Estimating Temporal Trends using Indirect Surveys

Indirect surveys, in which respondents provide information about other people they know, have been proposed for scenarios where privacy is important or where the population to be surveyed is hard to reach. As an example, during various stages of the COVID-19 pandemic surveys, including indirect surveys, have been used to estimate the number of cases or the level of vaccination. The Network Scale-up Method (NSUM) is the classical approach to developing such estimates but was designed with discrete, time-limited indirect surveys in mind. Further, it requires asking for or estimating the number of individuals in each respondent's network. In recent years, surveys are being increasingly deployed online and collecting data continuously (e.g., COVID-19 surveys on Facebook during much of the pandemic). Conventional NSUM can be applied to these scenarios by analyzing the data independently during each time interval, but this misses the opportunity of leveraging the temporal dimension. Understanding the advantage of simply smoothing NSUM results to various degrees is not trivial. We propose to use the responses from indirect surveys collected over time and develop analytical tools (i) to prove that indirect surveys can be used to provide better estimates for the size of the hidden population compared to direct surveys, and (ii) to identify appropriate aggregations over time to further improve the estimates. We demonstrate through simulations that our approach outperforms traditional NSUM and direct surveying methods to estimate the size of a time-varying hidden population. We also demonstrate the superiority of our approach on an existing indirect survey dataset on COVID-19 confirmed cases.