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REVIEW 3 major objections 6 minor 42 references

Estimating the Number of Opioid Overdoses in British Columbia Using Relational Evidence with Tree Structure

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Linked administrative health records, read as a tree of care pathways, imply that opioid overdoses in British Columbia from 2015 to 2017 were roughly 70–100% more numerous than the 34,113 confirmed events.

desk verdict A careful, honest application of two population-size estimators to BC overdose data; the qualitative undercount is credible, but the headline numbers are mostly prior-driven and the WMM's circularity needs a fix. read the letter →

arxiv 2506.21024 v1 pith:UBNHMQZD submitted 2025-06-26 stat.AP

Mallory J Flynn , Paul Gustafson , Michael A. Irvine This is my paper · ORCID
classification stat.AP MSC 62P1062F15
keywords opioidoverdosepopulationsizeestimationweightedmultipliermethodBayesianhierarchicalmodeltree-structureddatahealthadministrativeBritishColumbiahiddenpopulations
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

This paper sets out to estimate the total number of opioid overdose events in British Columbia during 2015–2017 by treating linked administrative health records as a tree whose root is the unknown total and whose leaves are mutually exclusive reporting pathways. It applies two estimation strategies: a weighted multiplier method that back-calculates from each observed leaf and combines the path estimates by variance-minimizing weights, and a hierarchical Bayesian model that propagates uncertainty through branching probabilities and adds nodes for records missed inside the healthcare system. Both approaches produce totals far above the 34,113 events confirmed in the cohort: about 59,445 by the weighted multiplier method and about 68,978 by the Bayesian model. If these estimates are right, administrative data alone understate the overdose burden by more than 70%, and services sized to the recorded count miss the largest part of the problem.

What carries the argument

The central object is a reporting-pathway tree: the unknown total $Z$ sits at the root, and each observed leaf is a mutually exclusive route an overdose takes through data sources such as emergency care, hospital admission, coroner records, vital statistics, and unattended events. The weighted multiplier method walks backward from each leaf, dividing observed counts by estimated branching probabilities along the path, then averages the path-specific estimates with weights chosen to minimize variance. The Bayesian model instead puts Dirichlet priors on every branch, adds latent data-uncertainty nodes so observed counts may undercount, treats $Z$ with a lognormal prior, and updates everything by Markov chain Monte Carlo; the unattended branch's branching probability $p$, with prior mean 0.4, is what converts the recorded total into tens of thousands of additional events.

What would settle it

If an independent, population-scale measurement of the unattended share existed—say, a mandatory registry of bystander naloxone administrations combined with ambulance call data—and it put that share near 20% rather than 40%, the two models' totals would drop toward the recorded 34,113 and the paper's central conclusion would fail.

Watch

Extended reading notes

Core claim

On its own terms, this paper claims that the hidden population of opioid overdoses in British Columbia is large and that two different estimators converge on the same qualitative conclusion. The confirmed cohort records 34,113 events, but the weighted multiplier method estimates $Z = 59{,}445$ (95% interval 56,815–62,196) and the hierarchical Bayesian model estimates $Z = 68{,}978$ (95% credible interval 52,634–93,145). The Bayesian model locates most of the missing mass in the healthcare-unattended arm: an estimated $26{,}585$ unattended events, of which roughly 89.8% survived without care. It also finds missed events inside the attended arm—about 16% of attended events uncounted at one level—so the gap between the two methods is roughly the size of those internally missed records. The paper concludes that there may be over 70% more events occurring than the raw administrative total suggests.

Load-bearing premise

The load-bearing premise is that about 40% of overdoses are never attended by healthcare, a proportion that comes from expert prior knowledge rather than from observed data; if the true unattended share differs, the headline estimate moves by tens of thousands of events.

Editorial extensions

If this is right

  • If the Bayesian estimate is correct, the true number of overdose events in British Columbia in 2015–2017 was about twice the 34,113 confirmed events, meaning planning that uses only administrative counts would be sized for less than half the burden.
  • The hidden events are concentrated in the unattended arm: roughly 26,585 events, about 89.8% of them non-fatal, which implies prevention and harm-reduction services reach a population largely invisible to hospital-based surveillance.
  • Administrative records also miss attended events: the model estimates about 8,000 missed events inside the attended branch, roughly the difference between the Bayesian and weighted-multiplier totals, so even the counted side has an uncounted remainder.
  • Aggregating leaf nodes barely changes the root estimates, so jurisdictions with less granular linked data can still use these methods for total-population estimation when the same tree skeleton is available.
  • The weighted multiplier method offers a simpler and more interpretable alternative, but because it treats observed counts as exact, its confidence intervals are likely too narrow when undercounting is present.

Reading between the lines

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

  • Beyond the paper: the most cost-effective next measurement is not more record linkage but a direct estimate of the unattended share $p$, for example a follow-up survey of bystander naloxone administrations, because the sensitivity analysis shows that moving this prior swings the total by about 70%.
  • Beyond the paper: the aggregate gap of 25,000–35,000 events mixes three distinct hidden populations—unattended non-fatal, unattended fatal, and attended-but-unrecorded—with different policy levers, so decision-makers should decompose the estimate before allocating resources.
  • Beyond the paper: the method could be validated by applying it to a jurisdiction with a near-complete overdose registry; if the tree-based estimate substantially overstates that registry count, the unattended-share prior would be the part to question.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper estimates the total number of opioid overdose events in British Columbia during 2015–2017 using a tree-structured linked cohort of 34,113 observed events. Two estimators are compared: a weighted multiplier method (WMM) with back-calculation along root-to-leaf paths, and a hierarchical Bayesian model with latent data-uncertainty nodes. The Bayesian model yields a posterior mean of Z = 68,978 (95% credible interval 52,634–93,145); the WMM yields a mean of 59,445 (95% interval 56,815–62,196). The paper concludes that the true number may be over 70% higher than the raw healthcare-attended count. The authors perform MCMC convergence checks, prior sensitivity analyses, and data-deletion value-of-information experiments.

Significance. The paper addresses an important public health measurement problem with a rich linked dataset and provides a careful comparison of two population-size estimation approaches, including reproducible R packages and extensive MCMC diagnostics. The sensitivity analyses are a genuine strength: the authors explicitly test alternative priors and report that inference is strongly affected by the prior on the healthcare-unattended proportion. However, as the posterior means of the key branching probabilities remain close to their priors, the headline 'over 70% more events' is not identified by the data but largely restates expert prior knowledge. The qualitative conclusion that the administrative counts are an undercount is defensible; the quantitative claim requires much more prominent caveats.

major comments (3)
  1. [Section 3.2 / Table 5] The posterior means of p (0.376), r_I (0.156), s_L (0.089), t_R (0.072), and u_U (0.081) are nearly identical to the prior means specified in Section 2.3 (0.4, 0.167, 0.091, 0.074, 0.077). This shows that the observed leaf counts provide almost no information about the unattended proportion and data-uncertainty rates, which are the parameters that drive the difference between Z and the observed count. The conclusion's "over 70% more events" should therefore be presented as a prior-dependent projection, and the Section 3.3.1 finding that moving the p prior to its upper expert bound increases Z by roughly 70% should be displayed in the main text as a central result, not only summarized qualitatively.
  2. [Section 2.2 / Tables 1 and 2] The WMM's Beta branching parameters for the healthcare-attended arm are constructed from the same POC counts that serve as leaf observations (e.g., p_BF uses x=18,312 out of n=34,113, which is also the total observed cohort). As the authors acknowledge in Section 2.2, this violates the independence assumption underlying the back-calculation, so each leaf estimate is effectively the observed parent count divided by a proportion that is itself derived from that same count. The reported WMM confidence interval (56,815–62,196) ignores this circularity and treats the leaf counts as exact, making it artificially narrow; the quantile-based interval (41,067–109,830) is a more honest reflection of uncertainty, and the paper should say so explicitly when presenting the WMM results.
  3. [Section 3.3.1] The sensitivity analysis is reported only in qualitative terms in the main text, with the numerical posterior summaries in the supplementary. Because the central estimate is prior-dominated, the main text needs a table or figure showing posterior means and credible intervals for Z and A under each alternative prior (for p, q, and Z). Without these numbers, readers cannot quantify how much of the headline claim is driven by prior choices, and the claim "there may be over 70% more events" is not adequately qualified.
minor comments (6)
  1. [Section 1] In the second paragraph, "a similar percentage of accidental, apparent overdose toxicity deaths are occurred among individuals" should read "occur" or "are occurring."
  2. [Section 4] In the Discussion, "a extension of the WMM methodology" should be "an extension."
  3. [References] Reference 17 contains the typo "wiht" for "with," and Reference 36 contains "appraoch" and "estiamting."
  4. [Section 3.1] The paper reports two different 95% intervals for the WMM (a quantile-based interval and a confidence interval) without explaining why the quantile interval is so much wider; please clarify which interval should be used for inference and why.
  5. [Section 2.2 / Tables 3 and 4] The WMM assigns negative weights to some paths (M=-0.067, Q=-0.012 in the full tree; T=-0.025, Q=-0.009 in the simplified tree); this should be explained, since negative weights in a variance-minimizing weighted mean are unintuitive and may indicate that the method is extrapolating beyond the observed data.
  6. [Section 2.3] The sentence "The other parameters are set to be equal, so that uniform prior weight is assigned to all other branches at each level" is slightly misleading given that the Dirichlet parameters are not equal (e.g., r ~ Dir(5,5,5,5,4)); please rephrase to say that the non-data-uncertainty branches within each sibling group receive equal weight.

Circularity Check

1 steps flagged · score 6.0 of 10

The WMM's multiple-path estimate collapses by construction to the observed cohort total rescaled by the root-branch prior; the Bayesian model is prior-sensitive but not itself circular.

  1. self definitional [Section 2.2 (WMM Model Framework), Tables 1-2; Discussion, Section 4]
    "While these sums are not used to inform node counts, they are used to inform parameters of the Beta and Dirichlet branching distributions in the healthcare-attended arm of the tree. ... Beta(x+1, n-x+1) branch distributions are used ... x represents the number of individuals in the informing sample survey who were counted at V, while the values n are given by the total number of individuals in the survey. ..."

    For a leaf counted as x_L with parent total n_B = 34,113, Table 2 sets the corresponding branch probability to x_L / n_B (e.g., p_BF = 18,312 / 34,113). The WMM back-calculates Z from that leaf as x_L / (p_ZB * p_BL), which algebraically cancels x_L and returns n_B / p_ZB = 34,113 / (3/5) = 56,855. Every healthcare-attended leaf yields the same number, so the 'multiple paths' in the WMM are not independent evidence; the weighted estimate is just a rescaling of the observed cohort total by the expert root-branch prior. The paper concedes this dependency in the quoted passage, but still presents the WMM paths as separate evidence streams and the resulting total as a distinct estimate. This is a reduction of the 'prediction' to the input cohort total and the root prior by construction.

full rationale

The Bayesian hierarchical model is a genuine evidence-synthesis procedure: it combines expert Dirichlet priors with observed leaf counts through a likelihood, and its posterior means are not identical to its priors even though they remain close (Table 5 vs. Section 2.3). The paper itself flags in Section 2.1 that the Bayesian model is expected to rely heavily on prior inputs, and Section 3.3.1 shows that moving the unattended-proportion prior to its upper bound changes Z by about 70%; this is a sensitivity caveat rather than a circular reduction, but it does mean the headline 'over 70% more events' is prior-dominated rather than data-identified. The clearer circularity is in the WMM, one of the paper's two central estimators. Its branching distributions in the healthcare-attended arm are constructed from the same POC leaf counts that are then used as the leaf evidence for back-calculation, so each root-to-leaf path collapses to the same quantity: cohort total divided by the root-branch prior. The paper explicitly acknowledges that the branching parameters are 'not independent from the marginal counts,' yet still reports the WMM result as a separate, multiply-evidenced estimate. Because the WMM estimate reduces by construction while the Bayesian model retains some independent content, the overall circularity is partial.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The tree structure, the observed counts, and especially the expert priors on the unattended branch are the real inputs behind the estimate. The WMM further treats observed counts as exact while using the same counts to set branch probabilities, making its back-calculations partially circular. The Bayesian model is more honest about uncertainty but compensates with prior-heavy latent nodes.

free parameters (5)
  • WMM branch Beta parameters for healthcare-attended arm = e.g., p_BF=18312/34113, p_BG=15328/34113, p_BH=473/34113
    Observed POC counts are used directly as x and n in Beta distributions for branching probabilities, so the branch probabilities are the same numbers as the leaf evidence (Section 2.2, Tables 1 and 2).
  • Bayesian prior for p (unattended proportion) = Dirichlet(10,15), mean 0.4
    Expert-elicited prior; sensitivity analysis shows the posterior mean of Z changes by about 70% when this prior is moved to the upper bound of expert knowledge (Sections 2.3 and 3.3.1).
  • Bayesian prior for q (unattended fatality proportion) = Dirichlet(1,10), mean ~0.091
    Expert-elicited prior for the chance that an unattended overdose is fatal; it controls the size of the invisible fatal branch (Section 2.3).
  • Bayesian LogNormal hyperparameters for Z = LogNormal(log(51000), 0.38)
    Chosen so that roughly 70% of the prior mass lies between expert bounds (34,113 and 76,621); the posterior mean 68,978 is near the upper bound, indicating the prior strongly influences the result (Section 2.3).
  • Data uncertainty prior percentages = 5-10% for nodes L, R, U; ~15% for node I
    Expert knowledge encoded as Dirichlet parameters for the latent under-count nodes; these percentages are not data-derived (Section 2.3).
assumptions (4)
  • domain assumption The tree structure in Figure 1 and its simplifications correctly represents all reporting pathways for opioid overdose events in BC, 2015-2017.
    The entire estimation rests on this structure; any unmodeled pathway or double-counting would bias the root estimate (Section 2.2, Figures 1-4).
  • domain assumption The linked POC data accurately matches individuals across administrative datasets, and observed leaf counts are unbiased except for the explicitly modeled uncertainty nodes.
    Linkage errors would change leaf counts and branch probabilities; the paper assumes the uncertainty nodes absorb any under-counting (Sections 2.2-2.3).
  • domain assumption Expert-elicited priors for p, q, and Z are reasonable approximations to the true values.
    The posterior for Z shifts substantially under plausible prior changes (Section 3.3.1), so the estimate is not data-dominated.
  • standard math Standard Bayesian MCMC via JAGS converges and the effective sample sizes and trace plots indicate reliable posterior estimates.
    The paper reports N_eff values in Table 6 and trace/ACF plots in the supplementary, and uses 10 million iterations with 5 million burn-in (Section 2.3).
invented entities (1)
  • Data uncertainty latent nodes L, I, R, U
    purpose: Represent overdose events missed by administrative data at various levels of the tree
    These nodes have no observed data; their posterior estimates (e.g., s_L mean 0.089, r_I mean 0.156) come almost entirely from expert prior percentages, so they are not independently identifiable or falsifiable outside the model.

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Pith. "Pith review of Estimating the Number of Opioid Overdoses in British Columbia Using Relational Evidence with Tree Structure." pith.science (2026). https://pith.science/paper/UBNHMQZD

@misc{pith2026250621024,
  author       = {Pith},
  title        = {Pith review of: Estimating the Number of Opioid Overdoses in British Columbia Using Relational Evidence with Tree Structure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UBNHMQZD}},
  note         = {Machine review of arXiv:2506.21024}
}
read the original abstract

In many fields, populations of interest are hidden from data for a variety of reasons, though their magnitude remains important in determining resource allocation and appropriate policy. In public health and epidemiology, linkages or relationships between sources of data may exist due to intake structure of care providers, referrals, or other related health programming. These relationships often admit a tree structure, with the target population represented by the root, and paths from root-to-leaf representing pathways of care after a health event. In the Canadian province of British Columbia (BC), significant efforts have been made in creating an opioid overdose cohort, a tree-like linked data structure which tracks the movement of individuals along pathways of care after an overdose. In this application, the root node represents the target population, the total number of overdose events occurring in BC during the specified time period. We compare and contrast two methods of estimating the target population size - a weighted multiplier method based on back-calculating estimates from a number of paths and combining these estimates via a variance-minimizing weighted mean, and a fully Bayesian hierarchical model.

Figures

Figures reproduced from arXiv: 2506.21024 by the authors.

Figure 3
Figure 3. For this simplified tree, we have  ∗ = {𝐹 , 𝐻, 𝐽, 𝐾, 𝑂, 𝑄, 𝑆, 𝑇 }. The healthcare unattended arm will use survey estimates or expert knowledge to inform the branching distributions and generate samples 𝑝𝑍𝐴, 𝑝𝐴𝐷, 𝑝𝐷𝐽 , 𝑝𝐷𝐾. The WMM procedure reflects data uncertainty only in the sampling of branching probabilities, and marginal counts are assumed exact in this application. For the purpose of this analysis, back-calc… view at source ↗

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Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [1]

    FischerB,KeatesA,BuhringerG,RemierJ,RehmJ.Non-medicaluseofprescriptionopioidandprescriptionopioid-related harms: why so markedly higher in North America compared to the rest of the world?.Addiction.2014; 109:177–81

    work page 2014

  2. [2]

    Vital signs: Changes in opioid prescribing in the United States, 2006-2015.Morb Mortal Wkly Rep.2017; 66:697–704

    Guy J, others . Vital signs: Changes in opioid prescribing in the United States, 2006-2015.Morb Mortal Wkly Rep.2017; 66:697–704

    work page 2006

  3. [3]

    JanjuaN,others.Identifyinginjectiondruguseandestimatingpopulationsizeofpeoplewhoinjectdrugsusinghealthcare administrative datasets.Int J Drug Policy.2018; 55:31–39

    work page 2018

  4. [4]

    Canada. oOPHA. Opioid- and Stimulant-related Harms in Canada.Federal, provincial and territorial Special Advisory CommitteeontheEpidemicofOpioidOverdoses.2023;https://health-infobase.canada.ca/substance-related-harms/opioids- stimulants/

    work page 2023

  5. [5]

    Prevention of Prescription Opioid Misuse and Projected Overdose Deaths in the United States.JAMA Network Open2019; 2(2):e187621-e187621

    Chen Q, Larochelle MR, Weaver D, et al. Prevention of Prescription Opioid Misuse and Projected Overdose Deaths in the United States.JAMA Network Open2019; 2(2):e187621-e187621. doi: :10.1001/jamanetworkopen.2018.7621

    work page arXiv 2018

  6. [6]

    doi: https://doi.org/10.1016/j.drugalcdep.2017.12.032

    BaldwinN,GrayR,GoelA,WoodE,BuxtonJ,RiebL.Fentanylandheroincontainedinseizedillicitdrugsandoverdose- relateddeathsinBritishColumbia,Canada:Anobservationalanalysis.DrugandAlcoholDependence2018;185:322-327. doi: https://doi.org/10.1016/j.drugalcdep.2017.12.032

    work page doi:10.1016/j.drugalcdep.2017.12.032

  7. [7]

    Canada.S.Table13-10-0114-01Lifeexpectancyandotherelementsofthecompletelifetable,three-yearestimates,Canada, all provinces except Prince Edward Island.https://doi.org/10.25318/1310011401-eng2022

    work page doi:10.25318/1310011401-eng2022

  8. [8]

    Fentanyl-detected illicit drug overdose deaths January 1, 2012 to February 28, 2017

    British Columbia oCS. Fentanyl-detected illicit drug overdose deaths January 1, 2012 to February 28, 2017. http://www.webcitation.org/78lHkI0Bw2017

    work page 2012

Show all 42 references
  1. [9]

    Illicit drug overdose deaths January 1, 2007 to March 31, 2017

    British Columbia oCS. Illicit drug overdose deaths January 1, 2007 to March 31, 2017. http://www.webcitation.org/78lI1v4nV2017

    2007

  2. [10]

    The Daily 2020-01-28 - Life Tables, 2016/2018.https://www150.statcan.gc.ca/n1/daily- quotidien/200128/dq200128a-eng.htm2020

    Canada S. The Daily 2020-01-28 - Life Tables, 2016/2018.https://www150.statcan.gc.ca/n1/daily- quotidien/200128/dq200128a-eng.htm2020

    2020

  3. [11]

    Impact of drug overdose-related deaths on life expectancy at birth in British Columbia.Health Promot Chronic Dis Prev Can.2018; 38:248–51

    Ye X, Sutherland J, Henry B, Tyndall M, Kendall P. Impact of drug overdose-related deaths on life expectancy at birth in British Columbia.Health Promot Chronic Dis Prev Can.2018; 38:248–51

    2018

  4. [12]

    IrvineM,BuxtonJ,OtterstatterM,etal.Distributionoftake-homeopioidantagonistkitsduringasyntheticopioidepidemic in British Columbia, Canada: a modelling study.Lancet Public Health.2018; 3:e215-25

    2018

  5. [13]

    Modelling the combined impact of interventions in averting deaths during a synthetic- opioid overdose epidemic.Addiction.2019; 114:1602-1613

    Irvine M, Kuo M, Buxton J, et al. Modelling the combined impact of interventions in averting deaths during a synthetic- opioid overdose epidemic.Addiction.2019; 114:1602-1613

    2019

  6. [14]

    Development and characteristics of the Provincial Overdose Cohort in British Columbia, Canada.PLoS ONE.2019; 14(1):e0210129

    MacDougall L, Smolina K, Otterstatter M, et al. Development and characteristics of the Provincial Overdose Cohort in British Columbia, Canada.PLoS ONE.2019; 14(1):e0210129

    2019

  7. [15]

    OpioidOverdosesS.A.C.o.t.E.oOP.Nationalreport:Opioid-relatedHarmsinCanadaWeb-basedReport.https://health- infobase.canada.ca/substance-related-harms/opioids2019

  8. [16]

    Development and characteristics of the Provincial Overdose Cohort in British Columbia, Canada

    Macdougall L, others . Development and characteristics of the Provincial Overdose Cohort in British Columbia, Canada. PLoS One.2019; 14(1):e0210129

    2019

  9. [17]

    FlynnM,GustafsonP.Leveragingrelationalevidence:populationsizeestimationontree-structureddatawihttheweighted multiplier method.Preprint2025; Department of Statistics, University of British Columbia

  10. [18]

    AutoWMM and JAGStree - R packages for population size estimation on relational tree-structured data.Preprint2025; Department of Statistics, University of British Columbia

    Flynn M, Gustafson P. AutoWMM and JAGStree - R packages for population size estimation on relational tree-structured data.Preprint2025; Department of Statistics, University of British Columbia. 20 Mallory J FlynnET AL

  11. [19]

    BC Provincial Overdose Cohort

    (2017) BM. BC Provincial Overdose Cohort. V1.British Columbia Ministry of Health [publisher]. Data Extract2017; https://www.popdata.bc.ca/data

    2017

  12. [20]

    PharmaNet..British Columbia Ministry of Health [publisher]

    (2017) B. PharmaNet..British Columbia Ministry of Health [publisher]. Data Extract2017; https://www.popdata.bc.ca/data

    2017

  13. [21]

    National Ambulatory care reporting system (NACRS).British Columbia Ministry of Health [publisher]

    (2017) C. National Ambulatory care reporting system (NACRS).British Columbia Ministry of Health [publisher]. Data Extract2017; https://www.popdata.bc.ca/data

    2017

  14. [22]

    Discharge Abstract Database.British Columbia Ministry of Health [publisher]

    (2017) C. Discharge Abstract Database.British Columbia Ministry of Health [publisher]. Data Extract2017; https://www.popdata.bc.ca/data

    2017

  15. [23]

    Medical Services Plan (MSP) Payment Information File.British Columbia Ministry of Health [publisher]

    (2017) BM. Medical Services Plan (MSP) Payment Information File.British Columbia Ministry of Health [publisher]. Data Extract2017; https://www.popdata.bc.ca/data

    2017

  16. [24]

    Using Linked Data to Identify Pathways of Reporting Overdose Events in British Columbia, 2015 - 2017.International Journal of Population Data Science2022; 7:1

    Graham E, Zhao B, Flynn M, et al. Using Linked Data to Identify Pathways of Reporting Overdose Events in British Columbia, 2015 - 2017.International Journal of Population Data Science2022; 7:1

    2015

  17. [25]

    AntaG,OlivaJ,BravoM,DeMateoS,Domingo-SalvanyA.Estimatingtheprevalenceofdruginjectionusingamultiplier method based on a register of new HIV diagnoses.European Journal of Public Health.2010; 21(5):646-648

    2010

  18. [26]

    DeAngelisD,HickmanM,YangS.EstimatingLong-TermTrendsintheIncidenceandPrevalenceofOpiateUse/Injecting DrugUseandtheNumberofFormerUsers:Back-CalculationMethodsandOpiateOverdoseDeaths.AmericanJournalof Epidemiology.2004; 160(10):994-1004

    2004

  19. [27]

    KhalidF,HamadF,OthmanA,others.Estimatingthenumberofpeoplewhoinjectdrugs,femalesexworkers,andmenwho have sex with men, Unguja Island, Zanzibar: results and synthesis of multiple methods.AIDS Behav.2014; 18:S25-S31

    2014

  20. [28]

    BirrellP,GillO,DelpechV,etal.HIVincidenceinmenwhohavesexwithmeninEnglandandWales2001-10:anationwide population study.Lancet Public Health.2013; 13:313-18

    2013

  21. [29]

    Estimating the size of the MSM population in metro Vancouver, Canada, using multiple methods and diverse data sources.J Urban Health.2017; 95:188-195

    Rich A, Lachowsky N, Sereda P, et al. Estimating the size of the MSM population in metro Vancouver, Canada, using multiple methods and diverse data sources.J Urban Health.2017; 95:188-195

    2017

  22. [30]

    How many men who have sex with mend and female sex workers live in El Salvador? Using respondent-driven sampling and capture recapture to estimate population sizes.Sex Z Transm

    Paz-Bailey G, Jacobson J, Guardado M, others . How many men who have sex with mend and female sex workers live in El Salvador? Using respondent-driven sampling and capture recapture to estimate population sizes.Sex Z Transm. Infect. 2011; 87:279-282

    2011

  23. [31]

    Johnston L, Saumtallyb A, Corcealb S, others . High HIV and hepatitis C prevalence amongst injecting drug users in Mauritius: findings from a population size estimation and respondent driven sampling survey.Int J Drug Policy.2011; 22:252-258

    2011

  24. [32]

    Modeling infectious disease dynamics in the complex landscape of global health.Science2015; 347(6227):aaa4339

    Heesterbeek H, Anderson R, Andreasen V, Bansal S, De Angelis D, others . Modeling infectious disease dynamics in the complex landscape of global health.Science2015; 347(6227):aaa4339

  25. [33]

    Prevost T, Presanis A, Taylor A, Golderg D, Hutchinson S, De Angelis D. Estimating the number of people with hepatitis C virus who have ever injected drugs and have yet to be diagnose: an evidence synthesis approach for Scotland.Addiction 2015; 110:1287-1300

    2015

  26. [34]

    SweetingM,DeAngelisD,AdesA,HickmanM.Estimatingtheprevalenceofex-injectingdruguseinthepopulation.Stat. Meth. in Med. Research2009; 18:381-396

  27. [35]

    Irvine M, Konrad B, Michelow W, Balshaw R, Gilbert M, Coombs D. A novel Bayesian approach to predicting reductions in HIV incidence following increased testing interventions among gay, bisexual and other men who have sex with men in Vancouver, Canada.J.R. Soc. Interface2018; 1...

  28. [36]

    An Evidence synthesis appraoch to estiamting the incidence of seasonal influenza in the Netherlands.Influ

    McDonald S, Presanis A, De Angelis D, et al. An Evidence synthesis appraoch to estiamting the incidence of seasonal influenza in the Netherlands.Influ. Other Respir. Viruses2014; 8(1):33-41. Mallory J FlynnET AL 21

  29. [37]

    Correlates of seeking emergency medical help in the even of an overdose in British Columbia, Canada: Findings from the Take Home Naloxone program.Int J Drug Policy.2019; 71:157-163

    Karamouzian M, Kuo M, Crabtree A, Buxton J. Correlates of seeking emergency medical help in the even of an overdose in British Columbia, Canada: Findings from the Take Home Naloxone program.Int J Drug Policy.2019; 71:157-163

    2019

  30. [38]

    Vancouver, BC

    GeorgeR,SteinbergA,BuxtonJ.BCHarmReductionClientSurvey:BackgroundandSignificantFindingsthroughoutthe Years. Vancouver, BC. BC Centre for Disease Control.http://www.bccdc.ca/Health-Professionals-Site/Documents/Harm- Reduction-Reports/2021

    2021

  31. [39]

    CCENDU Bulletin: Calling 911 in Drug Poisoning Situations.https://ccsa.ca/sites/default/files/2019- 04/CCSA-CCENDU-Calling-911-Drug-Poisoning-2017-en.pdf2017

    Drug Use oCCEN. CCENDU Bulletin: Calling 911 in Drug Poisoning Situations.https://ccsa.ca/sites/default/files/2019- 04/CCSA-CCENDU-Calling-911-Drug-Poisoning-2017-en.pdf2017

    2019

  32. [40]

    Vancouver, BC

    MoustaqimBarretteA,PapamihaliK,BuxtonJ.TakeHomeNaloxoneProgramReport:ReviewofDatatoDecember2018. Vancouver, BC. BC Centre for Disease Control.https://towardtheheart.com/assets/uploads2019

  33. [41]

    R Foundation for Statistical Computing; Vienna, Austria: 2018

    Team RC.R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing; Vienna, Austria: 2018

    2018

  34. [42]

    Beyond a catalogue of differences: A theoretical frame and good practice guidelines for researching sex/gender in human health.Soc

    Springer K, Mager Stellman J, Jordan-Young R. Beyond a catalogue of differences: A theoretical frame and good practice guidelines for researching sex/gender in human health.Soc. Sci. Med.2012; 74(11):1817-1824. How to cite this article:M.J.Flynn,andP.Gustafson,andM.A.Irvine(20...

    2025

Pith tools

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