Discrete time representation of the formula for calculating DALYs

The global burden of disease (GBD) was measured using a new indicator called disability-adjusted life years (DALYs). The formula to calculate DALYs is based on the idea of time being a continuous variable, which is not consistent with the way economic and health data are collected and reported, and is also different from the concept of time used in the vast majority of policy analyses. Use of this formula gives rise to a time-aggregation bias in the estimates of GBD. Based on discrete time representation and the key principles outlined in the GBD study, a new formula for estimating DALYs is derived in this paper. The properties of the two formulae are compared and contrasted and the implications of using the new formula are discussed. The results show that there is an appreciable difference in percentage terms (14.06%) between the burden of cataract in Sub-Saharan Africa in 1990 calculated using the new and the old formulae. The global burden of diseases and injuries as previously reported in the GDB study may, therefore, be underestimated and the relative positions of some diseases and injuries, and hence the relative priorities of related interventions, may shift if the more appropriate, discrete-time formula is used. The difference is greatest for diseases of short duration (e.g. infectious diseases).