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I'm wondering what are some good approaches for analyzing trials where non-responders are dropped out at some set point. This is not my field, so I may be unaware of standard things!

Let's say there are 100 patients, divided 50/50 into treatment and control groups (given by an indicator variable Trt). We are measuring a normally-distributed outcome Y. The trial goes for 10 weeks (with a baseline Y taken at week 0), then the patients whose scores have not improved by (say) at least 20% (considered non-responders) are removed from the study (to seek other treatments) and are no longer followed. The trial then continues for another 10 weeks. For simplicity, assume that the only missing data is the outcomes for the non-responders after week 10.

This is plugged into a longitudinal model with random slopes and intercepts and Trt as a level-two predictor for slope (since the baseline measure shouldn't depend on group assignment).

I've seen the following approaches:

  1. Ignore the fact that the missing data is not missing at random.
  2. Carry forward the final measurement for the non-responders.
  3. Do multiple imputation to complete the data set for the non-responders.

My understanding is that no one likes 2, and 3 is okay up to standard caveats about imputation. The problem with 1 seems subtler, and I'm not sure how to properly perform inference in that situation.

My questions are: is there an acceptable way to do Option 1? Are there other approaches? For example, would it be feasible to include nonresponsiveness in the model (maybe using BUGS)? Any references would be greatly appreciated!

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    $\begingroup$ Due to their flaws, I would not use the proposed methods as primary analysis in a clinical trial but might consider them as sensitivity analysis to support the main findings. Depending on the study objectives, you could think of the following endpoints: A) Response after 10 weeks (Y/N), B) Change in Y after 10 weeks, C) Change in Y after 10 weeks only for the responder, D) Change in Y after 20 weeks only for responder. Those endpoints could be analysed by simple descriptive statistics, c.i.s and tests and would not be affected by the informative nature of your "drop-outs" $\endgroup$ – Michael M Sep 26 '13 at 9:01
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When the dropout probability is anticipated to be significant, it is best to design the study so that missing data are more likely to be missing at random. In your case this could be accomplished by having weekly visits. The continuous responses before withdrawal from treatment would be predictive of post-withdrawal values, and a full likelihood "use all available data" approach (i.e., generalized least squares, mixed effects model, or a full Bayesian model) would be very efficient and easy to interpret. It assumes that missings are missing at random given previous responses and baseline covariates, and no imputation is needed. This works a little better if the mean time-response profile is modeled as a smooth function.

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