A new method to estimate the diversification rate of a lineage from a phylogeny of recent species is presented. This uses survival models to analyse the ages of the species as derived from the phylogeny. Survival models can analyse missing data where the exact date of death is unknown (censoring). This approach allows us to include missing data (species not included in a detailed phylogenetic study) in the analysis, provided a minimum age is known for these species. Three models are presented, with emphasis on temporal variation in diversification rates. The maximum likelihood method and Akaike information criteria are used to derive estimators and tests of hypotheses. A simulation study demonstrates that the method is able to detect a temporal variation in diversification rate only when it is present, avoiding type I and type II errors. A lineage with ten species may be sufficient to detect a temporal variation in diversification rate even with 50% of missing data. An application is presented with data from a phylogeny of birds of the genus Ramphocelus.