A framework for sample size calculations in longitudinal surveys to measure net and gross changes

In longitudinal surveys, repeated measurements are collected from the same sample units over time to measure gross change (i.e., change at the level of individual sample members). Longitudinal samples are sometimes supplemented by fresh sample to measure net change (i.e., change at the aggregate level). That is, in each measurement wave, while one part of the sample is newly recruited (fresh), another part overlaps with previously interviewed sample (repeated interviews). Many aspects of survey design of longitudinal surveys have been studied extensively, such as definition of target population, sample design, survey weighting, intervals between interviews, nonresponse, and panel attrition. Although the impact of the overlap between samples on the statistical power has been studied, sample size determination lacks a formulation that takes account of these factors in longitudinal surveys that aim to measure net and gross changes simultaneously. In this study, we propose a framework for sample size calculation to measure net and gross changes in estimated means or proportions concurrently in longitudinal surveys. We present a framework to compute panel and fresh sample sizes for varying levels of net and gross change. Finally, we illustrate the framework using nchange, an R package we developed to execute the algorithm of the proposed framework. The framework and the R package will support researchers to determine sample sizes targeting specific power of analysis with respect to measuring net and gross changes in rotating- or split-panel surveys.