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

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 aking and funding. To this purpose, only data from the ational survey on Health Conditions and Appeal to Medicare an be used, in which, however, no direct measurement of uch condition is taken. Fourteen items are available from the uestionnaire, which survey a set of functions concerning the bility of a person to accomplish everyday tasks such as etting washed and dressed, eating and walking. Latent Class Models can then be employed to classify the population according to ierent levels of a latent variable connected with disability. he survey, however, is designed to provide reliable estimates t the level of Administrative Regions { NUTS2 level. Administrative Regions in Italy are divided into Health Districts and the local Authorities are interested in uantifying 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 resent application is that the variable of interest is not bserved. We propose to tackle the problem of classifying the opulation and getting small area estimates as a whole within a Hierarchical Bayesian framework in which the probability of elonging to each latent class changes with covariates. Age by sex by marital status counts are available for each unicipality from administrative registers and can be used to this end. The functional form of the influence of age in learnt rom the data using penalized splines. A random effect capturing the variability of the small areas is also introduced.