Robust adaptive survey design for time changes in mixed-mode response propensities

Adaptive survey designs (ASDs) tailor recruitment protocols to population subgroups that are relevant to a survey. In recent years, effective ASD optimization has been the topic of research and several applications. However, the performance of an optimized ASD over time is sensitive to time changes in response propensities. How adaptation strategies can adjust to such variation over time is not yet fully understood. In this paper, we propose a robust optimization approach in the context of sequential mixed-mode surveys employing Bayesian analysis. The approach is formulated as a mathematical programming problem that explicitly accounts for uncertainty due to time change. ASD decisions can then be made by considering time-dependent variation in conditional mode response propensities and between-mode correlations in response propensities. The approach is demonstrated using a case study: the 2014-2017 Dutch Health Survey. We evaluate the sensitivity of ASD performance to 1) the budget level and 2) the length of applicable historic time-series data. We find there is only a moderate dependence on the budget level and the dependence on historic data is moderated by the amount of seasonality during the year.