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Normalization and Scaling Factors

IFs initializes the base year (2010) data using age, sex, cause, and country-specific mortality data for 2010 provided by the Global Burden of Disease (GBD), courtesy of Colin Mathers at the World Health Organization.  Those data are for infants and then for 5-year age categories up to 85+.  To fill holes we used the same base rates for 1-4 as for infants and for all 5-year age categories above 85, subject to normalization to total mortality for the age category.  The model then computes normalization and scaling factors which reconcile the results of the forecast regression models with these initial data. 

The normalization factor helps match the sum of all mortalities in the health module to the mortality computed in the population module in the base year (2010).  This process assures that we have initial conditions consistent with UNPD mortality data in our base year (i.e., the sum of all deaths will be the same as the UNPD mortality data for each 5-year age and sex category for the year 2010).  The normalization factor uses all types of mortality except for AIDS in the numerator and denominator:

Normalization equation 1

The scaling factor sets the historic proportions across the different causes of mortality, assuring consistency of total deaths forecast using the GBD formulations and our 2010 values of driving variables with the cause-specific mortality data in the GBD’s detailed death file.  The scaling factor uses distal driver regression results for the denominator and GBD 2010 data for the numerator:

Normalization equation 2

These adjustments mean that, except for the total mortality by age and sex of the UN, our numbers in the 2010 base year will not match other data precisely, but that the overall pattern of deaths by cause should be quite close to the GBD data. [1]   In the forecasts themselves, we keep the multiplicative scaling and normalization parameters constant over time because there is no clear reason for changing them in the base, but have added parameters to control convergence in scenarios: hlgbdconvdown , hlgbdconvup , hlscaleconvdown , where the first parameter controls the normalization factor when is greater than 1, the second one controls the normalization factor when is smaller than 1, and the last one controls the scaling factor when is greater than 1.

 



[1] Complicating initialization further, the UNPD presents its data in 5-year ranges, including 2005-2010 and 2010-2015.  The age- and sex-specific survivor-table values in those ranges therefore do not correspond to specific years like our base of 2010.  After correspondence with Kirill Andreev of the UNPD, which we acknowledge appreciatively, we decided to average the mortality values in the two 5-year ranges ending and beginning with 2010.