Is it possible meta-analyse results with no reported correlation between exposure and outcome? I am attempting to pool results about the relationship between change in body composition and change in metabolic markers (e.g. cholesterol, triglycerides etc.) from a variety of studies. Most of these studies are RCTs (with results at the level of the study, or trial arms), with BMI as the primary outcome and metabolic markers as secondary outcomes. I am not interested in deriving a pooled estimate of the effect of the intervention on primary or secondary outcomes, but rather the pooled effect of change in primary outcome on secondary outcomes.
Results reported include:


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*Primary outcome - baseline (BL), follow-up (FU), change from BL to FU, relevant standard deviations

*Secondary outcomes - as for primary outcome


No studies reported the relationship between primary and secondary outcomes (either correlation or association).
My options for pooling results from these studies seem to be:


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*Calculate study-level change in secondary outcomes as a function of change in primary outcome (this broadly seems to be treating them as ecological studies, hence title of question). Meta regression of change in secondary outcomes on change in primary seems to be an option here - but how should I weight the individual studies?

*Multivariate meta-analysis (? outside my comfort zone!) - allowing me to derive simultaneous intervention effects on primary and secondary outcomes. Not sure this gains me a lot though.

*Borrow methods from multivariate MA (e.g. 1 and 2) to estimate or impute within study correlation, allowing me to estimate the standardised regression coefficient of secondary on primary outcomes. Thereby enabling pooling of unadjusted standardised coefficients.


However, none of these 3 options will lead to an informative meta-analysis (see comments below).
My question is therefore: 
Are there any better approaches I can use to derive a pooled estimate of change in primary outcome on secondary outcomes, given no studies reported correlations between these outcomes?
Edit 1: to focus the question
 A: Your option 1 is doable (and I have done this to examine mediation, albeit indirectly). However, what you are testing is whether treatment-related change in the primary outcome is related to treatment-related change in the secondary outcome. This is not the same thing as the correlation between the two outcomes. Also, you have an ecological validity challenge: you don't know that the same people who are changing on the one outcome are the same as those changing on the other. In my own work, I have examined whether change in a proximal outcome (employment resulting from prison-based educational programming) was related to the distal changes in future criminality (i.e., arrest).
In terms of the analysis, you can use inverse-variance weighted meta-analytic regression methods. Keep in mind that this does not account for any error in the effect size that is being used as the independent variable. Essentially, you are assessing whether the observed change in the primary outcome is related to change in the secondary outcome. I hope this helps.
