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.

The WHO estimates of excess mortality associated with the COVID-19 pandemic.

The World Health Organization has a mandate to compile and disseminate statistics on mortality, and we have been tracking the progression of the COVID-19 pandemic since the beginning of 20201. Reported statistics on COVID-19 mortality are problematic for many countries owing to variations in testing access, differential diagnostic capacity and inconsistent certification of COVID-19 as cause of death. Beyond what is directly attributable to it, the pandemic has caused extensive collateral damage that has led to losses of lives and livelihoods. Here we report a comprehensive and consistent measurement of the impact of the COVID-19 pandemic by estimating excess deaths, by month, for 2020 and 2021. We predict the pandemic period all-cause deaths in locations lacking complete reported data using an overdispersed Poisson count framework that applies Bayesian inference techniques to quantify uncertainty. We estimate 14.83 million excess deaths globally, 2.74 times more deaths than the 5.42 million reported as due to COVID-19 for the period. There are wide variations in the excess death estimates across the six World Health Organization regions. We describe the data and methods used to generate these estimates and highlight the need for better reporting where gaps persist. We discuss various summary measures, and the hazards of ranking countries' epidemic responses.

A Latent Disease Model to Reduce Detection Bias in Cancer Risk Prediction Studies.

In studies of cancer risk, detection bias arises when risk factors are associated with screening patterns, affecting the likelihood and timing of diagnosis. To eliminate detection bias in a screened cohort, we propose modeling the latent onset of cancer and estimating the association between risk factors and onset rather than diagnosis. We apply this framework to estimate the increase in prostate cancer risk associated with black race and family history using data from the SELECT prostate cancer prevention trial, in which men were screened and biopsied according to community practices. A positive family history was associated with a hazard ratio (HR) of prostate cancer onset of 1.8, lower than the corresponding HR of prostate cancer diagnosis (HR = 2.2). This result comports with a finding that men in SELECT with a family history were more likely to be biopsied following a positive PSA test than men with no family history. For black race, the HRs for onset and diagnosis were similar, consistent with similar patterns of screening and biopsy by race. If individual screening and diagnosis histories are available, latent disease modeling can be used to decouple risk of disease from risk of disease diagnosis and reduce detection bias.

Undetectable prostate-specific antigen after short-course androgen deprivation therapy for biochemically recurrent patients correlates with metastasis-free survival and prostate cancer-specific survival.

BACKGROUND: Optimal utilization of novel therapies for advanced prostate cancer is challenging without a validated surrogate efficacy endpoint. Ongoing trials are using durable undetectable prostate-specific antigen (PSA) levels as a marker of efficacy. The clinical relevance of prolonged undetectable PSA after a short course of androgen deprivation therapy (ADT) is uncertain. METHODS: The University of Washington Caisis database was queried for radical prostatectomy patients who received 6-12 months of ADT after biochemical recurrence (BCR), defined as PSA ≥0.2 ng/mL and no radiographically detectable metastasis. Proportions of men with undetectable PSA 12 and 24 months after ending ADT were compared to a hypothesized 5% rate using exact binomial tests. Associations with patient and tumor characteristics were examined using logistic regression, and associations with risk of subsequent metastasis and death were evaluated by log-rank tests. RESULTS: After ineligibility exclusions, 23/93 (25%; 95%CI 16-35%; P < 0.001) and 14/93 (15%; 95%CI 9-24%; P < 0.001) had undetectable PSA 12 and 24 months after ending ADT, respectively. Detectable PSA at 12 months was associated with increased risk of metastasis (P = 0.006), prostate cancer-specific death (P = 0.028), and death from any cause (P = 0.065). Being 1 year older at diagnosis was associated with a 14% (95%CI 5-24%; P = 0.006) decrease in the odds of having a detectable PSA after controlling for PSA at diagnosis, PSA doubling time, grade group, and time from initial therapy to BCR. CONCLUSIONS: This single-institution retrospective analysis shows that it is not uncommon to have undetectable PSA 12 or 24 months after a short course of ADT. No baseline prognostic characteristic other than age was associated with a durable (12 month) undetectable PSA. Because a durable undetectable PSA was associated with lower risks of metastasis and prostate cancer-specific death, it may be a reasonable clinical trial endpoint.