Variance models of the last age interval and their impact on life expectancy at subnational scales

Exact confidence intervals for population growth rate, longevity and generation time

By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into its dynamics. Although point estimates of demographic parameters have been available since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces the first mathematical expression for calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. The key finding is the accurate estimation of the confidence interval for r, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organized in extended life tables or as a matrix of vital rates. We have developed and provided accompanying code to facilitate these computations.

Flexible parametric methods for calculating life expectancy in small populations

BACKGROUND

Life expectancy is a simple measure of assessing health differences between two or more populations but current life expectancy calculations are not reliable for small populations. A potential solution to this is to borrow strength from larger populations from the same source, but this has not formally been investigated.

METHODS

Using data on 451,222 individuals from the Clinical Practice Research Datalink on the presence/absence of intellectual disability and type 2 diabetes mellitus, we compared stratified and combined flexible parametric models, and Chiang's methods, for calculating life expectancy. Confidence intervals were calculated using the Delta method, Chiang's adjusted life table approach and bootstrapping.

RESULTS

The flexible parametric models allowed calculation of life expectancy by exact age and beyond traditional life expectancy age thresholds. The combined model that fit age interaction effects as a spline term provided less bias and greater statistical precision for small covariate subgroups by borrowing strength from the larger subgroups. However, careful consideration of the distribution of events in the smallest group was needed.

CONCLUSIONS

Life expectancy is a simple measure to compare health differences between populations. The use of combined flexible parametric methods to calculate life expectancy in small samples has shown promising results by allowing life expectancy to be modelled by exact age, greater statistical precision, less bias and prediction of different covariate patterns without stratification. We recommend further investigation of their application for both policymakers and researchers.

Estimation of confidence intervals for decompositions and other complex demographic estimators

BACKGROUND

While the use of standard errors and confidence intervals is common in regression-based studies in the population sciences, it is far less common in studies using formal demographic measures and methods, including demographic decompositions.

OBJECTIVE

This article describes and provides explicit instructions for using four different approaches for computing standard errors for complex demographic estimators.

METHODS

Standard errors for Arriaga's decomposition of life expectancy differences are computed using the delta method, the Poisson bootstrap, the binomial bootstrap, and the Monte Carlo approaches. The methods are demonstrated using a 50% sample of vital statistics data on age-specific mortality among urban women in the Pacific region of the United States in 1990 and 2019.

RESULTS

All four methods for computing standard errors returned similar estimates, with the delta method, Poisson bootstrap, and Monte Carlo approaches being the most consistent. The Monte Carlo approach is recommended for general use, while the delta method is recommended for specific cases.

CONTRIBUTION

This study documents multiple ways of estimating statistical uncertainty for complex demographic estimators and describes in detail how to apply these various methods to nearly any rate-based demographic measure. It also provides advice on when the use of standard errors is and is not appropriate in demographic studies. Explicit formulae for computing standard errors for Arriaga's decomposition using the delta method approach are derived.

Immortal time bias for life-long conditions in retrospective observational studies using electronic health records

Background

Immortal time bias is common in observational studies but is typically described for pharmacoepidemiology studies where there is a delay between cohort entry and treatment initiation.

Methods

This study used the Clinical Practice Research Datalink (CPRD) and linked national mortality data in England from 2000 to 2019 to investigate immortal time bias for a specific life-long condition, intellectual disability. Life expectancy (Chiang’s abridged life table approach) was compared for 33,867 exposed and 980,586 unexposed individuals aged 10+ years using five methods: (1) treating immortal time as observation time; (2) excluding time before date of first exposure diagnosis; (3) matching cohort entry to first exposure diagnosis; (4) excluding time before proxy date of inputting first exposure diagnosis (by the physician); and (5) treating exposure as a time-dependent measure.

Results

When not considered in the design or analysis (Method 1), immortal time bias led to disproportionately high life expectancy for the exposed population during the first calendar period (additional years expected to live: 2000–2004: 65.6 [95% CI: 63.6,67.6]) compared to the later calendar periods (2005–2009: 59.9 [58.8,60.9]; 2010–2014: 58.0 [57.1,58.9]; 2015–2019: 58.2 [56.8,59.7]). Date of entry of diagnosis (Method 4) was unreliable in this CPRD cohort. The final methods (Method 2, 3 and 5) appeared to solve the main theoretical problem but residual bias may have remained.

Conclusions

We conclude that immortal time bias is a significant issue for studies of life-long conditions that use electronic health record data and requires careful consideration of how clinical diagnoses are entered onto electronic health record systems.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01581-1.

Comparative Methodologic and Practical Considerations for Life Expectancy as a Public Health Mortality Measure

INTRODUCTION

Life expectancy is a public health metric used to assess mortality. We describe life expectancy calculations for US counties and present methodologic considerations compared with years of potential life lost before age 75 (YPLL-75) and premature age-adjusted mortality (PAAM), 2 commonly used length-of-life metrics.

METHODS

We used death data from the National Center for Health Statistics for 2015-2017 and other health measures from the 2019 County Health Rankings & Roadmaps. We calculated life expectancy from birth at the county level using an abridged life table and the Chiang method of variance. Studentized residuals identified counties with discordant life expectancy and YPLL-75 or PAAM values. Correlations tested associations of life expectancy with key health measures (eg, smoking, child poverty, uninsured).

RESULTS

Among 3073 US counties, life expectancy ranged from 62.4 to 98.0 years, with a mean of 77.4 years. Life expectancy was strongly and negatively correlated with YPLL-75 (r = -0.91) and PAAM (r = -0.95) at the county level. Life expectancy was also associated with other key health metrics, such as smoking, employment, and education rates, where an improvement in the health factor indicated improvement in the respective length-of-life measure. Counties with discordant life expectancy and YPLL-75 or PAAM values had differing age structures.

PRACTICE IMPLICATIONS

Commonly used length-of-life metrics in population health settings are differentiated by methodological matters, such as computation complexity, data availability, and differential risk among age groups, especially among the very old or very young. The choice of metric should consider these factors, in addition to practical concerns, such as the communication needs of the audience.

Life Expectancy At The US-Mexico Border: Evidence Of Disparities By Place, Race, And Ethnicity

The mortality experience for the cluster of US counties in the US-Mexico border region has not been well described. We calculated 2016-18 life expectancy for the border region (counties within 100 kilometers of the border), making key comparisons to the US overall and to nonborder counties in border states. Life expectancy from birth for the border region was 81.1 years, which was greater than for the US and for the nonborder counties of border states. However, the disparity in life expectancy between racial/ethnic subgroups in the border region was also greater, within a range of more than thirteen years. Although White, Black, and Asian residents of the border region could expect to live significantly longer than residents of the US and nonborder counties of border states, Hispanic and American Indian residents could not. Understanding the mortality experience via life expectancy can help public health professionals and leaders prioritize efforts to ensure that all border residents have an equal opportunity to live a long, healthy life.