Prior to 1901, healthcare was not very advanced. I'm guessing the rise of technology, doctor credentialing, and the development of most modern drugs may have something to do with the price increase.
That can only account for half the increase, since the countries with the next highest cost for health care spend roughly 50% per capita compared to the US......
I would instead say the problem is:
1: Monopolies and oligopolies (patents, letting the AMA control medical school accredation, etc). Solution is to charter mini-AMA's to provide competition, and to enact compulsatory licensing of patents in medical fields.
2: The fact that the health care and health insurance markets are both entirely consumer opaque. Consumers don't have any control over their money in these markets and the common-sense protections are missing. For example, when I go to get my car worked on, I have a right to a written estimate before repairs are begun. Why don't I have a right to a written estimate before non-emergency medical care is provided?
The first thing you have to recognize is that when Democrats and Republicans both talk about reforming our medical system to address these, they believe that more corporate power, and less consumer power will correct this problem. Unfortunately, pricing is a coercive negotiation, and so that will only accelerate the problem.
Advances in technology drive down costs, not the reverse. They prevent diseases, reduce the need for more expensive procedures, etc.
Credentialling of doctors as it currently stands is an artificial guild system which restricts the number of doctors. It doesn't make medicine safer, but does increase doctor salaries. This is one of the ways government interferes with healthcare to artificially restrict supply-- the AMA did some effective lobbying once upon a time.
Drugs also reduce the need for hospital stays and thus costs by curing or preventing conditions that would otherwise get worse.
