Confidence intervals vs. confidence bands for survival curves
When Prism computes survival curves, it can also compute the 95% confidence interval at each time point (using two alternative methods). The methods are approximations, but can be interpreted like any confidence interval. You know the observed survival percentage at a certain time in your study, and can be 95% confident (given a set of assumptions) that the confidence interval contains the true population value (which you could only know for sure if you had an infinite amount of data).
When these confidence intervals are plotted as error bars (left graph below) there is no problem. Prism can also connect the ends of the error bars, and create a shaded region (right graph below). This survival curve plots the survival of a sample of only seven people, so the confidence intervals are very wide. Prism file.
The shaded region looks like the confidence bands computed by linear and nonlinear regression, so it is tempting to interpret these regions as confidence bands. But it is not correct to say that you can be 95% certain that these bands contain the entire survival curve. It is only correct to say that at any time point, there is a 95% chance that the interval contains the true percentage survival. The true survival curve (which you can't know) may be within the confidence intervals at some time points and outside the confidence intervals at other time points.
It is possible (but not with Prism) to compute true confidence bands for survival curves, and these are wider than the confidence intervals shown above. The graph below (from Coviello) shows the survival curve in black (the sample was large, so the steps are small), the confidence limits in green, and the confidence bands in red. Confidence bands that are 95% certain to contain the entire survival curve (red) are wider than the confidence intervals for individual time points.
(Thanks to Joe Felsenstein for pointing out the distinction between confidence intervals and confidence bands in survival curves. )