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I am trying to conduct a meta analysis for dose response studies where I am using fractional polynomial transformation from predefined family of powers. Now data fitting using all possible combinations will yield large number of possible models where some of them are clearly not good while there are few models that produce low heterogeneity. Now to choose the best model there is the problem of the dimensionality similarity. All models have the same number of parameters so using AIC or BIC is just a reflection for the likelihood. Any suggestions to proper model selection method in this case? Thanks

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