This talk will be two-fold: the first part will give a short introduction into univariate density estimation under log-concavity and summarize a few key results. In a second part, I will discuss more efficient treatment effect estimation in pre-specified subgroups for time-to-event outcomes. In randomized controlled trials, the homogeneity of treatment effect estimates in pre-defined subgroups based on clinical, laboratory, genetic, or other baseline markers is frequently investigated using forest plots. However, the interpretation of naïve subgroup-specific treatment effect estimates requires great care because of the smaller sample size of subgroups (implying large variability of estimated effect sizes) and the frequently large number of investigated subgroups. Treatment effect estimates in subgroups with a lower mean-square error based on frequentist and Bayesian shrinkage, Bayesian model averaging, and the bootstrap have recently been investigated but focused on continuous outcomes. We propose two novel general strategies for treatment effect estimation in subgroups for survival outcomes. The first strategy is to build a flexible model based on all available observations including all relevant subgroups and subgroup-treatment interactions as covariates. This model is then marginalized to obtain subgroup-specific effect estimates. We propose to use the average hazard ratio corresponding to the odds of concordance for this marginalization. The second strategy is based on simple subgroup-specific models which are combined via (penalized) composite likelihood. We implement these strategies to obtain shrinkage estimators using lasso and ridge penalties. With this, we can interpolate between the two extreme scenarios of either taking the overall estimate as best estimate in every subgroup, or computing effect estimates within each subgroup separately. We illustrate under which scenarios this strategy provides a pronounced improvement in mean squared error compared to the extreme strategies. The methods are illustrated with data from a large randomized registration trial in follicular lymphoma.