Multiple Systems Estimation (or Capture-Recapture Estimation) to Inform Public Policy

A Capture-Recapture-based Ascertainment Probability Weighting Method for Effect Estimation With Under-ascertained Outcomes

Outcome under-ascertainment, characterized by the incomplete identification or reporting of cases, poses a substantial challenge in epidemiologic research. While capture-recapture methods can estimate unknown case numbers, their role in estimating exposure effects in observational studies is not well established. This paper presents an ascertainment probability weighting framework that integrates capture-recapture and propensity score weighting. We propose a nonparametric estimator of effects on binary outcomes that combines exposure propensity scores with data from two conditionally independent outcome measurements to simultaneously adjust for confounding and under-ascertainment. Demonstrating its practical application, we apply the method to estimate the relationship between health care work and coronavirus disease 2019 testing in a Swedish region. We find that ascertainment probability weighting greatly influences the estimated association compared to conventional inverse probability weighting, underscoring the importance of accounting for under-ascertainment in studies with limited outcome data coverage. We conclude with practical guidelines for the method's implementation, discussing its strengths, limitations, and suitable scenarios for application.

The central role of the identifying assumption in population size estimation

The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the population size should be produced based on that data set, as models with different identifying assumptions can produce arbitrarily different population size estimates-even with identical observed data fits. Approaches to multiple-systems estimation often do not explicitly specify identifying assumptions. This makes it difficult to decouple the specification of the model for the observed data from the identifying assumption and to provide justification for the identifying assumption. We present a re-framing of the multiple-systems estimation problem that leads to an approach that decouples the specification of the observed-data model from the identifying assumption, and discuss how common models fit into this framing. This approach takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study estimating the number of civilian casualties in the Kosovo war.

Rejoinder to the discussion on "The central role of the identifying assumption in population size estimation"

We organize the discussants' major comments into the following categories: sensitivity analyses, zero counts, model selection, the marginal no-highest-order interaction (NHOI) assumption, and the usefulness of our proposed framework.

Estimating population size: The importance of model and estimator choice

We consider estimator and model choice when estimating abundance from capture-recapture data. Our work is motivated by a mark-recapture distance sampling example, where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences, we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effects models.

Massachusetts Prevalence of Opioid Use Disorder Estimation Revisited: Comparing a Bayesian Approach to Standard Capture-Recapture Methods

BACKGROUND

The National Survey on Drug Use and Health (NSDUH) estimated the prevalence of opioid use disorder (OUD) among the civilian, noninstitutionalized people aged 12 years or older in Massachusetts as 1.2% between 2015 and 2017. Accurate estimation of the prevalence of OUD is critical to the success of treatment and resource planning. Various indirect estimation approaches have been used but are subject to data availability and infrastructure-related issues.

METHODS

We used 2015 data from the Massachusetts Public Health Data Warehouse (PHD) to compare the results of two approaches to estimating OUD prevalence in the Massachusetts population. First, we used a seven-dataset capture-recapture analysis under log-linear model parameterization, controlling for the source dependence and effects of age, sex, and county through stratification. Second, we applied a benchmark-multiplier method in a Bayesian framework by linking health care claims data to death certificate data assuming an extrapolation of death rates from observed untreated OUD to unobserved OUD.

RESULTS

Our estimates for OUD prevalence among Massachusetts residents (aged 18-64 years) were 4.62% (95% CI = 4.59%, 4.64%) in the capture-recapture approach and 4.29% (95% CrI = 3.49%, 5.32%) in the Bayesian model. Both estimates were approximately four times higher than NSDUH estimates.

CONCLUSION

The synthesis of our findings suggests that the disease surveillance system misses a large portion of the population with OUD. Our study also suggests that concurrent use of multiple methods improves the justification and facilitates the triangulation and interpretation of the resulting estimates.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT04111939.

The prevalence of opioid use disorder in Kentucky's counties: A two-year multi-sample capture-recapture analysis

BACKGROUND

Kentucky has one of the highest opioid overdose mortality rates in the United States. Accurate estimates of people with opioid use disorder (OUD) are critical to plan for the scope of interventions required to reduce overdose and opioid misuse. Commonly used household surveys are known to underestimate OUD at the state-level and do not provide county-level estimates.

METHODS

We performed a multi-sample capture-recapture analysis to estimate OUD prevalence in Kentucky in 2018 and 2019. We utilized four statewide datasets that were linked at the individual level: 1) Registry of Vital Statistics, 2) Emergency Medical Services (EMS), 3) Kentucky's Prescription Drug Monitoring Program (PDMP), and 4) Kentucky Medicaid. We included persons aged 18-64 years who resided in Kentucky between 2018 and 2019. We identified individuals with administrative data consistent with OUD in each of the datasets, including a fatal opioid-involved overdose (Vital Statistics), EMS runs for suspected opioid overdose, receipt of buprenorphine for OUD treatment (PDMP), or Medicaid claims for OUD. Observed and estimated counts of OUD cases and prevalence of OUD among the adult population in Kentucky.

RESULTS

The estimated statewide OUD prevalence was 5.5 % and 5.9 % for 2018 and 2019, respectively, ranging from 1.3 % to 17.7 % across Kentucky counties. As expected, counties with the highest OUD rates were Appalachian counties (eastern area) of the state.

CONCLUSIONS

Our analysis reveals a substantially larger proportion of KY residents have OUD than previously estimated. Our approach offers a model for states needing county-level estimates of OUD.

A Bayesian approach to correct the under-count of cancer registry statistics before population-based cancer registry program

Aim

This study aims to correct undercounts in cancer data before initiating a population-based cancer registry program, employing an innovative Bayesian methodology.

Background

Underestimation is a widespread issue in cancer registries within developing countries.

Methods

This secondary study utilized cancer registry data. We employed the Bayesian approach to correct undercounting in cancer data from 2005 to 2010, using the ratio of pathology to population-based data in the Golestan province as the initial value.

Results

The results of this study showed that the lowest percentage of undercounting belonged to Khorasan Razavi province with an average of 21% and the highest percentage belonged to Sistan and Baluchestan province with an average of 38%.The average age-standardized incidence rate (ASR) for all provinces of the country except Golestan province was equal to 105.72 (Confidence interval (CI) 95% 105.35-106.09) per 100,000 and after Bayesian correction was 137.17 (CI 95% 136.74-137.60) per 100,000. In 2010 the amount of ASR before Bayesian correction was 100.28 (CI 95% 124.39-127.09) per 100,000 for women and 136.49 (CI 95% 171.20-174.38) per 100,000 for men. Also, after implementing the Bayesian correction, ASR increased to 125.74 per 100,000 for women and 172.79 per 100,000 for men.

Conclusion

The study demonstrates the effectiveness of the Bayesian approach in correcting undercounting in cancer registries. By utilizing the Bayesian method, the average ASR after Bayesian correction with a 29.74 percent change was 137.17 per 100,000. These corrected estimates provide more accurate information on cancer burden and can contribute to improved public health programs and policy evaluation. Furthermore, this research emphasizes the suitability of the Bayesian method for addressing underestimation in cancer registries. It also underscores its pivotal role in shaping the trajectory of future investigations in this field.

Cross-sectional study investigating the prevalence and causes of vision impairment in Northwest Portugal using capture-recapture

OBJECTIVES

The aim of this study was to estimate the prevalence and causes of vision impairment (VI) in Portugal.

SETTING

Information about people with VI was obtained from primary care centres, blind association (ACAPO) and from hospitals (the PCVIP study) in the Northwest of Portugal during a period spanning years 2014-2015. Causes of VI were obtained from hospitals.

PARTICIPANTS

Administrative and medical records of people with visual acuity in the better seeing eye of 0.5 decimal (0.30logMAR) or worse and/or visual field less than 20° were investigated. Capture-recapture with log-linear models was applied to estimate the number of individuals missing from lists of cases obtained from available sources.

PRIMARY AND SECONDARY OUTCOME MEASURES

Log-linear models were used to estimate the crude prevalence and the category specific prevalence of VI.

RESULTS

Crude prevalence of VI was 1.97% (95% CI 1.56% to 2.54%), and standardised prevalence was 1% (95% CI 0.78% to 1.27%). The age-specific prevalence was 3.27% (95% CI 2.36% to 4.90%), older than 64 years, 0.64% (95% CI 0.49% to 0.88%), aged 25-64 years, and 0.07% (95% CI 0.045% to 0.13%), aged less than 25 years. The female-to-male ratio was 1.3, that is, higher prevalence among females. The five leading causes of VI were diabetic retinopathy, cataract, age-related macular degeneration, glaucoma and disorders of the globe.

CONCLUSIONS

The prevalence of VI in Portugal was within the expected range and in line with other European countries. A significant number of cases of VI might be due to preventable cases and, therefore, a reduction of the prevalence of VI in Portugal seems possible. Women and old people were more likely to have VI and, therefore, these groups require extra attention. Future studies are necessary to characterise temporal changes in prevalence of VI in Portugal.

Multifile Partitioning for Record Linkage and Duplicate Detection

Merging datafiles containing information on overlapping sets of entities is a challenging task in the absence of unique identifiers, and is further complicated when some entities are duplicated in the datafiles. Most approaches to this problem have focused on linking two files assumed to be free of duplicates, or on detecting which records in a single file are duplicates. However, it is common in practice to encounter scenarios that fit somewhere in between or beyond these two settings. We propose a Bayesian approach for the general setting of multifile record linkage and duplicate detection. We use a novel partition representation to propose a structured prior for partitions that can incorporate prior information about the data collection processes of the datafiles in a flexible manner, and extend previous models for comparison data to accommodate the multifile setting. We also introduce a family of loss functions to derive Bayes estimates of partitions that allow uncertain portions of the partitions to be left unresolved. The performance of our proposed methodology is explored through extensive simulations.

Use of Population-Based Surveys for Estimating the Population Size of Persons Who Inject Drugs in the United States

BACKGROUND

In the United States, injection is an increasingly common route of administration for opioids and other substances. Estimates of the number of persons who inject drugs (PWID) are needed for monitoring risk-specific infectious disease rates and health services coverage.

METHODS

We reviewed design and instruments for 4 national household surveys, 2012-2016, for their ability to produce unbiased injection drug use (IDU) prevalence estimates. We explored potential analytic adjustments for reducing biases through use of external data on (1) arrest, (2) narcotic overdose mortality, and (3) biomarker-based sensitivity of self-reported illicit drug use.

RESULTS

Estimated national past 12 months IDU prevalence ranged from 0.24% to 0.59% across surveys. All surveys excluded unstably housed and incarcerated persons, and estimates were based on <60 respondents reporting IDU behavior in 3 surveys. No surveys asked participants about nonmedical injection of prescription drugs. Analytic adjustments did not appreciably change IDU prevalence estimates due to suboptimal specificity of data points.

CONCLUSIONS

PWID population size estimates in the United States are based on small numbers and are likely biased by undercoverage of key populations and self-report. Novel methods as discussed in this article may improve our understanding of PWID population size and their health needs.

The definition and measurement of heterogeneity

Heterogeneity is an important concept in psychiatric research and science more broadly. It negatively impacts effect size estimates under case-control paradigms, and it exposes important flaws in our existing categorical nosology. Yet, our field has no precise definition of heterogeneity proper. We tend to quantify heterogeneity by measuring associated correlates such as entropy or variance: practices which are akin to accepting the radius of a sphere as a measure of its volume. Under a definition of heterogeneity as the degree to which a system deviates from perfect conformity, this paper argues that its proper measure roughly corresponds to the size of a system's event/sample space, and has units known as numbers equivalent. We arrive at this conclusion through focused review of more than 100 years of (re)discoveries of indices by ecologists, economists, statistical physicists, and others. In parallel, we review psychiatric approaches for quantifying heterogeneity, including but not limited to studies of symptom heterogeneity, microbiome biodiversity, cluster-counting, and time-series analyses. We argue that using numbers equivalent heterogeneity measures could improve the interpretability and synthesis of psychiatric research on heterogeneity. However, significant limitations must be overcome for these measures-largely developed for economic and ecological research-to be useful in modern translational psychiatric science.

Size of the Adult HIV-Infected Population Adjusted for the Unreported AIDS Mortality in the Santa Catarina State, Brazil, 2008-2017

OBJECTIVE

To estimate the number of 15-79-year-old individuals infected with HIV in the Santa Catarina state, Brazil, during the period 2008-2017.

METHODS

Three official registers of the HIV-infected individuals were compiled: SINAN for the HIV/AIDS epidemiological surveillance, SIM for mortality and SISCEL for the HIV viral load and CD4/CD8 cell count. Their records were linked by a unique personal identifier. Capture-recapture estimates were obtained by log-linear modelling with both the main effects and interaction between the registers, adjusted for age, sex and period. An adjustment for underreporting of AIDS-related deaths used published data on ill-defined causes of death and AIDS mortality.

RESULTS

After data sorting, 67340 HIV/AIDS records were identified: 29734 (44.2%) by SINAN, 5540 (8.2%) by SIM and 32066 (47.6%) by SISCEL. After record linkage, the HIV population size was estimated at 45707, whereas the capture-recapture method added 44 individuals. The number of new HIV/AIDS notifications per year increased significantly in 2014-2017 compared to the period 2011-2013 among 15-34-year-old men and less so for older men and women. Including 1512 unreported AIDS-related deaths gave an estimated 47263 HIV-infected individuals with 95% confidence interval (CI) of 47245-47282 and corresponding incidence of 93 (95% CI 91-96) p/100000. Case ascertainment of 62.9%, 78.5% and 67.8% was estimated for SINAN, SIM and SISCEL, respectively.

CONCLUSION

Three major HIV/AIDS registers in Brazil showed significant under-notification of the HIV/AIDS epidemiological surveillance amenable to significant improvement by routine record linkage.

Estimating the prevalence of congenital heart disease among adolescents and adults in Colorado adjusted for incomplete case ascertainment

BACKGROUND

Congenital heart defects (CHDs), the most common type of birth defect in the United States, are increasing in prevalence in the general population. Though CHD prevalence at birth has been well described in the United States at about 1%, little is known about long-term survival and prevalence of CHDs beyond childhood. This study aimed to estimate the prevalence of CHDs among adolescents and adults in Colorado.

METHODS

The prevalence of CHDs among adolescents and adults residing in Colorado during 2011 to 2013 was estimated using log-linear capture-recapture methods to account for incomplete case ascertainment. Five case-finding data sources were used for this analysis including electronic health record data from 4 major health systems and a state-legislated all payer claims database.

RESULTS

Twelve thousand two hundred ninety-three unique individuals with CHDs (2481 adolescents and 9812 adults) were identified in one or more primary data sources. We estimated the crude prevalence of CHDs in adolescents and adults in Colorado to be 3.22 per 1000 individuals (95% CI 3.19-3.53). After accounting for incomplete case ascertainment, the final capture-recapture model yielded an estimated total adolescent and adult CHD population of 23,194 (95% CI 22,419-23,565) and an adjusted prevalence of 6.07 per 1000 individuals (95% CI 5.86-6.16), indicating 47% of the cases in the catchment area were not identified in the case-identifying data sources.

CONCLUSION

This statewide study yielded new information on the prevalence of CHDs in adolescents and adults. These high prevalence rates underscore the need for additional specialized care facilities for this population with CHDs.

Estimating overdispersion in sparse multinomial data

Multinomial data arise in many areas of the life sciences, such as mark-recapture studies and phylogenetics, and will often by overdispersed, with the variance being higher than predicted by a multinomial model. The quasi-likelihood approach to modeling this overdispersion involves the assumption that the variance is proportional to that specified by the multinomial model. As this approach does not require specification of the full distribution of the response variable, it can be more robust than fitting a Dirichlet-multinomial model or adding a random effect to the linear predictor. Estimation of the amount of overdispersion is often based on Pearson's statistic X² or the deviance D. For many types of study, such as mark-recapture, the data will be sparse. The estimator based on X² can then be highly variable, and that based on D can have a large negative bias. We derive a new estimator, which has a smaller asymptotic variance than that based on X² , the difference being most marked for sparse data. We illustrate the numerical difference between the three estimators using a mark-recapture study of swifts and compare their performance via a simulation study. The new estimator has the lowest root mean squared error across a range of scenarios, especially when the data are very sparse.