Simultaneous confidence bands for ratios of survival functions via empirical likelihood

We derive a simultaneous confidence band for the ratio of two survival functions based on independent right-censored data. Earlier authors have studied such bands for the difference of two survival functions, but the ratio provides a more appropriate comparison in some applications, e.g., in comparing two treatments in biomedical settings. Our approach is formulated in terms of empirical likelihood and allows us to avoid the use of simulation techniques that are often needed for Wald-type confidence bands. By the transformation-preserving property we also obtain confidence bands for the difference in the cumulative hazard functions. The approach is illustrated with a real data example.