We discuss the use of Bayesian P-spline and of the composite link model to estimate survival functions and hazard ratios from interval-censored data. If one further assumes proportionality of the hazards, the proposed strategy provides a smoothed estimate of the baseline hazard along with estimates of global covariate effects. The frequentist properties of our Bayesian estimators are assessed by an extensive simulation study. We further illustrate the methodology by two examples showing that the proportionality of the hazards might also be found inappropriate from interval-censored data. Copyright © 2010 John Wiley & Sons, Ltd.