On the Probability Model for Asthma Attacks

In environmental epidemiology, the impact of environmental agents on symptoms or health status is of interest. This influence is described quantitatively in the theory of Whittemore & Keller (1979). They formulated a logistic model for individuals that is useful in evaluation of panel studies in which each participant protocols whether he does or does not have a certain symptom each day. In the present paper an equation for the prevalence of symptoms in the study population that is defined as the fraction of symptomatic subjects is deduced from the model for individuals. The model for the aggregated quantity depends on the individualsʹ parameters in a nonlinear manner. The relationship between the individual-based model and the corresponding population-based model is illustrated by means of a simulated panel. Bayesian estimates of the parameters are calculated and compared for both approaches. Bayesian inference enables to apply the prevalence model to a population of non-identical individuals. For such a heterogeneous population, we observe an attenuation of environmental effects on the aggregated symptom prevalence in comparison to the individual-based approach. The presented theory is applicable not only to panel studies but also in time-series analysis of prevalences and incidences.