A colleague has a dataset from a before and after study looking at a continuous outcome that was measured in individuals before and after an intervention. An unknown but not insubstantial proportion of the individuals were only measured before or after the intervention.  However, due to an oversight following changes to the study design due to ethics they have only now realised that there is no way to link the before and after measurements that were made to the same individuals, i.e. there is no person ID.  Consequently, the data consists of a mix of paired and independent samples, but can only be treated as independent samples.  Are there any reasonable ways to mitigate this problem or address it, e.g. via some kind of sensitivity analysis?
An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B).
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