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Stopping Rules for Surveys

One aspect of responsive design that hasn't really been considered is when to stop collecting data. Groves and Heeringa (2006) argue that you should change your data collection strategy when it ceases to bring in interviews that change your estimate. But when should you stop?

It seems like the answer to the question should be driven by some estimate of the risk of nonresponse bias. But given that the response rate appears to be a poor proxy measure for this risk, what should we do?

Rao, Glickman and Glynn proposed a rule for binary survey outcome variables. Now, Raghu and I have an article accepted at Statistics in Medicine that proposes a rule that uses imputation methods and recommends stopping data collection when the probability that additional data (i.e. more interviews) will change your estimate is sufficiently small. The rule is for normally distributed data. The rule is discussed in my dissertation as well.
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  1. Andy PeytchevDecember 1, 2009 at 12:32 PM

    James, I really like the idea of stopping rules and yours seems very intriguing. I hope to read your article soon :) Without having read it, it makes me wonder how estimates for different variables and different statistics (e.g., MSE) can be handled in any one of these approaches. Within a responsive design, however, it seems even more difficult to incorporate cost. When do you release a few more sample replicates instead of collecting increasingly expensive interviews? Not only does it bring in cost, but such a stopping rule would incorporate variance that is not due to nonresponse. Mindboggling, but thanks for the thought-provoking post.

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  2. Andy PeytchevDecember 1, 2009 at 12:59 PM

    For some reason my comment did not get posted... James, I wonder how contradictory criteria can be managed, such as MSE. The other somewhat related part that is missing from stopping rules are tradeoffs, such as cost (I look forward to reading your article - this is just a thought in general). At what point do you decide to add additional sample replicates instead of pursuing expensive cases, even if they still can affect estimates? Both stopping and releasing replicates are options that may contradict each other, or rather, nonorthogonal options. It would go beyond nonresponse bias and variance...

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  3. James WagnerDecember 2, 2009 at 9:38 AM

    Thanks for the comments! The criteria are not necessarily contradictory. The rule does depend on a sufficient sample size to determine that you are satisfied that the risk of your estimate changing with further data collection is small. What the sample size might be, you won't know ahead of time (you might try simulations).

    Of course, surveys also have targets for sampling error, so I suggest that you have another rule for that target. Once both rules have been met, you can stop.

    I haven't incorporated cost. In simulation, it looks like we might be going too long on some surveys. But you could imagine we are stopping too soon on others.

    There's a lot more to do. Currently, this setup relies on a single statistic (as does most sample design theory). How do we handle multi-purpose surveys? As you mention, cost issues are another issue.

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  4. dewiqq.ccJuly 18, 2019 at 11:51 AM

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