Estimating age- and sex-specific mortality rates for small areas with TOPALS regression: an application to Brazil in 2010

Abstract

High variability in recorded vital events creates serious problems for small-area mortality estimation by age and sex. Many existing approaches to fitting local mortality schedules, including those most often used in Brazil, estimate rates by making rigid mathematical assumptions about local age patterns. Such methods assume that all areas within a larger area (for example, microregions within a mesoregion) have identically-shaped log mortality schedules by age. We propose a more flexible statistical estimation method that combines Poisson regression with the TOPALS relational model (DE BEER, 2012). We use the new method to estimate age-specific mortality rates in Brazilian small areas (states, mesoregions, microregions, and municipalities) in 2010. Results for Minas Gerais show notable differences in the age patterns of mortality between adjacent small areas, demonstrating the advantages of using a flexible functional form in regression models.

Temporal and spatial estimates of adult mortality for small areas in Brazil, 1980-2010

“…This often happens due to the problem of few events recorded in the denominator and/or numerator of the measures of interest resulting in unstable estimates. Such instability is even worse when sub-national groups are disaggregated by age and sex (Gonzaga and Schmertmann, 2016;Assunção et al 2005). Therefore, in small populations the estimated rates generally have extreme values leading to a large variability in the rates that do not reflect the true level of heterogeneity of the geographic location (Bernadinelli and Montomoli, 1992;Assunção et al, 2005).…”

Regional Disparities in Brazilian Adult Mortality: an analysis using Modal Age at Death (M) and Compression of Mortality (IQR)

“…Then, to generate a smoothed complete mortality schedule by age we applied two methods: Log-Quad (Wilmoth et al 2012) and TOPALS (Gonzaga &Schmertmann, 2016).…”

“…Another important feature of the method is that it can handle well when there are zero deaths or people counted in a specific year or age. In the original paper, Gonzaga and Schmertmann (2016) assert that TOPALS can be used in two ways: to estimate complete schedule of log mortality rates in areas where the coverage of vital registration is not a problem and to smooth death rates prior to correcting for undercount. In our work, since the first step was to use DDM estimates to correct for potential problems with registration system, we will use the TOPALS estimates in both ways, approximately.…”

“…We use Modal age at death and measures of mortality compression to analyze regional and gender differences. We estimate age-specific mortality rates by single ages using two approaches: Wilmoth and colleagues (2012) Log-Quad approaches and Topal´s method proposed by Gonzaga and Schmertmann (2016). Our results show that provincial disparities in mortality in general across regions of the country.…”

“…It is important to understand how such differences relate to trends and differences in adult mortality. There are several studies about trends in infant and child mortality (BARUFI et al, 2012), but much less is known about adult mortality (DUARTE et al, 2002;GONZAGA & SCHMERTMANN, 2016). We are also interested in understanding whether there is a convergence or divergence in adult mortality in Brazil.…”