How many times have you seen an abstract summarizing the results from a study or clinical trial in multiple myeloma that reads something like this:

The median progression-free survival (PFS) for 24 patients taking drug X was 18 months, and the median overall survival (OS) was 73 months.

So what useful conclusion can you make from this?

In a nutshell, not too much.

First, you need to understand what the "median" is. In statistical terms, if you have a set of values arranged in numerical order, the median is the middle value.  There are some minor nuances depending on whether you have an even or odd number of values, but basically this means half the values are above the median and half are below.

Using the sample abstract above, this would mean half the patients had PFS less than 18 months, and half had PFS greater than 18 months.  Similarly, half had OS less than 73 months, and half had OS greater than 73 months.

What's missing in the abstract, however, is how the values spread out above and below the median.  To clarify what I mean, here are three examples, all with a median progression-free survival of 18 months, yet very different ranges and distributions:

1. 24 patients, all with PFS of 18 months
2. 10 patients with PFS of 1 month, 14 with PFS of 18 months
3. 14 with PFS of 18 months, 10 with PFS of 120 months

In the first case, all patients were progression free for 18 months, then relapsed.  In the second case, slightly less than half relapsed after 1 month, and nobody was progression free past 18 months.  In the third case, all patients were progression free for 18 months and 10 patients went progression free for 120 months (i.e., 10 years).

Granted, these are probably not realistic scenarios, but they do illustrate the point.

The two additional pieces of information I would like to see are the range of the values and a measure of the distribution of the values over the range.

The range is easy; it is simply the minimum and maximum value.

The distribution is a bit trickier, and there are a few different methods for expressing it.  One method I personally find useful is something called the median absolute deviation.

I won't get into the mathematics of how you determine the median absolute deviation (search for it on Wikipedia if you really want to know), but it basically means that half the values in a set of values will be within the median absolute deviation from the median, and half the values will be greater than the median absolute deviation from the median.  Everybody got that? 

Perhaps an example would help.

Using the example above with a median PFS of 18 months, if the median absolute deviation was 4 months, then half the patients would have a PFS within 4 months of the 18 months, or somewhere between 14 and 22 months. The other half of the patients would be more than 4 months from the median, so either less than 14 months or greater than 22 months.

The smaller the absolute deviation, the less spread out the values tend to be, and conversely, the greater the value, the more spread out they tend to be.

In conclusion, I would much prefer to read an abstract similar to the following:

The median progression-free survival (PFS) for 24 patients taking drug X was 18 months, with a minimum PFS of 3.6 months, a maximum PFS of 42 months, and a median absolute deviation of 4 months.  The median overall survival (OS) was 73 months, with a minimum OS of 17 months, a maximum OS of 131 months, and a median absolute deviation of 23 months.

I don't know about everyone else, but for me, this sure seems to provide significantly more useful information.

Peace, and live for a cure.