Comment by graeme

Depends if they meant rates or rates by age. If you mean population rates, then rising life expectancy caused by a decrease in other causes of death would absolutely increased overall pop alzheimer's rates.

If other causes of death were eliminated, you might also see an increase in alzheimer's amongst those in the same age bracket. This might be clearest with an example.

Suppose we eliminated heart disease. Life expectancy would increase. What would happen to the rates of other disease? They would go up within age groups. Because you still have to die of something. If heart disease can't take someone out, that means some other factor will be available. Much of the time people have more than one condition.