the sex crossover age during the pandemic might reflect differential pandemic-related stressors on adolescent girls, an inference the paper does not make but that could motivate targeted mental health screening in schools or primary care."],"forward_implications":["Provides a reusable template for analyzing recurrent healthcare utilization data when exact event origins are masked and non-users are missing.","Demonstrates that event-history stratification matters: the risk factors for a first MHED visit differ from those for subsequent visits, and the cumulative risk after a first visit is much higher.","Quantifies COVID-era changes: per-year visit volume rose during the pandemic while per-person visit frequency fell, and the female share of visits increased.","Shows that the age at which girls overtake boys in MHED risk moved earlier during the pandemic, pointing to age-specific windows for intervention.","The framework can be transferred to other zero-truncated recurrent event settings with evolving temporal patterns, such as chronic disease care episodes."],"fun_headline_variants":["Pandemic shifted pediatric mental-health ED visit patterns, model finds","Stepwise analysis tracks COVID-era changes in kids' mental health ED visits","Pediatric mental-health ED visits evolved across COVID periods, study shows","Model reveals pandemic altered children's mental-health ED visit trends","COVID changed pediatric mental health ED visits: sex gap and frequency shift"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The assumption that a child's birthdate, which determines their observation window, is independent of their mental-health visit pattern; if birth cohort is associated with the visit process, the period-specific estimates are biased.","fun_headline_variants_meta":{"raw":{"variants":["Pandemic shifted pediatric mental-health ED visit patterns, model finds","Stepwise analysis tracks COVID-era changes in kids' mental health ED visits","Pediatric mental-health ED visits evolved across COVID periods, study shows","Model reveals pandemic altered children's mental-health ED visit trends","COVID changed pediatric mental health ED visits: sex gap and frequency shift"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000186,"raw_usage":{"total_tokens":1124,"prompt_tokens":665,"completion_tokens":459,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":409,"completion_tokens_details":{"reasoning_tokens":370}},"tokens_in":409,"tokens_out":459,"duration_ms":4711,"temperature":1.0,"reasoning_tokens":370,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T00:28:06.426202+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A sensitivity analysis that adds birth-cohort terms or uses inverse probability of censoring weighting and checks whether the estimated period-specific rate curves and sex-effect crossover ages change materially; if they do, the independent-censoring assumption does not hold.","supporting_citations":[],"review_version":1}