Poisson regression with a surrogate X: an analysis of vitamin A and Indonesian children's mortality

"A Poisson regression model with a surrogate X variable is proposed to help to assess the efficacy of vitamin A in reducing child mortality in Indonesia. In a recent community trial, the mortality rate in villages receiving vitamin A supplementation was 35% less than in control villages. However, at base-line, control villages were found to have slightly higher rates of xerophthalmia, an ocular disease caused by vitamin A deficiency. It was therefore desirable to adjust the mortality comparison for base-line vitamin A levels as indicated by xerophthalmia prevalence. This paper presents a parametric errors-in-X regression model developed for this purpose. Likelihood methods for fitting and inference are discussed. The model is illustrated on the Indonesian data set."