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It is often taken for granted that an ageing population will lead to an increased burden for the health care sector. However, for several diseases of big public health impact the rates have actually come down for a substantial period of time. In this study we investigate how much the incidence rates for myocardial infarction (MI), stroke, and cancer will have to decline in order to counterbalance future demographic changes (changes in population size and age structure) and compare these figures with observed historical trends. Information on incidence rates were obtained from the National Board of Health and Welfare and referred to the total Swedish population. Population projections were obtained from Statistics Sweden. We projected the number of MI events to increase 50-60% between 2010 and 2050. The decline in incidence rates that is required to keep the number of events constant over time is, on average, 1.2%/year for men and 0.9%/year for women, somewhat higher than the trend for the past 10 years. For stroke the corresponding figures were 1.3% (men) and 1% (women), well in line with historical trends. For cancer the results indicate an increasing number of events in the future. Population ageing is more important than population growth when projecting future number of MI, stroke and cancer events. The required changes in incidence rates in order to counterbalance the demographic changes are well in line with historical figures for stroke, almost in line regarding MI, but not in line regarding cancer. For diseases with age dependence similar to these diseases, a reduction of incidence rates in the order of 1-2% is sufficient to offset the challenges of the ageing population. These are changes that have been observed for several diseases indicating that the challenges posed by the ageing population may not be as severe as they may seem when considering the demographic component alone.