  Indirect surveys, in which respondents provide information about other people
they know, have been proposed for estimating (nowcasting) the size of a
\emph{hidden population} where privacy is important or the hidden population is
hard to reach. Examples include estimating casualties in an earthquake,
conditions among female sex workers, and the prevalence of drug use and
infectious diseases. The Network Scale-up Method (NSUM) is the classical
approach to developing estimates from indirect surveys, but it was designed for
one-shot surveys. Further, it requires certain assumptions and asking for or
estimating the number of individuals in each respondent's network. In recent
years, surveys have been increasingly deployed online and can collect 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 at each point in time, but this misses the opportunity of
leveraging the temporal dimension. We propose to use the responses from
indirect surveys collected over time and develop analytical tools (i) to prove
that indirect surveys can provide better estimates for the trends of the hidden
population over time, as compared to direct surveys and (ii) to identify
appropriate temporal aggregations to improve the estimates. We demonstrate
through extensive simulations that our approach outperforms traditional NSUM
and direct surveying methods. We also empirically demonstrate the superiority
of our approach on a real indirect survey dataset of COVID-19 cases.
