The Life Table Population Identity: Discovery, Formulations, Proof, Extensions, and Applications

Changes in emergency department visits and mortality during the COVID-19 pandemic: a retrospective analysis of 956 hospitals

BACKGROUND

During the COVID-19 pandemic, many non-COVID-19 emergency department (ED) visits were indirectly affected. ED visits and mortality were assessed during different pandemic time periods compared with pre-pandemic.

METHODS

The study used data from 41 million Iran Health Insurance Organization members. The outcomes were non-COVID-19 ED visits and associated mortality in 956 hospitals. An analysis of ED visits was conducted both for all-cause and cause-specific conditions: cardiovascular diseases (CVD), mental and substance use disorders, unintentional injuries, and self-harm. In addition, total in-hospital ED mortality was analyzed. A negative binomial regression and a Poisson regression with a log link were used to estimate the incidence rate ratio (IRR) of visits and mortality relative risk (RR).

RESULTS

1,789,831 ED visits and 12,377 deaths were reported during the study. Pre-pandemic (Sep 2019 to Feb 2020), there were 2,767 non-COVID-19 visits rate per million person-month, which decreased to 1,884 during the first COVID-19 wave with a national lockdown from Feb 20 to Apr 19, 2020 (IRR 0.68, [0.56-0.84]). The non-COVID-19 ED mortality risk was 8.17 per 1,000 visit-month during the pre-pandemic period, rising to 12.80 during the first wave of COVID-19 (RR 1.57, [1.49-165]). Non-COVID-19 ED visit rates decreased during the first pandemic year from Sep 2020 to Feb 2021 (IRR 0.73, [0.63-0.86]), but increased after COVID-19 vaccination two years later from Sep 2021 to Feb 2022 (IRR 1.11, [0.96-0.17]). The total ED mortality risk for non-COVID-19 was significantly higher after the COVID-19 outbreak in the first (RR 1.66, [1.59-1.72]) and second years (RR 1.27, [1.22-1.32]) of the pandemic. The visit incidence rate for mental health and substance use disorders declined from 8.18 per million person-month to 4.57 (IRR 0.53, [0.32 to 0.90]) in the first wave. In the second year, unintentional injury visits increased significantly compared with pre-pandemic (IRR 1.63, [1.30-2.03]). As compared to before the pandemic, there was no significant change in CVD and self-harm visit rates during the pandemic. Cardiac arrest was the leading cause of death in Iran hospitals' EDs.

CONCLUSION

In the first year of the COVID-19 pandemic, non-COVID-19 hospital ED visits declined and mortality risk increased. Despite two years since the COVID-19 outbreak, non-COVID-19 ED mortality risk remains high.

Congressional Symmetry: Years Remaining Mirror Years Served in the U.S. House and Senate

Our overarching goal in this paper was to both test and identify applications for a fundamental theorem of replacement-level populations known as the Stationary Population Identity (SPI), a mathematical model that equates the fraction of a population age x and the fraction with x years to live. Since true stationarity is virtually non-existent in human populations as well as in populations of non-human species, we used historical data on the memberships in both chambers of the U.S. Congress as population proxies. We conceived their fixed numbers (e.g., 100 Senators; 435 Representatives) as stationary populations, and their years served and years remaining as the equivalent of life lived and life remaining. Our main result was the affirmation of the mathematical prediction-i.e., the robust symmetry of years served and years remaining in Congress over the approximately 230 years of its existence (1789-2022). A number of applications emerged from this regularity and the distributional patterns therein including (1) new metrics such as Congressional half-life and other quantiles (e.g., 95% turnover); (2) predictability of the distribution of member's years remaining; (3) the extraordinary information content of a single number-the mean number of years served [i.e., derive birth (b) and death (d) rates; use of d as exponential rate parameter for model life tables]; (4) the concept of and metrics associated with period-specific populations (Congress); (5) Congressional life cycle concept with Formation, Growth, Senescence and Extinction Phases; and (6) longitudinal party transition rates for 100% Life Cycle turnover (Democrat/Republican) i.e., each seat from predecessor party-to-incumbent party and from incumbent party-to-successor party. Although our focus is on the use of historical data for Congressional members, we believe that most of the results are general and thus both relevant and applicable to most types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).

Stationary status of discrete and continuous age-structured population models

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals. This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.

A Partition Theorem for a Randomly Selected Large Population

A theorem on the partitioning of a randomly selected large population into stationary and non-stationary components by using a property of the stationary population identity is stated and proved. The methods of partitioning demonstrated are original and these are helpful in real-world situations where age-wise data is available. Applications of this theorem for practical purposes are summarized at the end.

A model for the relationship between wing fray and chronological and ovarian ages in tsetse (Glossina spp)

Age-dependent mortality changes in haematophagous insects are difficult to measure but are important determinants of population dynamics and vectorial capacity. A Markov process was used to model age-dependent changes in wing fray in tsetse (Glossina spp), calibrated using published mark-recapture data for male G. m. morsitans in Tanzania. The model was applied to female G. m. morsitans, captured in Zimbabwe using a vehicle-mounted electric net and subjected to ovarian dissection and wing fray analysis. Rates of fray increased significantly with age in males but not females, where the rate was constant for ovarian categories 0-3. A jump in mean fray between ovarian categories 3 and 4 + 4n is consistent with the latter category including flies that have ovulated 4, 8, 12, 16 times and so on. The magnitude of the jump could, theoretically, facilitate improved mortality estimates. In practice, although knowledge of fly mortality was required for modelling wing fray, mortality estimates derived from ovarian dissection data are independent of patterns and rates of change in wing fray. Significantly better fits to ovarian age data resulted when age-specific mortality was modelled as the sum of two exponentials, with high mortality in young and old flies, than when mortality was constant at 2.3% per day.

On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations

A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.