Giovanna Ranalli

small area estimation for a latent variable: the case of disability in the Italian National Health Interview Survey

(Joint work with E. Fabrizi, Catholic UnivERSITY, Piacenza, Italy and G. E. Montanari, University of Perugia, Italy)

Quantifying the amount of population in a condition of severe disability that requires intensive care is very important in Italy for its consequences on Health system organization, policy making and funding. To this purpose, only data from the National survey on Health Conditions and Appeal to Medicare can be used, in which, however, no direct measurement of such condition is taken. Fourteen items are available from the questionnaire, which survey a set of functions concerning the ability of a person to accomplish everyday tasks such as getting washed and dressed, eating and walking. Latent Class Models can then be employed to classify the population according to different levels of a latent variable connected with disability. The survey, however, is designed to provide reliable estimates at the level of Administrative Regions -- NUTS2 level. Administrative Regions in Italy are divided into Health Districts and the local Authorities are interested in quantifying the amount of population that belong to each latent class for each District and, possibly, age class. Therefore, small area estimation techniques should be used. The challenge of the present application is that the variable of interest is not observed. We propose to tackle the problem of classifying the population and getting small area estimates as a whole within a Hierarchical Bayesian framework in which the probability of belonging to each latent class changes with covariates. Age by sex by marital status counts are available for each municipality from administrative registers and can be used to this end. The functional form of the influence of age in learnt from the data using penalized splines. A random effect capturing the variability of the small areas is also introduced.