Confidence bands in survival analysis

Providing estimates of uncertainty for statistical quantities is important for statistical inference. When the statistical quantity of interest is a survival curve, which is a function over time, the appropriate type of uncertainty estimate is a confidence band constructed to account for the correlation between points on the curve, we will call this a simultaneous confidence band. This, however, is not the type of confidence band provided in standard software, which is constructed by joining the confidence intervals at given time points.

We show that this type of band does not have desirable joint/simultaneous coverage properties in comparison to simultaneous bands.

There are different ways of constructing simultaneous confidence bands, and we find that bands based on the likelihood ratio appear to have the most desirable properties. Although there is no standard software available in the three major statistical packages to compute likelihood-based simultaneous bands, we summarise and give code to use available statistical software to construct other simultaneous forms of bands, which we illustrate using a study of colon cancer.

There is a need for more user-friendly statistical software to compute simultaneous confidence bands using the available methods.