Prediction intervals for penalized longitudinal models with multisource summary measures: An application to childhood malnutrition

In many global health analyses, it is of interest to examine countries' progress using indicators of socio‐economic conditions based on national surveys from varying sources. This results in longitudinal data where heteroscedastic summary measures, rather than individual level data, are available. Administration of national surveys can be sporadic, resulting in sparse data measurements for some countries. Furthermore, the trend of the indicators over time is usually nonlinear and varies by country. It is of interest to track the current level of indicators to determine if countries are meeting certain thresholds, such as those indicated in the United Nations Sustainable Development Goals. In addition, estimation of confidence and prediction intervals are vital to determine true changes in prevalence and where data is low in quantity and/or quality. In this article, we use heteroscedastic penalized longitudinal models with survey summary data to estimate yearly prevalence of malnutrition quantities. We develop and compare methods to estimate confidence and prediction intervals using asymptotic and parametric bootstrap techniques. The intervals can incorporate data from multiple sources or other general data‐smoothing steps. The methods are applied to African countries in the UNICEF‐WHO‐The World Bank joint child malnutrition data set. The properties of the intervals are demonstrated through simulation studies and cross‐validation of real data.