How Where you are on a Survival Curve Changes the Odds!
It is easy to look at a survival curve and take it to somehow represent your prognosis forever. But in fact your odds change over time, and the good news is that they usually improve. Survival curves, interpreted correctly, chart the way the odds change over time. Your survival odds, given the pre-condition of having already survived a certain length of time, are technically referred to as conditional survival (the term relates to conditional probability in mathematics). It is very likely that you will never encounter this term elsewhere, even if you read technical articles on your cancer, because this important concept is all too little recognized. This is too bad since it turns out that there is hope to be found here.
A Hypothetical Example
Suppose you had Stage III “horrendoma” (a hypothetical really nasty cancer) and you had surgery which removed all of the cancer. You research the literature and find a recent survival curve which applies to patients with Stage III horrendoma. It’s a really rough curve – but at least it appears to flatten out after a few years. Here’s the curve:
Now suppose that when you find this curve you have already been in remission for three years. Notice that by three years, 70% of people with stage III horrendoma have died. Does this mean you are 70% dead? Presumably not! In fact, you are alive and well and wondering how this survival curve applies to you now that you’ve made it three years. Notice because that the curve flattens dramatically, the greatest risk is in the first few years. At three years you’ve passed most of that – you’re one of the fortunate ones. You are now looking at the only part of the curve after three years. Here’s how the survival curve looks to you now:
Originally, your chance of surviving five years was only about 20% or 1 in 5. But now starting out on the flatter part of the curve, your chance of surviving five more years is about 66% or 2 in 3. So even though you had stage III horrendoma which has a terrible prognosis, your prognosis has changed dramatically for the better. To be sure you still have a serious risk, but it’s much much less than it was three years ago.
Here’s a little more on how the way time has changed your curve. Notice that the curve starts at 100% again. The only part of the curve that matters to you is the part that predicts your odds in the future, and that is the part starting at three years after surgery and extending into the future from there. So the part of the survival curve starting at “now” and extending as far as the curve goes is scaled up proportionally so it starts at 100% again. Another way to look at it is that you are 100% alive now and interested in your future odds.
The scaling also increases the size of the remaining steps. Notice that the one step left in the curve is now bigger looking then it was in the original curve, where it went from about 30% to about 20%. But this is 1/3 of the way from that point to zero. After scaling, the step still goes 1/3 of the way to zero only 1/3 of the way from 100% is a bigger step then 1/3 of the way from 30%. Notice also that the curve doesn’t stretch out as far into the future as it does for the patient who has just had surgery and is at the top of the curve.
The Real World
Getting further along on a survival curve isn’t automatically guaranteed to improve the odds for the future. It depends on the shape of the curve. If it flattens, as in my example, then your odds improve. But if the curve doesn’t flatten, the odds do not improve over time. It turns out though, that for a wide range of advanced cancers, including cancers with a terrible prognosis, there is evidence that the odds actually do improve with time just as in my example! For more information, see my review of a very interesting technical article on conditional survival in advanced cancer. My experience is that most survival curves for less advanced cancer are obviously decreasing risk curves, and usually end with a plateau indicating probable cures.
Of course, time since diagnosis is not the only factor affecting prognosis. Many other things come into it. If you have advanced cancer and have survived years, and are in stable remission you are more likely going to experience continued extended survival than if you have relapsed with widespread disease and rapidly growing tumors. Even in this case it’s possible you will find a way back into remission and again beat the odds. Similarly if you had surgery for localized cancer, survived until the risk is low, but then unfortunately relapsed, your future survival odds are compromised despite your “good time.” I believe that significant events such as getting into remission, relapsing or choosing a promising treatment are forks in the road (bifurcation points) at which your survival curve changes, because the most comparable group of people with whom to compare you changes abruptly changes when new information about your situation becomes known. As an example see my Postcards from Beyond The Zero, a statistical story of how my own survival curves has changed with events and choices.
This CancerGuide Page By Steve Dunn. © Steve Dunn
Page Created: 2002, Last Updated: April 11, 2002