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; doi:10.1093/jnci/djn251
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© The Author 2008. Published by Oxford University Press.
CORRESPONDENCE |
Re: Visualizing Length of Survival in Time-to-Event Studies: A Complement to Kaplan–Meier Plots
Affiliations of authors: Department of Medicine and Public Health, Medical Statistics Unit, Second University of Napoli (NL, CG)
Correspondence to: Nicola Lama, PhD, Department of Medicine and Public Health, Second University of Napoli, Via Luciano Armanni 5, 80138 Napoli, Italy (e-mail: nicola.lama{at}unina2.it).
Royston et al. (1) recently suggested a method of presenting data that was complementary to Kaplan–Meier curves, with the aim to supplement ordinary survival probability plots with a direct and intuitive indication of the variability in survival times among individual patients. They showed how survival time histograms could be obtained by imputing censored survival times with values predicted by a log-normal model.
We agree with Royston et al. (1) that Kaplan–Meier plots tend to conceal survival time variability, thus obscuring the impact of the treatment. We also agree the actual benefits of the treatment depend not only on the hazard ratio but also on the shape of the underlying probability distribution, which is disease related (2). Hence, common measures of effects on the vertical axis of the survival function and time plane (eg, the hazard ratio) ought to be supplemented with measures of the corresponding effects on the horizontal axis (eg, the median or any appropriate quantile time).
We think the histograms proposed by Royston et al. (1) might be useful as diagnostic tools for modeling purposes (eg, for mixture or subgroup recognition). We believe, however, that the imputation method they suggested is not necessary for graphic display purposes and that some clinicians might not feel comfortable with plots that use random-generated data rather than the actual data. We also believe that simple distribution percentiles highlight differences on the magnitude of the effect between populations better than histogram plots by focusing attention on a few striking points. A simple box-and-whiskers plot can be drawn by use of empirical quantiles from Kaplan–Meier survival estimates and should suffice to provide a clear picture of the location and scale of the time-to-event distribution. Box-plot whiskers could be drawn from the 5th to the 95th percentiles or to the largest percentile estimable from the survival curve.
We present a simple simulation study to show box plots for a hypothetical trial in which experimental and control treatment events were generated from two exponential distributions with rates 
EXP = 0.75CTRL and CTRL = 0.1, respectively. Total sample size was set to 300 and censoring was uniformly distributed on (0,c), where c was chosen to provide 10% and 50% censoring rates. Theoretical median values of log(2)/ are equal to 9.24 and 6.93 for the experimental and control arms, respectively. Sample medians computed from the simulated (not censored) dataset were 9.18 and 7.63, respectively. The corresponding median values estimated from survival curves were 9.18 and 7.6, respectively, for a 10% censoring rate and 9.23 and 7.67 for a 50% censoring rate.
Box plots for the two censoring rates of 10% (Figure 1, A) and 50% (Figure 1, B) are presented. The upper limit in Figure 1, B is the 87th percentile, the largest estimate from both the survival curves, although the high 50% censoring rate. This graph appears to be a convenient way to graphically depict and compare the two distributions. Low confidence should, however, be attached to the whiskers' upper limits because of the sparse data in the right tails of survival curves, typically for high censoring rates. Reliability could be improved by choosing a rule for the upper quantile to be estimated (eg, a minimum of 20 subjects at risk).
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Funding
Ciro Gallo was Partially supported by no-profit charity AIRC (Italian Association for Research on Cancer) (CG)
REFERENCES
1. Royston P, Parmer 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. Spruance SL, Reid JE, Grace M, Samore M. Hazard ratio in clinical trials. Antimicrob Agents Chemother. (2004) 48(8):2787–2792.
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J Natl Cancer Inst 2008 100: 1188-1189.
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