question: fitting two datasets

[Linas Mockus]

Hi,

I have a question about fitting two datasets - drug concentration in plasma and urine in the same model. There are very few urine points while plasma is quite rich. Urine fit is very poor while plasma is very good. I wonder if there are legitimate ways to increase the weight of urine data.

Thanks for any insight,
Linas

[Linas Mockus]

Just to clarify - while plasma data has 10 points for each individual urine data has only a single point per individual. Because of this my guess the urine fit is poor. What is the proper way to improve the fit?

[Bob Carpenter]

There's no magic bullet. Your can collect more data,
add more prior information, or formulate a better model.

I'm assuming you're pooling across individuals already, or
that would go first on the list.

- Bob

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[Linas Mockus]

Thanks, Bob. Since data is retrospective I had to use informative prior. The fit of urine improved significantly (very good) without really affecting concentration. This is why FDA doesn't like Bayes - strong prior and few data points and you can get anything.Hopefully in this case I can justify the prior that 5% error in urine measurements is reasonable.

Linas

[Andrew Gelman]

You write:  "This is why FDA doesn't like Bayes - strong prior and few data points and you can get anything."

That's ok for me.  The point is that FDA should require that the prior be science-based.  For example, consider the normal(0, infinity) priors that are implicitly used by the fat-arms-and-political-attitudes crowd.  Those are really strong priors, not at all supported by science!

P.S. to Linas:  I'll quote this exchange on blog (along with any reply you might have).  Do you have any objection to your name being used?  This exchange is already public (as it's on an open list) but if you'd rather not have your name used on the blog, I understand.

A

On Apr 13, 2017, at 9:41 AM, Linas Mockus <linasm...@gmail.com> wrote:

Thanks, Bob. Since data is retrospective I had to use informative prior. The fit of urine improved significantly (very good) without really affecting concentration. This is why FDA doesn't like Bayes - strong prior and few data points and you can get anything.Hopefully in this case I can justify the prior that 5% error in urine measurements is reasonable.

Linas

[lmockus]

Andrew, 

I think if you read clinical studies for medical devices carefully enough the allowance for informative priors as long as they are scientifically based is there (we need to doublecheck). But prevailing recommendation is using non informative priors. Therefore my guess the conception is that FDA is not supporting strong priors. We can't deny that FDA has prominent Bayesists. The recent comment about using informative prior by FDA statistician was "how we defend the approach with industry" so there are some other aspects that are not so visible. In my case the strong prior is justified since 5% error in urine measurements is tight but still in the realm of reasonable. Since we had only few data points it was the only way to reconstruct the parameters and show that PBPK models fit clinical data well. 

Perhaps it would be preferable to leave my name out.

Linas

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[Andrew Gelman]

OK, I'll share this discussion but without your name.  (Remember, though, that the stan-users list is public!)

A

[lmockus]

Andrew,

No problem, I don't think that my name substantiates the blog - I am not a prominent scientist. However, I completely agree with you - priors should be scientifically justified. Personally I am struggling with this - what prior should I use. When I have lots of data it becomes easy - slightly informative prior which makes sense works fine since data does the talking. There are some problematic situations - when you get several modes. Then I define the more informative prior on a parameter which leads to multiple modes - usually it is easy to figure out if parameters have physical meaning. When I have few data points (as in this case) I had to use reasonably tight prior based on historical experience in order to demonstrate that a good model is indeed good. I still plan to relax the prior and see how the fit changes.