Is it more appropriate to use random effect model in meta analysis when studies have high heterogeneity but they are not randomised? I am using case control studies for a meta analysis. The participation selection is not random but the studies used different statistical analysis methods with their results and there is significant heterogeneity between studies used (Using a random effects model for meta analysis I2 = 95%, p=<0.00001). Also a previous meta analysis used random effects to account for high heterogeneity. Is this correct and to reference the previous study?

Over a decade ago, the standard practice was to use a fixed-effect model when statistical heterogeneity was low and a random-effects model with high heterogeneity. That concept is both out-dated and wrong as a random-effects model does not magically make the pooling valid when the results of the individual studies are markedly different. That doesn't mean that we don't still see this argument come up time and time again.
There are several issues to consider when deciding whether a fixed-effect or random-effects model should be used. This should be decided a priori based on the study designs, anticipated variations in populations, intervention details, etc. In your case, I would even reconsider if pooling should be done in the first place. There is definitely a lot of factors to consider before making the decision on how best to present the evidence summary, but the decision on model should not be based on the I-squared value.
