Br J Gen Pract. 2007 May 1; 57(538): 410.
PMCID: PMC2047022

# Survival statistics

Michael Campbell, Professor, Director of Health Services Research, Editor Statistics in Medicine
Medical Statistics Group, ScHARR, Regent's Court, Sheffield. E-mail: ku.oc.dleiffehs@llebpmaC.J.M
Jenny V Freeman, Lecturer in Medical Statistics

The article by Neal et al1 looking at survival from cancer by fast track referral is of considerable interest. It has some nice looking survival curves. However, we feel that they raise some issues around the appropriate interpretation and display of survival data, particularly when there are many censored observations, as is the case here.

The main points about the data display are:

• Table 2 contains mean survival times with standard errors and confidence intervals. We appreciate that the statistical package SPSS produces these as routine, but that does not mean they should be quoted, as this raises the question of how to interpret a mean when some of the data are censored? This is particularly apparent in the case of the urgent referrals for prostate cancer, in which there was only one death, and yet somehow a standard error and confidence interval was calculated. It would perhaps be more appropriate to refer to this as mean follow-up time. For this group the mean survival is given as 755.7 days, and yet Figure 3 suggests this will be exceeded by no more than 3 (out of 45) censored survival times.
• The survival curves have different starting points for the y-axis, giving the impression, for example, that mortality from prostate cancer is comparable to the others. A better plot is to show the cumulative mortality curves showing increasing curves, which all start at zero and have the same scales.2
• While it is a good idea to show the censored data on the survival curves, in the paper one of the labels for the curves is an open box, which is not used in the figures.
• Figures should always indicate sample sizes, and these do not. In order to improve the plots one suggestion is to give the numbers at risk along the x-axis. This would then make apparent why some of the curves drop suddenly to zero, the reason being the longest survival time is a death.

At a more fundamental level is the issue of when is a non-significant result indicative of no difference. Lack of evidence to support a difference is not evidence of no difference. A non-significant difference in, say, prostate cancer survival, does not necessarily mean ‘no difference’ as stated in the abstract. One should present an estimate of the hazard ratio and a confidence interval, and if this confidence interval is narrow enough to exclude a clinically meaningful difference, only then one can conclude there is no difference.

## REFERENCES

1. Neal RD, Allgar VK, Ali N, et al. Stage, survival and delays in lung, colorectal, prostate and ovarian cancer. Br J Gen Pract. 2007;57(536):212–219. [PubMed]
2. Pocock SJ, Clayton TC, Altman DG. Survival plots of time-to event outcomes in clinical trials: good practice and pitfalls. Lancet. 2002;539(9318):1686–1689. [PubMed]

Articles from The British Journal of General Practice are provided here courtesy of Royal College of General Practitioners

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