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A General Age-Specific Mortality Model With an Example Indexed by Child Mortality or Both Child and Adult Mortality

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Demography

Abstract

The majority of countries in Africa and nearly one-third of all countries require mortality models to infer the complete age schedules of mortality that are required to conduct population estimates, projections/forecasts, and other tasks in demography and epidemiology. Models that relate child mortality to mortality at other ages are important because almost all countries have measures of child mortality. A general, parameterizable component model (SVD-Comp) of mortality is defined using the singular value decomposition and calibrated to the relationship between child or child/adult mortality and mortality at other ages in the observed mortality schedules of the Human Mortality Database. Cross-validation is used to validate the model, and the predictive performance of the model is compared with that of the log-quadratic (Log-Quad) model, which is designed to do the same thing. Prediction and cross-validation tests indicate that the child mortality–calibrated SVD-Comp is able to accurately represent the observed mortality schedules in the Human Mortality Database, is robust to the selection of mortality schedules used for calibration, and performs better than the Log-Quad model. The child mortality–calibrated SVD-Comp can be used where and when child mortality is available but mortality at other ages is unknown.

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Notes

  1. The core ideas underlying the Wilmoth model appear in his doctoral dissertation (Wilmoth 1988), with further refinement in the following years, culminating in the English-language summary (Wilmoth 1990).

  2. The first left singular vector of the HMD residuals are massaged slightly to ensure all elements of v are positive and smooth.

  3. If desired, k is chosen so that the resulting mortality schedule matches an input value 45q15.

  4. This is the expression used to model the first residual in Wilmoth’s age/period/cohort model, shown in Eq. (2).

  5. SVDs are calculated using the svd function in the base package of R.

  6. This ensures that the whole data cloud is separated from the origin by an amount that is substantially greater than the typical value of each logit-transformed mortality rate, and therefore each age group has roughly equivalent leverage in the optimization required to identify the first new dimension of the SVD. The remaining dimensions are effectively identified on a centered data cloud.

  7. The SVD-Comp life tables are constructed using standard procedures in one-year age groups with nax values taken from the HMD life tables. The Log-Quad life tables are constructed using R code provided by Wilmoth et al. (2012) in five-year age groups.

  8. For components i ∈ {2, 3, 4}, kernel smoother with Gaussian kernel and bandwidth = i + 1 for ages i and older.

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Acknowledgments

This work was supported in part by Grants R01 HD086227 and R01 HD054511 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD). The funder had no part in the design, execution, or interpretation of the work. Tables of regression coefficients were formatted using the LaTeX package stargazer (Hlavac 2015).

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Authors and Affiliations

  1. Department of Sociology, The Ohio State University, Columbus, Ohio, USA

    Samuel J. Clark

  2. MRC/Wits Rural Public Health and Health Transitions Research Unit (Agincourt), School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa

    Samuel J. Clark

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Clark, S.J. A General Age-Specific Mortality Model With an Example Indexed by Child Mortality or Both Child and Adult Mortality. Demography 56, 1131–1159 (2019). https://doi.org/10.1007/s13524-019-00785-3

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