How to deal with dropouts from a waiting list control group?

Question

Many treatment studies compare a treatment group with a waiting list control group, for example to adjust for spontaneous remissions. Unfortunately, many more participants drop out from the waiting list control group than from the treatment group.

One reason for participants dropping out from the waiting list group might be that the condition for which they had been seeking treatment has disappeared and that they no longer are interested in participating in a treatment they no longer need. Unfortunately these dropouts make the waiting list group "more sick" on average than it would have been, thus confounding results. Other dropouts may differ in personality or other relevant factors from the remaining participants, thus reducing the quality of the random group assignment.

How do you deal with these dropouts in data preparation and analysis?

I often see that participants are matched according to age, gender and socioeconomic status. But this does not compensate for spontaneous remission dropout or other factors of which we might be unaware. Are there other, maybe better methods?

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Answer 1

One thing you want to think about is the distribution of missingness or "missingness mechanism." See the figure below from Schafer & Graham (2002). Your missing data are missing at random (MAR) if the missingness is unrelated to the missing data itself, but missing not at random (MNAR) if the missingness is related to the missing data itself. For instance, your missing data are MNAR if you are missing depression scores for some subjects and the probability of a score being missing is significantly associated with that depression score itself (e.g., healthier people are more likely to drop out). However, your missing data are MAR if this association disappears after controlling for other predictors for which complete data is known (e.g., gender, SES, and personality). This is one of the reasons that it can be very helpful to collect as much data about a person at intake as possible.

Of course, you can't determine the association between Y and the other variables when data is missing so MAR is usually an assumption rather than a demonstrable property (unless you obtain followup data from non-respondents). However, it is still an important thing to think about as the accuracy of MAR-based methods will depend on how well this assumption holds.

The two most popular missing data techniques for MAR data are maximum likelihood (ML) and multiple imputation (MI). ML methods draw inferences from a likelihood function based on a model for the complete data. MI methods generate multiple plausible alternative versions of the complete data and then combine the results from each version. There are also new methods being developed all the time and dealing with MNAR data is a definite priority. See Schafer & Graham (2002) for more.

References

Enders, C. K. (2010). Applied missing data analysis. New York, NY: Guilford Press.

Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177.