The reason rates are going up is that more people are seeking care for expensive conditions they would otherwise just suck up and deal with until they end up in the ER or dead.
The only way we will bring costs down is by reducing demand, either through a healthier population (unlikely) or stricter controls on care. We are apparently unable as a society to avoid becoming overweight and unhealthy, so we will at some point have to decide if we are going to pay $100k to treat someone's cancer, stroke or heart failure. If not, how will we reduce the cost? Force companies to provide drugs for lower prices yet also force them to continue to produce these rather than other profitable enterprises, choose less effective & cheaper drugs, or force patients to forgo treatment. I think at some point a combination of the latter two will occur. We will limit people's access to expensive chemotherapy and immune-modulating drugs (costs run in the tens of thousands, often with little improvement in survival or symptoms).
I'll give a concrete example using colon cancer chemotherapy since it is a common, yet expensive to treat, disease.
State of art treatment in 1990: 5-fluorouracil, $1k. 69% of patients alive at 5 years.
State of art treatment in 2015: 5-fluorouracil + oxaliplatin, $17k. 73% of patients alive at 5 years. Thus, treating 100 patients with this regimen would save 4 people.
Total cost to save 4 people = 16* 100 = $1.6 million
About 80,000 people per year are diagnosed with this stage of colon cancer. Total chemotherapy costs are now $17,000 * 80,000 = $1.36 billion vs $80 million with the slightly less effective but much cheaper therapy. Out of the 80k treated, 3.2k will be alive at 5 years because of the extra chemotherapy.
That's the hard calculations we face if we want to rein in healthcare costs.
