Abstract:  For species with five or more sightings, quantitative techniques exist to test whether a species is extinct on the basis of distribution of sightings. However, 70% of purportedly extinct mammals are known from fewer than five sightings, and such models do not include some important indicators of the likelihood of extinction such as threats, biological traits, search effort, and demography. Previously, we developed a quantitative method that we based on species’ traits in which we used Cox proportional hazards regression to calculate the probability of rediscovery of species regarded as extinct. Here, we used two versions of the Cox regression model to determine the probability of extinction in purportedly extinct mammals and compared the results of these two models with those of stationary Poisson, nonparametric, and Weibull sighting‐distribution models. For mammals with five or more sightings, the stationary Poisson model categorized all but two critically endangered (flagged as possibly extinct) species in our data set as extinct, and results with this model were consistent with current categories of the International Union for the Conservation of Nature. The scores of probability of rediscovery for individual species in one version of our Cox regression model were correlated with scores assigned by the stationary Poisson model. Thus, we used this Cox regression model to determine the probability of extinction of mammals with sparse records. On the basis of the Cox regression model, the most likely mammals to be rediscovered were the Montane monkey‐faced bat (Pteralopex pulchra), Armenian myotis (Myotis hajastanicus), Alcorn's pocket gopher (Pappogeomys alcorni), and Wimmer's shrew (Crocidura wimmeri). The Cox model categorized two species that have recently disappeared as extinct: the baiji (Lipotes vexillifer) and the Christmas Island pipistrelle (Pipistrellus murrayi). Our new method can be used to test whether species with few records or recent last‐sighting dates are likely to be extinct.