The message of medians

Stephen J Gould's article, "The Median is not the Message" is a must read for everyone with any sort of cancer.

Results of particular treatments are usually reported as median survivals. This means the time at which 50% of people are dead and 50% are still alive. Medians are sensible figures when calculated on populations based on a normal distribution as represented by my second curve. But survival curves, as can be seen from the first illustration, do not look like this. They are extremely right skewed.

The median of the whole population is pressed up against the left hand edge of the graph at zero days because the normal distribution would contain all those who were going to get the cancer that we don't (and can't) know about. So we start on the downward slope from the time that the cancer is diagnosed. But that is a time some way into the disease. Some people are only diagnosed on the day that they die, having had the disease for many years undiagnosed. For CLL, we know that virtually all cases have had a long period when they had MBL before the diagnosis was makeable, and even when the diagnosis was makeable with a blood test, most people don't have blood tests.

On the survival curve, those with the most advanced and drug-resistant disease die soonest. By the time you get to the median survival the survivors are mainly those who had good prognostic factors at the beginning: low white count, no lymph nodes or spleen, mutated IgVH genes, low ZAP-70, low CD38 and del 13q14 on one chromosome. We know that some patients with these characteristics live out beyond 20 years and that they tend to die from old age. Indeed the ACOR list reported a man in New Mexico who had had the disease for 52 years. That survival curve had a very long tail indeed. As far as CLL is concerned the tail is abbreviated by the fact that everybody dies and that CLL patients cannot live longer than life itself. It is also a snapshot of the time it was drawn and it cannot take account of treatments that will appear in the next 20 years.

As far as my cancer is concerned, the median survival on this treatment is given as 22 months. But the 50% who die in this time are those who are really ill when they present, including those with massive liver secondaries, ascites, and bowel obstruction. I have all the good prognostic features: a primary so small as to be unfindable, localized spread, no liver involvement and no ascites, a well differentiated histology, low CEA levels, no symptoms and a 6 month observation which showed no progression on the CT scan. I should be on the right hand edge of the tail of that survival curve.