Prior distributions for observational studies - Is it worth it?

Recently I read a retrospective cohort published in BMJ (https://www.bmj.com/content/351/bmj.h3190.short) using an approach I hadn’t seen yet.

They studied the association of SSRIs with birth defects in their database using Bayesian methods. However, they first did a systematic review (SR) to find similar studies. Then they performed a meta-analysis (MA) for each birth defect to get an overall estimate based on previously published studies. Lastly, they used the meta-analytic result as the prior distribution for the exposure parameter in their logistic regression model with no down weight (see Table 3). They assigned vague priors for all other parameters in the model.

In summary, they performed an SR + MA + analyzed their cohort. Yet, very little attention - if not zero - was put into assessing the bias of the studies collected from the SR. They did mention what the included confounders were but did not go any further.

Although I quite enjoy the Bayesian framework, I am not sure about this approach. Observational studies are always more worrisome regarding bias and confounding. Thus using prior distributions based on other studies with no down weight tends to worry me.

Question 1: What do you all think? Is it worth performing an SR + MA to use prior evidence to inform our analysis and potentially bias our results (in an observational study)?

Question 2: The author performed a sensitivity analysis using a vague prior to the exposure parameter. They mainly found little difference in results. Is this enough to reassure no increase in bias was inserted into the model when using informative priors?

Question 3: If the answer to the question above was “Yes”, why worry about doing a Bayesian analysis using prior evidence in observational studies? Of note, the author did not state any posterior probability, just 95% credible intervals.

Question 4: Are you aware of any other observational studies using Bayesian methods? I would love to read more examples. I am only aware of these two thus far: https://bit.ly/3BFR4pQ + https://bit.ly/3yOmNmH

Thanks!

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i guess if instead of using the estimate from the meta-analysis as a prior distribution they simply extended the meta-analysis to include their cohort estimate it would be less contentious, but nevertheless analogous? and heterogeneity would be presented rather than lost in the prior

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An excellent point. Bayesianism’s coherence is such a profound advantage. If you ‘believe in’ the Bayesian framework, why not employ it wholesale instead of piecewise?

In that case they wouldn’t be able to perform an individual patient analysis (logistic regression adjusting for patient covariates)

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they can adjust for covariates when analysing their cohort in both approaches, bayes does feel more flexible tho

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Interesting! Do you have any reference for such model? As you mentioned, it would be nice to quantify heterogeneity while adjusting for covariates specific to their cohort

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visual display, you dont need a reference for that