Addressing Bias from Coarsened Self-reported Data in Health Surveillance Systems

Estimating health indicators for sub-populations is a recurrent challenge in public health surveillance. When complex survey data are used, self-reported outcomes are often affected by coarsening mechanisms, such as rounding and digit preference, that reduce data resolution and may bias tail-related indicators. We consider PASSI, the Italian Behavioral Risk Factor Surveillance System, which monitors health behaviours among adults through continuous surveys. This paper develops a Bayesian framework for coarsened smoking intensity among daily smokers, allowing rounding to be non-ignorable through dependence on latent consumption. The model combines an ordinal regression for rounding behaviour with a flexible two-component lognormal mixture for true cigarettes smoked, fitted via a survey-weighted pseudo-likelihood in Stan. Model-based predictions yield a coarsening-adjusted Hájek estimator of heavy smoking prevalence, with variance propagating both sampling and coarsening uncertainty, at national and regional levels.