How to estimate mortality trends from grouped vital statistics

Area of Science:

• Epidemiology
• Biostatistics
• Demography

Background:

• Population-level mortality data are often aggregated into broad age classes (e.g., 5-year groups), with open-ended intervals for older individuals.
• This coarse grouping complicates the accurate capture of detailed age-specific mortality patterns and trends, particularly for the elderly.
• Existing methods struggle to extract granular mortality insights from coarsely aggregated demographic data.

Purpose of the Study:

• To introduce and illustrate the penalized composite link model (PCLM) for ungrouping aggregated mortality data.
• To model detailed cancer mortality surfaces using PCLM, enabling the estimation of smooth age-specific distributions.
• To demonstrate the model's applicability in analyzing age-at-death distributions from comprehensive cancer registry data.

Main Methods:

• Developed a two-dimensional regression model based on B-splines to estimate smooth age-specific distributions from grouped data.
• Employed a penalized likelihood maximization approach within the penalized composite link model (PCLM) framework.
• Applied the PCLM to analyze cancer mortality data in Denmark (1980-2014) from the Danish Cancer Society and Human Mortality Database.

Main Results:

• The PCLM accurately captures key mortality trends, including a post-1990s decrease in cancer mortality for ages 50-75.
• Identified a decrease in cancer mortality in later cohorts for younger and very elderly age groups.
• Validated the model's high accuracy by comparing PCLM-derived distributions with raw single-year-of-age data.

Conclusions:

• The penalized composite link model (PCLM) effectively generates detailed, smooth mortality surfaces from aggregated counts with minimal assumptions.
• PCLM assumes Poisson-distributed counts and smoothness of the estimated distribution, offering flexibility.
• This method holds significant potential for epidemiological research, enabling the extraction of valuable insights from aggregated mortality data without strict distributional shape assumptions.