Estimating the Underlying Death Rate of a Small Population: A Case Study of Counties in Kansas, Nebraska, North Dakota, and South Dakota

Abstract

While the crude death rate has well-known drawbacks, it remains a population health statistic of interest. One of its drawbacks is found exclusively in the context of a small population, where the number of deaths is subject to a high level of stochastic uncertainty. This can lead to dramatic variations in the crude death rate from year to year even though there is neither a corresponding change in the population nor its mortality regime. A simple method is presented for estimating the “underlying” mortality rates of areas with small populations where the number of deaths is subject to a high level of stochastic uncertainty. The idea is that the underlying rates generated by the estimation method should better reflect the mortality regimes of these small populations. The method is described and illustrated in a case study by estimating crude death rates for the 88 “small population” counties, representing approximately the first quartile of the 317 counties found in four Great Plains states, Kansas, Nebraska, North Dakota, and South Dakota. The method's validity is tested using a synthetic population in the form of a simulated data set generated from a model stable population with a crude death rate of 0.0194, representing Level 23 of the West Family Model Life Table for males. This synthetic population similar to the study population in that it has a slightly negative rate of population growth, with relatively high life expectancy (71.2) and mean age (43.1). The test indicates that the method is capable of producing estimates that represent underlying rates that reflect mortality regimes. Results shown here support the argument that the method can produce reasonable estimates of the underlying crude death rates for small populations subject to high levels of stochastic uncertainty.