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In an ITT randomized trial, there are one baseline response (y0) and 5 post-treatment follow-ups (y1...y5). Although the number of post-treatment follow-ups is predetermined, participants can drop out of the study. So, for example, ID 1 has responses y0, y1, y2. ID 2 has responses y0, y1, y2, y3, y4,y5. ID 3 only has response y0. I am planning to use linear mixed model for analysis.

In that case, do I need to impute the missing responses for each participant e.g. via last observation carried forward? Or no imputation needed for people who had at least one post-treatment response, which already satisfies the ITT requirement?

What if the missing response is at baseline, is multiple imputation the most common way?

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In that case, do I need to impute the missing responses for each participant e.g. via last observation carried forward?

No. There is no need to impute missing data prior to using linear mixed effects models. Imputation by last observation carried forward is also rarely appropriate. Note that linear mixed effects models will provide unbiased treatment effect estimates provided that data are missing at random. In other words, whether a data point is missing depends only on previous observations and/or model covariates. This may not be the case, for example, if people tend to drop-out because of a sudden worsening of symptoms.

What if the missing response is at baseline, is multiple imputation the most common way?

Presuming that you are including baseline score as a predictor (i.e., the RHS of the equation), multiple imputation seems to me an appropriate option (presuming only few are missing their baseline score). This way, everyone with outcome data is included in the analysis (satisfying ITT), and the uncertainty in imputed baseline scores is properly accounted for.

EDIT: First hyperlink went to wrong place. Now corrected.

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  • $\begingroup$ Say if the interaction between treatment and time of follow-up is included when running linear mixed model, due to missing outcomes, not everyone will be contributed to the treatment effect at each time point. Can it still satisfy the principle of ITT? $\endgroup$
    – aqen
    Jan 20, 2022 at 7:36
  • $\begingroup$ @aqen to my understanding, yes. The LMM uses all available measurements, thus satisfying ITT. Those participants who do not complete every time point still contribute to the estimated treatment effect. $\endgroup$
    – Lachlan
    Jan 21, 2022 at 6:21
  • $\begingroup$ @lachlan you can drop "completely" as the maximum likelihood use-all-available-data approach does not require missingness completely at random but just missing at random. $\endgroup$
    – Frank Harrell
    Jan 21, 2022 at 13:16
  • $\begingroup$ @FrankHarrell Thanks for the clarification. Corrected so that is clearer. $\endgroup$
    – Lachlan
    Jan 22, 2022 at 1:51

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