I am performing a bayesian meta-analysis and have struggled to properly account for variance of an independent variable.
In my model, I'm trying to understand how variation in X affects Y. Particularly for large values of X.
At present I have a linear model which includes terms for mu X * beta X. I also have recorded its standard error across all studies. I am particularly interested in estimating Y for high values of X. No included studies have a mean sufficiently large however I know from summary statistics that within these investigations older patients were included.
I've wondering what is conceptually the best way I can use individual study summary statistics to reduce my uncertainty at high values of X:
- Including the standard deviation of Variable X as a predictor in the model to account for within-study variability.
- Generating synthetic data for Variable X for n patients based on study-level summaries and then modelling the relationship with the study mea of Variable Y.
At present my model which relies only on mean values has vary large uncertainty when extrapolating X.
I would appreciate any insights or suggestions on how to more effectively model the variance of Variable X and its impact on Variable Y in a Bayesian meta-analysis framework. Are there specific modeling techniques or adjustments that could help reduce this uncertainty and yield more robust estimates?