Stopping rules for surveys with multiple waves of nonrespondent follow-up

In surveys with multiple waves of follow-up, nonrespondents to the first wave are sometimes followed intensively but this does not guarantee an increase in the response rate or an appreciable change in the estimate of interest. Most prior research has focused on stopping rules for Phase I clinical trials. To our knowledge there are no standard methods to stop follow-up in observational studies. Previous research suggests optimal stopping strategies where decisions are based on achieving a given precision for minimum cost or reducing cost for a given precision. In this paper, we propose three stopping rules that are based on assessing whether successive waves of sampling provide evidence that the parameter of interest is changing. Two of the rules rely on examining patterns of observed responses while the third rule uses missing data methods to multiply impute missing responses. We also present results from a simulation study to evaluate our proposed methods. Our simulations suggest that rules that adjust for nonresponse are preferred for decisions to discontinue follow-up since they reduce bias in the estimate of interest. The rules are not complicated and may be applied in a straightforward manner. Discontinuing follow-up would save time and possibly resources, and adjusting for the nonresponse in the analysis would reduce the impact of nonresponse bias.