Life expectancy and health outcomes

There's a literature on everything, so I expect someone's already done this. I'd be keen to see the result if someone has.

There are almost-certainly piles of disorders that are particularly damaging when you're older rather than younger, and where there are apparent differences in effect by ethnicity after correcting for age. 

I know that the Ministry of Health here has pointed to differences in Covid outcomes by ethnicity in multivariate analysis correcting for age but there will have to be lots of other ones.

There are two ways of thinking about age. You can think about it as years since birth. Or you can think about it as percent of expected life expectancy already expended. Same as how you can think about your fuel tank as how many litres of fuel you've used since you filled up, or as what percentage of the tank is left. 

Suppose that life expectancy at time of first birthday varies by ethnicity for whatever mix of environmental and genetic reasons. Fuel tanks vary in size. If you're counting litres of fuel used since the tank was full, there will be very different amounts left in the tank depending on the car. 

And suppose further that the true effect of some disorder on health outcomes depends on your remaining life expectancy before the disorder hit rather than your time since birth. Basically anyone who's at 95% of their life expectancy is going to have a rougher time with the illness regardless of whether that 95% mark hits at age 67 or age 80. 

If that's the underlying process, if you run a regression with health outcomes on the left-hand side, and age-in-years and ethnicity on the right-hand side along with whether someone catches the disorder, you're going to lump effects into ethnicity that might not really belong there for this particular disorder. 

It'll be true that a greater proportion of people with this ethnicity at that age die of the disorder, but the ethnicity variable will be a mix of underlying differences in mortality risk by ethnicity plus disorder-specific risks.

I'm not trying to criticise the MoH work here. I'm just wondering where this kind of thing has been considered in the literature. Do age-ethnicity interaction terms sort it out by allowing the effect of age on health outcomes to vary by ethnicity? MoH throws in a "hospital-registered co-morbidity" variable that will catch some of the 'effectively old for physical age' effect but wouldn't get all of it.

I just keep remembering that old Robert Fogel work looking at the health status of US Civil War enlistees, where the 50-year-olds of the 1850s were hitting the health problems of today's 70-year-olds. It'd be true to say that 50-year-olds of that era were at far higher risk of dying from heart attacks. But they were also way closer to end of expected life expectancy. So it wasn't just that heart attacks were worse then - it was that life expectancy was lower, people effectively aged more quickly, and something like a heart attack is worse when you're more run down. 

Other not-so-fun bit from that old NYT piece on the Fogel work, that could also be relevant these days:

Dr. Almond had a problem with the studies. They were not of randomly selected populations, he said, making it hard to know if other factors had contributed to the health effects. He wanted to see a rigorous test — a sickness or a deprivation that affected everyone, rich and poor, educated and not, and then went away. Then he realized there had been such an event: the 1918 flu.

The flu pandemic arrived in the United States in October 1918 and was gone by January 1919, afflicting a third of the pregnant women in the United States. What happened to their children? Dr. Almond asked.

He compared two populations: those whose mothers were pregnant during the flu epidemic and those whose mothers were pregnant shortly before or shortly after the epidemic.

To his astonishment, Dr. Almond found that the children of women who were pregnant during the influenza epidemic had more illness, especially diabetes, for which the incidence was 20 percent higher by age 61. They also got less education — they were 15 percent less likely to graduate from high school. The men’s incomes were 5 percent to 7 percent lower, and the families were more likely to receive welfare.

The effects, Dr. Almond said, occurred in whites and nonwhites, in rich and poor, in men and women. He convinced himself, he said, that there was something to the Barker hypothesis.