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Forecasting Technology for the Distal Driver Formulation of Mortality

Although two IFs variables, namely GDP per capita at purchasing power parity (GDPPCP) and years of adult education (EDYRSAG25) drive the distal formulation in most of our forecasting and scenario analysis, the technology parameter (the beta on time) in the distal equation is very powerful.  We therefore want some control over it, ideally with ability to differentiate that control with respect to level of income of countries and with respect to the age structure of mortality. For a basic approach to providing such control, we follow the Global Burden of Disease (GBD) project in modifying the regression models for child mortality low-income countries.  But we have extended that GBD approach to allow some additional parametric control.

The control system in IFs uses a switching parameter ( hlmortmodsw ) in interaction with three other parameters (with their default values those are hltechbase =1, hltechlinc =0.25, and hltechssa =0); see the table below for a summary of the application of those parameters. 

In the default mode ( hlmortmodsw = 1), IFs uses the GBD approach to modifying the technology (time) coefficients for children under 5 in recognition of slower than expected historical progress in many countries. [1]   Specifically, for children under 5 in low-income countries in four regions (Africa, Europe, SE Asia and West Pacific) the time variable is held constant (zero, or no technological advance, using hltechssa ); in low-income countries in the Middle East and North Africa the coefficient on time is reduced to 25 percent of its original value using the parameter hltechlinc

In the IFs implementation of the GBD approach to treatment of technology, we wished to change the patterns not just for children under 5, but also for older children and adults.  We decided, however, to regularize the somewhat ad hoc assignment of countries by the GBD to the low-income category by defining low-income as being less than $3,000 per capita and high-income as being above that level.  We use the parameter hltechlinc to control technological change for older children and adults in low-income countries regardless of geographical region; at its default setting that parameter reduces the coefficient on time to 25 percent of its original value.

  Age and Geographic Impact of the Parameters
Base or default values For children under 5 (GBD Geographic Classification) For older children and adults (IFs Geographic Classification)
hltechssa =0 Low Income Countries in mostly 4 regions (Africa, Europe, SE Asia and West Pac; also selected countries such as Haiti) Not used
hltechlinc =0.25
Low Income Countries in the Middle East and North Africa Low Income Countries (GDPPCP < $3k in 2010)
hltechbase =1 All other countries, mostly High Income and including most of Latin America High Income Countries (GDPPCP >= $3k in 2010)

For children older than 5 and adults in what IFs classifies as high-income countries (countries with GDP per capita at PPP in 2010 above $3,000), IFs uses the parameter hltechbase .  Thus in the default situation, technological change is unchanged from the basic value.      

These GBD technology factor modifications (and their extensions by IFs to adults and older children in our definition of low- and high-income countries) can be turned off in the model ( hlmortmodsw = 0). [2] When the switch is turned on, adjustments can also be made to hltechbase , hltechlinc , and hltechssa to build new scenarios. [3]   It is important for the user to know, however, that regardless of age or income level of countries, the model uses hltechbase for mortality from cardiovascular causes (which uses a different regression model for forecasting).

Changes to hltechbase can also be adjusted by using a shift parameter called hltechshift (0 by default), which adjusts the technology factor depending on the level of initial GDP per capita at PPP. 

technology equation

This adjustment increases the technology factor for high income countries more quickly than for middle or low-income countries.



[1] The Global   Burden of Disease (GBD) project  made low-income modifications after recognizing that historical child mortality data did not match back projections of the model (Mathers and Loncar 2006b: 9).  Note that the GBD approach to these modifications changed from the 2002 revision to the 2004 revision of the project. In the 2002 revision, the human capital (education) beta was reduced to half of its magnitude for sub-Saharan countries, and to 75 percent of its original magnitude for other low-income countries. This was done only if the beta on the human capital (education) term in the distal model formulation was negative (reducing mortality with increases in education).  Technological advance factor (time) was left constant (no advance) for sub-Saharan Africa and reduced to 25 percent for other low income countries.  The 2004 revision dropped the human capital modifications, but continued to reduce the coefficient on time.

[2]  Although not recommended, IFs also allows the user to use the original GBD 2002 modifications (as described in a previous footnote) by specifying  hlmortmodsw  = 2.

[3]  Given the results found for Intentional Injuries, where mortality was reaching unrealistic levels, we have limited the changes to  hltechbase  and  hltechlinc  to at most 1.5 for this particular cause of death in the 2004 revision ( hlmortmodsw  = 1).