Estimating and modelling mortality rates in the absence of population denominators

Mortality statistics are important indicators of the health and well-being of a population. The mortality rate is estimated by calculating the ratio between the number of occurred deaths and the size of the population. One major hurdle is that data on the denominator, i.e., the actual size of the population of interest, if available at all, can often be of poor quality and spills over to the estimation of the mortality rate. In this paper, we propose a way to estimate mortality rates by using death counts only, i.e., without the use of population size information. The major 'trick' is to interpret the sampling scheme as a right truncation problem within a survival analysis framework and to estimate the hazard function in reversed age-time. Thus, by analogy to the standard (forward) force of mortality and (forward) central mortality rate, we introduce the concepts of reverse force of mortality and reverse central mortality rate. Different structural assumptions on the hazard function will allow to move from reverse-time quantities back to forward-time quantities. We illustrate our approach using data from the Human Mortality Database (https://www.mortality.org) and compare our mortality estimates with the estimates from traditional approaches that do make use of population denominators. Joint work with Munir Hiabu (University of Copenhagen)