E-ISSN : 2982-8007
Decomposition methods have been widely used to quantify the contributions of specific factors, such as age groups or causes of death, to mortality differences between populations or to temporal changes in mortality within the same population. However, when summary measures of mortality are derived from nonlinear functions, the application of traditional additive decomposition methods becomes problematic. Since the early 2000s, life table–based indicators of lifespan variation, in addition to age-standardized mortality rates and life expectancy, have been increasingly utilized, creating a demand for generalized decomposition methods applicable to a wide range of mortality indicators. Among the two major approaches to generalized decomposition, this study introduces the stepwise replacement algorithm and examines its practical application using illustrative data. Furthermore, for settings involving two populations observed at two time points, we present the contour replacement decomposition method, which extends the stepwise replacement algorithm to quantify contributions to both cross-sectional mortality differences between populations at the initial time point and differences in mortality change trajectories between populations over time.