Halfway is Almost There
A New Prognostic View for Diffused Large B-Cell Lymphoma Survivors
Several weeks ago my wife and I were running on our local bike trail and came across one of her friends. The friend asked how I was doing with my fight with cancer and I replied that my recent PET scan showed I have now been cancer free for two and a half years. She said, “That’s wonderful, you are halfway there”. For many cancers, like mine, if one survives cancer free for 5 years you are considered cured. Making it 5 years is a key milestone for most cancer patients. So measured in time I am halfway to being cured. However, by looking at it in a different way, by risk or probabilities, I am almost there.
When I was first diagnosed with aggressive cancer I was giving a probability of about 50% of making it 5 years and being cured. That scared the hell out of me. I would have preferred something like the 90% chance they give to Hodgkin’s lymphoma patients. Since my first diagnosis my oncologist doesn’t speak in terms of probability or numbers. He just says, “You are doing great”, or “it couldn’t be better”. Now, I don’t think I’m the only cancer patient that would like to hear quantitatively what my chances are of being cured, especially if those chances have improved over time. What if you had an accountant take care of your finances and during an annual review of your finances your accountant says, “You are doing great”. Would you be happy with that and no numbers? I don’t think most people would, they would want to know how much money they have in the bank.
I researched the internet for an answer. I looked at all the reputable cancer websites(1) and through many published medical papers on cancer survival studies, but they all show the same thing, survival probabilities for cancer patients who have been just diagnosed. Figure 1 below shows an example of such a plot. I obtained the data for this plot from a medical paper published on a study made in British Columbia.(2) The plot is the overall survival (in percent) of 365 patients with diffuse large B-cell lymphoma (DLBCL), the type of cancer I have. The way to read the plot is first pick a time on the horizontal axis, draw a vertical line until it reaches the curve, then at that intersection point draw a horizontal line to the vertical axis and read off the probability of surviving that period of time. For my disease, the probability of surviving 5-years is just under 70 percent, which means out of 100 patients, 70 of them will be still alive after 5 years from diagnosis.
From the plot in Figure 1 you can see the importance of 5 years. The curve is flat from 3.5 years to beyond 5 years, whereas the period from 0 to 1 year the curve is very steep. That means during the first year patients are lost very quickly, whereas after 3.5 years and beyond there were no patients lost to the disease. There are survival plots that go way beyond 5 years and they show that after 5 years it is rare that a patient is lost to the disease. Therefore making 5 years typically means your risk of dying from the disease is pretty low, and it’s time to be concerned of other things like car accidents or being struck by lightning. The problem is that these plots are only directly useful for recently diagnosed patients.
After some thought I got an idea that maybe I could take the published 5-year survival data for recently diagnosed patients, and convert it to data that shows probability of surviving 5 years based on how long one has already survived. That would take an equation that I would have to derive from some basic principles of probabilities. I won’t bore you with the theoretical details, but just in case you are interested you can read it later in the Appendix of this post. The equation I derived (see Equation 1 below) takes values from a survival rate like the one shown in Figure 1, and gives the probably of surviving 5 years based on how long one has already survived after diagnoses. In the equation P0(t=5) is the probably point read from the plot at 5 years and P0(t) is the probability point read at t years, where t years is the number of years one has already survived. P5(t) is what I call the Running 5-year survival rate, and is the probability of surviving 5 years based on how many years one has already survived since first diagnosis.
(1)
Figure 2 shows two curves based on data taken from the British Columbia paper on survival of DLBCL patients. The red curve is for all patients in the study, and the blue curve is for patients that meet a certain criteria – patients whose cancer was found in its early stages. Fortunately I happen to be in the better group. The way to read this plot is look up how long you have survived since diagnosis on the horizontal axis, draw a vertical line up to the curve, then at the intersection draw a horizontal line to the vertical axis and read off the probability of surviving to 5 years. I’ve drawn lines for myself at 2.5 years and you can see I now have about a 96% chance of surviving 5 years. However, notice at 3 years, my probability is 100%. I’m almost there! I’m almost to the point of being cured. Now I fully understand when my doctor says, “It couldn’t be better”.
Figure 2. Running 5-year survival rate based on years survived after diagnoses of diffused large B-cell lymphoma.
You have to be a little careful using these charts. For example, the fact that the blue curve in Figure 2 is at 100% after 3 years does not mean the TRUE probability of survival is 100%. It just means that after 3 years, the remaining survivors of the original 365 patients in that particular study didn’t die after 3 years. Science tells us that if we included many more patients in the study, say 10,000 patients or 100,000 patients, we would find that the blue curve will never go to exactly 100%. There is always some risk of the disease coming back. However, when the probability of surviving gets up to somewhere near 99%, one is doing very well, especially when you consider that about 1-in-4 males and 1-in-5 females will eventually die from some type of cancer.(3)
I’m excited about this. I find much more comfort in knowing quantitatively that my survival chances are so good and that nearly all the risk is gone after three years, not 5 years. My three year PET scan will be in March 2011, just before my 52nd birthday. There’s no 100% guarantee I’ll have a clean PET scan, but there are good reasons, scientific reasons, to be very hopeful. Whatever happens in the future, there is one absolute guarantee, I will thoroughly enjoy life to it its fullest.
Appendix
The following are some simple mathematics with statistics. The probability in percent P0(t) of surviving t years after diagnosis is defined as
(2)
where N(t) is the number of survivors at time t, and Np is the total number of patients at diagnosis in the study. What we want to know is the probability of surviving 5 years based on the number of years already survived (P5(t)) after diagnosis. P5(t) is defined as
(3)
where N5 is the number of survivors at 5 years and N(t) is the number of survivors at time t. So the probability of surviving 5 years after already surviving t years is the number of patients that have survived 5 years divided by the number of patients that have survived t years. Multiplying by 100 puts the probability in terms of percent. By combining Equations 2 and 3 and doing a little algebra we find that P5(t) can be expressed in terms of two probabilities,
(4)
which can be read directly off the published graphs and we do not need to know the actual number of patients in the study.
To accurately obtain values from published graphs, I use a trick that involves Microsoft PowerPoint software. I use the Print Screen keyboard key to copy an image of the graph into the Windows clipboard; then I paste the image into PowerPoint. I create a PowerPoint circle object and place the center of the circle over a point on the graph that I want to record location values. Within the Format AutoShape tool I click on the Position tab and read the horizontal and vertical position of the little circle. These are coordinate values from the PowerPoint coordinate system. I enter the coordinate values into an Excel spreadsheet and repeat the process until I have enough points that accurately represent the curve on the graph. The points from the PowerPoint grid coordinate system must be converted into the graph coordinate system. To make the transformation I record a couple of points from each of the graph axes into the Excel spreadsheet where the transformation from one coordinate system to the other can be made with the appropriate equation. Once I have the curve values into Excel I can then apply my equations to manipulate the data and create my own plots.
References
(1) www.mayoclinic.com/health/cancer/CA00049
(2) Laurie H. Sehn, et. al. ,”The revised International Prognostic Index (R-IPI) is a better predictor of outcome than the standard IPI for patients with diffuse large B-cell lymphoma treated with R-CHOP”, www.bloodjournal.org, October 5, 2010.
(3) www.cancer.org/Cancer/CancerBasics/lifetime-probability-of-developing-or-dying-from-cancer
