Carl P. Schmertmann’s research while affiliated with Florida State University and other places

Background: High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these purposes, but it in small samples it can often produce implausible age schedule estimates. Objective: I propose and evaluate a new type of P-spline model for estimating demographic rate schedules. These estimators, which I call D-splines, regularize and smooth high-dimensional splines by using demographic patterns rather than generic mathematical rules. Methods: I compare P-spline estimates of age-specific mortality rates to three alternative D-spline estimators, over a large number of simulated small populations with known rates. The penalties for the D-spline estimators are derived from patterns in the Human Mortality Database. Results: For mortality estimates in small populations, D-spline estimators generally have lower errors than standard P-splines. Conclusions: Using penalties based on demographic information about patterns and variability in rate schedules improves P-spline estimators for small populations. Contribution: This paper expands demographers' toolkit by developing a new category of P-spline estimators that are more reliable for estimating mortality in small populations.

Background: Identifying regions with low life expectancy is important to policy makers, in particular for allocating resources in the health system. Life expectancy estimates for small regions are, however, often unreliable and lead to statistical uncertainties when the underlying populations are relatively small. Methods: We combine the most recent German data available (2015-2017) with a Bayesian model that includes several methodological advances. This allows us to estimate male and female life expectancy with good precision for all 402 German districts and to quantify the uncertainty of those estimates. Results: Across districts, life expectancy varies between 75.8 and 81.2 years for men and from 81.8 to 85.7 years for women. The spatial pattern is similar for women and men. Rural districts in eastern Germany and some districts of the Ruhr region have relatively low life expectancy. Districts with relatively high life expectancies cluster in Baden-Wuerttemberg and southern Bavaria. Exploratory analysis shows that average income, population density, and number of physicians per 100 000 inhabitants are not strongly correlated with life expectancy at district level. In contrast, indicators that point to particularly disadvantaged segments of the population (unemployment rate, welfare benefits) are better predictors of life expectancy. Conclusions: We do not find a consistent urban-rural gap in life expectancy. Our results suggest that policies that improve living standards for poorer segment of the population are the most likely to reduce the existing differences in life expectancy.

The primary fertility index for a population, the total fertility rate (TFR), cannot be calculated for many areas and periods because it requires disaggregation of births by mother’s age. Here we discuss a flexible framework for estimating TFR using inputs as minimal as a population pyramid. We develop five variants, each with increasing complexity and data requirements. We test accuracy across a diverse set of data sources that comprise more than 2,400 fertility schedules with known TFR values, including the Human Fertility Database, Demographic and Health Surveys, U.S. counties, and nonhuman species. We show that even the simplest and least accurate variant has a median error of only 0.09 births per woman over 2,400 fertility schedules, suggesting accurate TFR estimation over a wide range of demographic conditions. We anticipate that this framework will extend fertility analysis to new subpopulations, periods, geographies, and even species. To demonstrate the framework’s utility in new applications, we produce subnational estimates of African fertility levels, reconstruct historical European TFRs for periods up to 150 years before the collection of detailed birth records, and estimate TFR for the United States conditional on race and household income.

We investigate a modern statistical approach to a classic deterministic demographic estimation technique. When vital event registration is missing or inadequate, it is possible to approximate a population's total fertility rate (TFR) from information about its distribution by age and sex. For example, if under-five child mortality is low then TFR is often close to seven times the child/woman ratio (CWR), the number of 0–4 year olds per 15–49-year-old woman. We analyse the formal relationship between CWR and TFR to identify sources of uncertainty in indirect estimates. We construct a Bayesian model for the statistical distribution of TFR conditional on the population's age–sex structure, in which unknown demographic quantities in the standard approximation are parameters with prior distributions. We apply the model in two case studies: to a small indigenous population in the Amazon region of Brazil that has extremely high fertility rates, and to the set of 159 counties in the US state of Georgia. A statistical approach yields important insights into the sources of error in indirect estimation, and their relative magnitudes.

High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with probabilistic prior information on death registration coverage derived from demographic estimation techniques, such as Death Distribution Methods, and from field audits by public health experts. We test the model on small-area data from Brazil. Incorporating external estimates of vital registration coverage though priors improves small-area mortality estimates by accounting for underregistration and automatically producing measures of uncertainty. Bayesian estimates show that when mortality levels in small areas are compared, noise often dominates signal. Differences in local point estimates of life expectancy are often small relative to uncertainty, even for relatively large areas in a populous country like Brazil.

We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with probabilistic prior information on death registration coverage – derived from demographic estimation techniques such as Death Distribution Methods, and from field audits done by public health experts. We test the model on small-area data from Brazil. Incorporating external estimates of vital registration coverage though priors improves small-area mortality estimates by accounting for under-registration, and by automatically producing measures of uncertainty.

A alta variabilidade dos dados nos registros vitais, em razão do baixo número de pessoas expostas, impõe sérios problemas para estimação da mortalidade por idade e sexo em pequenas áreas. Muitas abordagens atuais, incluindo as mais utilizadas no Brasil, estimam as taxas específicas de mortalidade assumindo pressupostos matemáticos rígidos sobre o verdadeiro padrão etário da mortalidade. Padronização indireta, por exemplo, assume que todas as áreas dentro de uma área maior (microrregiões em uma mesorregião, por exemplo) possuem um padrão de mortalidade idêntico, com diferença constante no nível das taxas logarítmicas por idade. Propomos um método estatístico mais flexível que combina regressão Poisson com um modelo relacional denominado TOPALS (DE BEER, 2012). Usamos o novo método para estimar as taxas específicas de mortalidade em pequenas áreas no Brasil (estados, mesorregiões, microrregiões e municípios) em 2010. Resultados para o estado de Minas Gerais mostram diferenças notáveis no padrão de mortalidade por idade entre pequenas áreas adjacentes, demonstrando as vantagens do uso de um método de estimação mais flexível.