In this article, we assess data integration methods for estimating composite indicators for small areas, where some single indicators are completely missing. Focusing on a multidimensional poverty index, with certain variables missing from the population Census, we propose two approaches using an auxiliary sample survey. One approach employs a generalized linear mixed model, while the other employs a two-step imputation technique. We evaluate these approaches through simulation studies, and an application based on the Colombia’s 2018 Great Integrated Household Survey as a case study.