5. Sensitivity and Uncertainty Analyses for Burden of Disease and Risk Factor Estimates

Uncertainty Estimates for All-Cause Mortality and Life Expectancies

Chapters 2 and 3 describe methods for estimating life tables for each of 192 WHO member states. For those countries with vital registration data projected using time series regression models on the parameters of the logit life table system, we accounted for uncertainty around the regression coefficients by taking 1,000 draws of the parameters using the regression estimates and variance-covariance matrix of the estimators. For each of the draws, we calculated a new life table. In cases where additional sources of information provided information on the limits of uncertainty ranges around ₅q₀ (the mortality risk for children under five years of age) and ₄₅q₁₅ (the mortality risk for adults between the ages of 15 and 60), the 1,000 draws were constrained so that each life table produced estimates within these specified ranges. The range of 1,000 life tables produced by these multiple draws reflects some of the uncertainty around the projected trends in mortality, notably, the imprecise quantification of systematic changes in the logit parameters over the time period captured in available vital registration data.

For countries that did not have time series data on mortality by age and sex, the following steps were undertaken. First, point estimates and ranges around ₅q₀ and ₄₅q₁₅ for males and females were developed on a country-by-country basis as described in chapter 2 and elsewhere (Lopez and others 2002). For countries where the ₅q₀ estimate for 2001 was based on an analysis of available data sources for earlier years, such as surveys and censuses, the uncertainty range for ₅q₀ was typically dominated by the uncertainty resulting from the scatter of survey-based direct and indirect estimates of child mortality for earlier years and the uncertainty in extrapolation of the trend to 2001, rather than the sampling error associated with individual estimates. For countries without usable information on levels of adult mortality, ₄₅q₁₅ was estimated, along with uncertainty ranges, based on regression models of ₄₅q₁₅ versus ₅q₀ as observed in a set of almost 2,000 life tables judged to be of good quality. Estimated levels of child and adult mortality were then applied to a modified logit life table model, using a global standard, to estimate the full life table in 2001; HIV/AIDS deaths and war deaths were added to total mortality rates where necessary. Uncertainty ranges for HIV/AIDS were estimated as described elsewhere (Grassly and others 2004). In countries with substantial numbers of war deaths, estimates of their uncertainty range were also incorporated into the life table uncertainty analysis.

Figure 5.12 plots the final estimated uncertainty ranges for ₅q₀ and ₄₅q₁₅ for 192 WHO member states for males and females. Using Monte Carlo simulation methods, 1,000 random life tables were generated by drawing samples from normal distributions around these inputs with variances defined in reference to the defined ranges of uncertainty for ₅q₀ and ₄₅q₁₅. In countries where uncertainty around ₅q₀ and ₄₅q₁₅ was considerable because of a paucity of survey or surveillance information, the samples were drawn from wide distributions, but then constrained within prior specified maximum and minimum possible values for ₅q₀ and ₄₅q₁₅. For each country, the results of this analysis were 1,000 different simulated life tables that were then used to describe ranges around key indicators, such as life expectancy at birth and age- and sex-specific mortality rates.
[Figure 5.12]

Figure 5.13 illustrates the resulting uncertainty ranges for life expectancy at birth for the World Bank regions (see map 1 inside the book's front cover). For high-income countries, where relatively complete death registration data are available, the uncertainty ranges for life expectancy at birth are around 0.07 years for females and 0.16 years for males. For regions such as Latin America and the Caribbean, where death registration data are available for most countries but are often incomplete, the uncertainty ranges are larger, typically around 0.5 years. For regions with partial data on child mortality only, where adult mortality is predicted from child mortality, the uncertainty ranges are much larger, and for Sub-Saharan Africa are typically around 5.0 years. Across the regions, this translates to considerable heterogeneity in uncertainty ranges for life expectancies at birth and for estimates of all-cause mortality levels.
[Figure 5.13]