Uncertainty Estimates for Regional Mortality by Cause
We use a simulation approach to estimate uncertainty ranges for deaths by cause for GBD 2001. These uncertainty ranges take into account uncertainty in the expected number of total deaths (life table uncertainty); uncertainty in the estimated proportions of broad cause Groups I, II, and III (where relevant for countries without vital registration data or with incomplete coverage); uncertainty in the diagnosis of underlying cause; uncertainty arising from the miscoding of underlying cause; and fundamental Poisson uncertainty in the estimated death rate arising from the observation of a finite number of deaths in a fixed time interval. This analysis was carried out by country.
As described in the previous section, a total of 1,000 life tables were developed for each of the 192 WHO member states to quantify the uncertainty distribution of key life table parameters. We then used the age-specific mortality rates from the 1,000 life tables to estimate the uncertainty distribution for the expected number of total deaths for 2001. Uncertainty in the underlying cause attribution was estimated in terms of the relative uncertainty of the proportion of deaths due to each specific cause. The estimates of cause-specific relative uncertainty were based on advice from nosologists and experts in the area of cross-country mortality analysis on the general levels of uncertainty in the attribution of specific causes within Groups I, II and III, together with detailed advice on particular causes with known higher levels of attribution uncertainty according to the ICD. Information on the latter causes derives from comparative analyses across countries, across time periods, and across ICD revisions, together with information from a variety of country-specific coding quality studies involving recoding or dual coding of deaths and comparisons with the original attributed causes.
Based on this advice, for cause distributions derived from vital registration data coded using ICD-10 (the 10th edition of the ICD), we generally assumed that diagnostic uncertainty and coding uncertainty together resulted in approximate relative 95 percent uncertainty ranges of 3 percent for Group I causes, 7 percent for Group II causes, and 2 percent for Group III causes. Larger uncertainty ranges were assumed for specific causes known to have greater levels of diagnostic or coding error; for WHO member states that have been using ICD-10 coding for less than three years; for member states still using ICD-9 coding (with particular attention to causes where coding rates between ICD-9 and ICD-10 are known to differ); and for member states using other cause coding systems or verbal autopsy methods, or where cause of death models were used to estimate death distributions across Groups I, II, and III. In the latter case, an additional relative uncertainty for the estimation of Group I, II, and III proportions was estimated from the prediction uncertainty ranges associated with the CodMod regression model (see chapter 3).
Uncertainty estimates also took into account the redistribution of general, cancer, cardiovascular, and injury ill-defined cause codes and incomplete coverage of vital registration data. The relative uncertainty range for each cause was then combined with the estimated uncertainty distribution for all-cause mortality to provide estimates of the uncertainty distributions of cause-specific mortality estimates for all ages and both sexes at the country level.
The analysis of uncertainty in cause of death estimates at the country level thus combines quantitative, country-specific information on uncertainty in all-cause mortality and, in some cases, also in major cause group distributions, together with quantified average relative uncertainty ranges for specific cause attributions based on expert advice and adjusted for specific causes and for country-specific information on data sources, type of cause information available, and indicators of data quality. Here we summarize these uncertainty estimates at the regional level to provide some indication of the range of uncertainty for cause-specific mortality estimates across the World Bank regions as reported in chapter 3. This requires some additional assumptions about the cross-country correlations in uncertainty distributions.
At one extreme, if all country-level estimates have uncorrelated uncertainty because they are derived from completely independent data sets, then even with high levels of uncertainty at the country level, there will be considerably less uncertainty at the regional or global level. At the other extreme, if the uncertainty in country-level estimates for a cause derives predominantly from a single source or assumption, for example, about the case fatality rate of malaria, that is applied in deriving each country estimate, then the uncertainty distributions will be highly correlated and the regional uncertainty will be of a similar relative magnitude as each of the country uncertainty ranges.
With respect to cross-country correlations for life table and cause of death estimates based on death registration data, we assumed that even though life table uncertainties would be uncorrelated, relative uncertainties in cause of death attribution for specific causes were likely to be correlated because of systematic errors in ICD coding practices across countries for specific causes. We arbitrarily set this correlation at 25 percent. For life table estimates not based on death registration data, we assumed some correlation in uncertainty because even though estimates of childhood mortality came from independent sources, the method for determining adult mortality was similar across countries. We therefore set this correlation at 50 percent.
We assumed that cross-country correlation for relative cause of death uncertainties in the absence of vital registration data would vary depending on the method of causal attribution. Attributions based on some data and country-level predictions or assumptions were assumed to have less correlation than those based simply on regional patterns. In the case of the latter, we set the correlation at 75 percent; in the former, we set it at 50 percent or 25 percent depending on the degree of independence of the underlying inputs. We assumed greater independence for cancers and maternal conditions and less independence for tuberculosis, HIV/AIDS, sexually transmitted infections, diarrheal diseases, childhood-cluster diseases, meningitis, tropical-cluster diseases, lower respiratory infections, and perinatal conditions. We set cross-country correlations for war and drug use disorders at 25 percent for all countries, including those with vital registration data, to reflect the different methods used to obtain estimates for these causes.
We derived 95 percent uncertainty intervals by cause for World Bank regions in 2001 from the foregoing assumptions using simulation methods. We constructed 1,000 draws with the required correlation structure between countries separately for each cause, and the 2.5th percentile and the 97.5th percentile of expected deaths were taken to be the lower and upper bounds of the corresponding uncertainty interval. Note that these ranges provide guidance on uncertainty in the underlying cause-specific death rates, as expressed in terms of expected deaths in the population in 2001. Uncertainty in population estimates is not included, and the uncertainty ranges relate to underlying death rates, not to the numbers of deaths that actually occurred in 2001.
Table 5.5 summarizes regional uncertainty ranges for total estimated deaths for selected causes for 2001. Uncertainty ranges for estimated all-cause deaths increase from around 1 percent for high-income countries to (-15 percent, +21 percent) for Sub-Saharan Africa. For specific causes, regional uncertainty ranges are generally higher, except for those causes for which cause-specific mortality estimates were available based on country-specific data from cause-specific surveillance systems (see chapter 3). For example, the uncertainty range for HIV/AIDS deaths in Sub-Saharan Africa is somewhat narrower than the all-cause mortality range, reflecting the substantial database for these estimates from antenatal clinic surveillance data and seroprevalence surveys, albeit still with considerable uncertainty arising from issues around the representativeness of the available data and the assumptions relating to survival and case fatality rates (Grassly and others 2004).
[Table .]
For most other causes, uncertainty ranges are greater than for the all-cause mortality estimates, because additional uncertainty is associated with cause attribution, as described earlier. For example, the relative uncertainty ranges for ischemic heart disease range from around 12 percent for high-income countries to (-24 percent, +34 percent) for Sub-Saharan Africa (table 5.5). While the uncertainty range for high-income countries may seem surprisingly large, it reflects not only uncertainty in overall mortality levels, but also uncertainty in the attribution of underlying cause and in the attribution of causes coded to cancer, cardiovascular, and injury ill-defined cause codes or to the ICD chapter for symptoms, signs, and ill-defined conditions. The proportion of deaths coded to these two groups of causes is surprisingly large for some high-income countries (Mathers and others 2005).
Figure 5.14 illustrates the relative insensitivity of the regional uncertainty ranges to the assumptions about cross-country correlation of uncertainty. The broad patterns of the uncertainty ranges for causes across regions provide useful additional guidance to policy makers in interpreting regional differences, particularly in judging which policy questions these estimates can help address and for which the uncertainty levels are too great to allow useful inferences.
[Figure
5.14]
