How to compare different conditions between patients and controls?

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How to compare different conditions between patients and controls?

Johannes Keyser
Dear John and DBDA community,
I'd like to get some input how to best model my data, and would be grateful for any help or pointers to literature.

My data set comprises two populations: patients and control subjects.
All subjects were repeatedly assessed - albeit in different conditions, because the treatment manipulation of the patients is not applicable for controls.
While our main interest pertains the patients' treatment conditions (4 levels), I'd like to compare them with the "natural variation" observed in the control group, who just repeated our experiments twice.
Thus abstractly, the patient group is split by a within-factor of 4 levels P1-P4, and the controls are split by a 2-level within factor, C1 and C2. What's the best method to compare these, assuming normal distributed response variables?

Currently I use one-way BANOVAs, extended by a subject factor to account for repeated measures. But with these models (4 and 2 levels, respectively), I think I can only model the two population groups separately in different models, which hinders direct comparisons between parameter estimates.

My questions in particular:
1) Can/should I extend the BANOVA model to include both populations?
2) Or is it possible to compare the parameters of different BANOVA models? If so, how?
3) Does this kind of design have a specific name? This might be handy to know to search for modeling examples.

Thank you very much in advance!
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Re: How to compare different conditions between patients and controls?

Johannes Keyser
I talked to a colleague, who was of the opinion that I can directly compare posteriors from different models, provided that they are in the same units and "play the same role" in the model.
In my example, it would be admissible to compare both BANOVAs' b0 parameters, i.e. their baselines. Using that comparison, I would at least be able to state whether the groups are different from each other on average.

Specifically, the comparison has to be directly computed from the MCMC chains. For each pair of values, randomly sampled from the chains, I would compute the difference, and thus build up a distribution of differences. This then may be inspected with the usual methods, e.g. using its 95% HDI.

While this sounds correct to me, I'd like to know some more details. How many samples should/can I draw from the chains? Should I inspect the autocorrelation? Any help and/or pointers to literature are greatly appreciated!

Cheers,
Johannes
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Re: How to compare different conditions between patients and controls?

John K. Kruschke
Administrator

Dear Johannes:

Regarding the model structure, yes, you should be able modify the ANOVA-style models to suit the structure of your data. This is not to say it is necessarily trivial or obvious how to do that, especially when trying to impose the sum-to-zero constraints (if you choose to do so). For example, see this blog post about a split-plot design, which is related to the sort of design you have:
http://doingbayesiandataanalysis.blogspot.com/2012/05/split-plot-design-in-jags-revised.html

Regarding computing differences: At every step in the MCMC chain, you can compute differences or ratios or other transformations of parameters in whatever way is meaningful. At each step in the chain, the parameters are *jointly* representative of the posterior distribution.

If you have split your data into two parts that are modeled separately, then the parameter values are, by definition, independent. You can then set the two chains side-by-side and take differences between them as if they were in a joint space.

Hope that helps...

--John




On Thu, Mar 13, 2014 at 1:47 PM, Johannes Keyser [via Doing Bayesian Data Analysis] <[hidden email]> wrote:
I talked to a colleague, who was of the opinion that I can directly compare posteriors, provided that they are in the same units and play the same "role" in the model.
In my example, it would be admissible to compare the b0 parameters, i.e. the BANOVA baselines from different models. Using that comparison, I would at least be able to state whether the groups are different from each other on average.

Specifically, the comparison has to be directly computed from the MCMC chains. For each pair of values, randomly sampled from the chains, I would compute the difference, and thus build up a distribution of differences. This then may be inspected with the usual methods, e.g. using its 95% HDI.

While this sounds correct to me, I'd like to know some more details. How many samples should/can I draw from the chains? Should I inspect the autocorrelation? Any help and/or pointers to literature are greatly appreciated!

Cheers,
Johannes


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Re: How to compare different conditions between patients and controls?

Johannes Keyser
Dear John, thank you very much for your answer.

I will look into the split-plot; currently however I am assuming our patients and controls to come from two separate populations, and thus don't see what kind of overarching distribution would be meaningful in this case. For simplicity, I therefore opt for the two-separate model option. As you said the comparisons are then independent but direct comparisons are still admissible.

That is, if you meant to actually say that - there's a splinter of doubt that you might have meant the opposite (and missed to write a "NOT"?), because your description seems to lead to the conclusion that one should NOT subtract independently estimated chains? Sorry to ask again, but I would feel much safer if you could once more emphasize whether any NOT ist missing :-).

Thanks again!
Johannes
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