Journal of the National Cancer Institute Advance Access originally published online on August 11, 2008
JNCI Journal of the National Cancer Institute 2008 100(16):1188-1189; doi:10.1093/jnci/djn252
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© The Author 2008. Published by Oxford University Press.
CORRESPONDENCE |
Response: Re: Visualizing Length of Survival in Time-to-Event Studies: A Complement to Kaplan–Meier Plots
Affiliations of authors: Cancer Group, MRC Clinical Trials Unit, London, UK (PR, MKBP); Centre for Statistics in Medicine, University of Oxford, UK (DGA)
Correspondence to: Patrick Royston, Cancer and Statistical Methodology Groups, MRC Clinical Trials Unit, 222 Euston Road, London NW1 2DA, UK (e-mail: pr{at}ctu.mrc.ac.uk).
Lama and Gallo propose an alternative to our approach in which individual survival times are displayed with box-and-whiskers plots (box plots) of percentiles of the survival distribution. Their suggestion is not new [eg, see figures 7 and 8 in Gentleman and Crowley (2)]. As stated by Gentleman and Crowley, "Thus, these methods [box plots] and the others suggested [including scatter plots] are not competitors, but, rather are supplementary [to Kaplan–Meier curves]" (our square brackets). This is also the primary message of our paper—to expand the presentation of survival data by the use of informative methods in addition to Kaplan–Meier curves.
Box plots are simple in the sense that their values can be read easily from Kaplan–Meier curves. However, they lose a lot of information because many individual values are summarized with only a few percentile points. The loss is considerable in the upper end of the survival distribution (ie, for those with the longest survival). Further, we do not believe that box plots have the visual impact of our graphical method. In Figure 1, we compare figure 4 from our article with a box-plot depiction of the same data. The graph was produced from observed and imputed data, but our software was not able to produce box plots from percentile estimates that were derived from censored survival data. The box plot, however, does provide information on percentiles of the distribution, which is valuable.
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We note that there are difficulties in producing box plots when the amount of censoring is high. For example, Lama and Gallo compared estimates of survival percentiles in a simulated two-arm trial with a hazard ratio of 0.75 and either 10% or 50% censored observations. Because of the censoring, high percentiles, such as the 95th percentile, are not estimable directly. Because not all percentile estimates are available, it is difficult to standardize the appearance of the box plot.
Because box plots in essence present summary statistics, to be most useful they should also present an indication of precision (eg, 95% confidence intervals). As far as we are aware, 95% confidence intervals are never presented, probably because it is impractical. As Lama and Gallo indicate, because of censoring estimates of upper centiles of survival time (ie, long times) in box plots are very imprecise, but such information cannot easily be displayed on the plot. Our scatter plots do not have and do not need an indication of precision. They are the closest you can reasonably get to raw observations of survival time.
Our method is more flexible than box plots. A prime example is figure 5 from our article, which is a scatter plot of observed versus predicted survival times and which cannot reasonably be emulated by box plots. We believe that the ability to explore outcomes at the individual level (eg, by using such scatter plots) gives a much better feel for the data than only that provided by summary statistics and is indeed a useful complement to Kaplan–Meier plots.
REFERENCES
1. Royston P, Parmar MKB, Altman DG. Visualizing length of survival in time-to-event studies: a complement to Kaplan-Meier plots. J Natl Cancer Inst. (2008) 100(2):92–97.
2. Gentleman R, Crowley J. Graphical methods for censored data. J Am Stat Assoc. (1991) 86:678–683.[CrossRef][Web of Science]
3. StataCorp. Stata Statistical Software: Release 10 (2007) College Station, TX: StataCorp.
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J Natl Cancer Inst 2008 100: 1188.
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