Average is described as a measure of the "middle" or "typical" value of a data set (Wikipedia). Unfortunately, this term is not very specific, as it can refer to the arithmetic mean, the median or the mode. Most people will think of an arithmetic mean when speaking about an average. Mean and median can be very different. How big the difference is, depends on the distribution, as is illustrated in figures 1 and 2. (The distribution of a dataset is just a way to described the histogram of the data. And the histogram is the kind of graph used in figures 1 and 2) The first figure presents a normal distribution, the second one a so called negative binomial distribution. In the first dataset, with normally distributed data, the mean is 100.69 and the median 100.98. So in that case it does not really matter whether the mean or the median is used. In the second dataset the mean is 98.34 and the median 75. This is a clear difference. (Definitely when we are speaking about survival and life expectancy.)
In studies analyzing survival data, it is most common to use the median survival time and not the mean. The logic very simple. Median survival time is defined as the time were 50% of the patients has died and 50% is still alive. The mean survival time is calculated by adding the survival times of all patients and divide the result by the number of patients. In order to be able to calculate the mean survival time, it is necessary to know the survival time for each patient. It can take quite a long time to get all information, as it can take years before all patients died. (The longer it takes, the better, actually.) However, when 50% of the patients died, the median survival time is known. As survival data are typically not normally distributed, the median will be different from the mean. (As survival data are skewed to the right, the median will be lower than the mean.) Therefore it takes less time to complete a study when the median survival time is used.
Furthermore, statisticians use a technique called "censoring" in order to be able to come to any conclusion in a reasonable amount of time. With this technique data from patients who are still alive at the end of a survival study can be included in the analyses. At the end of the study, the total survival time of patients who are still alive at that time is not known. However, the minimal survival time of those patients is known and can be used in the analyses. (For instance: if all patients treated with an old medicine died by the end of the study and all patients treated with a new medicine are still alive, it is possible to draw some conclusions from this information. That the exact survival time is not known, does not aect the conclusion.) It is possible to calculate a mean survival time from the censored data. The true mean survival time will always be underestimated with this technique. The reason is that patients who are living longer, have a higher change of being censored. Therefore, the longer survival times will not be recorded in the data, resulting in an estimated mean which is lower than the true one.
In the original article on the prostate cancer vaccine the authors mention a median survival of 25.8 months in patients receiving Provenge (Sipuleucel-T immunotherapy) and 21.7 months in the placebo group. (P.W. Kanto, C.S. Higano et al., Sipuleucel-T immunotherapy for castration-resistant prostate cancer, New England Journal of Medicine 2010 Jul 29;363(5):411-22) From what I wrote, you all will see now that the mean survival times in both groups can be further apart than the median survival times are. The author of the article on the website of the American Cancer Society was thus sloppy when he wrote that the patients lived on average four months longer with the new medicine.
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