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.

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.

Overdose and mortality risk following a non-fatal opioid overdose treated by Emergency Medical Services in King County, Washington.

BACKGROUND: Emergency Medical Services (EMS) agencies respond to hundreds of thousands of acute overdose events each year. We conducted a retrospective cohort study of EMS patients who survived a prior opioid overdose in 2019-2021 in King County, Washington. METHODS: A novel record linkage algorithm was applied to EMS electronic health records and the state vital statistics registry to identify repeat overdoses and deaths that occurred up to 3 years following the index opioid overdose. We measured overdose incidence rates and applied survival analysis techniques to assess all-cause and overdose-specific mortality risks. RESULTS: In the year following the index opioid overdose, the overdose (fatal or non-fatal) incidence rate was 23.3 per 100 person-year, overdose mortality rate was 2.7 per 100 person-year, and all-cause mortality rate was 5.2 per 100 person-year in this cohort of overdose survivors (n=4234). Overdose incidence was highest in the first 30 days following the index overdose (43 opioid overdoses and 4 fatal overdoses per 1000 person-months), declined precipitously, and then plateaued from the third month onwards (10-15 opioid overdoses and 1-2 fatal overdoses per 1000 person-months). Overdose incidence rates, measured at 30 days, were highest among overdose survivors who were young, male, and experienced a low severity index opioid overdose, but these differences diminished when measured at 12 months. CONCLUSIONS: Among EMS patients who survived an opioid overdose, the risk of subsequent overdose is high, especially in the weeks following the index opioid overdose. Non-fatal overdose may represent a pivotal time to connect patients with harm-reduction, treatment, and other support services.

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.

Comparing Methods for Record Linkage for Public Health Action: Matching Algorithm Validation Study.

BACKGROUND: Many public health departments use record linkage between surveillance data and external data sources to inform public health interventions. However, little guidance is available to inform these activities, and many health departments rely on deterministic algorithms that may miss many true matches. In the context of public health action, these missed matches lead to missed opportunities to deliver interventions and may exacerbate existing health inequities. OBJECTIVE: This study aimed to compare the performance of record linkage algorithms commonly used in public health practice. METHODS: We compared five deterministic (exact, Stenger, Ocampo 1, Ocampo 2, and Bosh) and two probabilistic record linkage algorithms (fastLink and beta record linkage [BRL]) using simulations and a real-world scenario. We simulated pairs of datasets with varying numbers of errors per record and the number of matching records between the two datasets (ie, overlap). We matched the datasets using each algorithm and calculated their recall (ie, sensitivity, the proportion of true matches identified by the algorithm) and precision (ie, positive predictive value, the proportion of matches identified by the algorithm that were true matches). We estimated the average computation time by performing a match with each algorithm 20 times while varying the size of the datasets being matched. In a real-world scenario, HIV and sexually transmitted disease surveillance data from King County, Washington, were matched to identify people living with HIV who had a syphilis diagnosis in 2017. We calculated the recall and precision of each algorithm compared with a composite standard based on the agreement in matching decisions across all the algorithms and manual review. RESULTS: In simulations, BRL and fastLink maintained a high recall at nearly all data quality levels, while being comparable with deterministic algorithms in terms of precision. Deterministic algorithms typically failed to identify matches in scenarios with low data quality. All the deterministic algorithms had a shorter average computation time than the probabilistic algorithms. BRL had the slowest overall computation time (14 min when both datasets contained 2000 records). In the real-world scenario, BRL had the lowest trade-off between recall (309/309, 100.0%) and precision (309/312, 99.0%). CONCLUSIONS: Probabilistic record linkage algorithms maximize the number of true matches identified, reducing gaps in the coverage of interventions and maximizing the reach of public health action.