What you are basically saying is "analysis => synthesis doesn't work."

I am pretty sure it is not going to let you take an effect size and a standard error from a correlation study and get out a accurate posterior distribution of the causal effect without doing something similar to what I'm proposing.

If there are two RCTs, we have two sets of outcomes: Y1(a), Y1(a') and Y2(a), Y2(a'). Even here, there is no one causal effect so far. We need to make some sort of assumption on how to combine these. For example, we may try to generalize regression models, and say that a lot of the way A affects Y is the same regression across the two studies, but some of the regression terms are allowed to differ to model population heterogeneity. This is what hierarchical models do. In general we have E[f(Y1(a), Y2(a))] - E[f(Y1(a'),Y2(a'))], for some f(.,.) that we should justify. At this level, things are completely non-parametric. We can model the relationship of A and Y1,Y2 however we want. We can model f however we want.

Ok, and how do we model them? I am proposing a multilevel mixture model to compare them.

If we have one RCT and one observational study, we still have Y1(a), Y1(a') for the RCT, and Y2(a), Y2(a') for the observational study. To determine the latter we use "interventionist approaches" to express them in terms of observational data. We then combine things using f(.,.) as before. As before we should justify all the modeling we are doing.

Which is not going to work since in most, if not all, of these studies, the original patient-level data is not going to be available and you're not even going to get a correlation matrix out of the published paper, and I haven't seen any intervention-style algorithms which work with just the effect sizes which is what is on offer.

To work with the sparse data that is available, you are going to have to do something in between a meta-analysis and an interventionist analysis.

I am proposing a multilevel mixture model to compare them.

Ok. You can use whatever statistical model you want, as long as we are clear what the underlying object is you are dealing with. The difficulty here isn't the statistical modeling, but being clear about what it is that is being estimated (in other words the interpretation of the parameters of the model). This is why I don't talk about statistical modeling at first.

haven't seen any intervention-style algorithms which work with just the effect sizes which is what is on offer.

If all you have is reported effect sizes you won't get anything good out. You need the data they used.

Open thread, Dec. 21 - Dec. 27, 2015

by MrMind 1 min read21st Dec 2015233 comments

2


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