| Summary: | The three-state (healthy, frail, and dead) population model is commonly used in time-series investigations of mortality displacement and particulate matter air pollution (PM). In this paper, the author proposes a new population model, called the mixture population model, that by allowing PM to have differential effects on individuals in the population, extends the population models currently used in investigations of mortality displacement. Using this new model, the properties of distributed lag models (DLM) of PM are investigated. In particular, the author derives a relationship between the parameters of the proposed population model and the estimates obtained from a DLM fitted to mortality arising from the model. This relationship provides insight into the interrelationships between the size of the frail population, the number of lags of PM included in a DLM and the proportion of the effect of PM on the healthy population that is estimable. The relationship will guide and contextualize future investigations by providing researchers with the knowledge to assess the consequences of the number of lags of PM included in a DLM in terms of what they can plausibly infer about the effect of PM on mortality based on this choice of lag. Keywords: Air pollution, Distributed lag models, Frail populations, Mixture population model, Mortality displacement, Particulate matter, Time-series
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