ASA Connect

I recently have become involved in analyses involving food allergies. The issue is estimating a safe dose or threshold at a population level. Patients are given oral food challenges at specific doses that increase over the course of the test, letting some time lapse between doses to avoid most of the carryover effect. When they start to have any symptoms, usually slight, the test is stopped. The minimum eliciting dose can then be established for the individual.

The question is how this applies to a population. It is usually framed as the threshold dose such that only a small fraction of individuals in the population, say 1%, will experience a reaction. The eliciting dose or EDp is the dose of allergen that produces a response in p% of the allergic population. Much work has been done on this by food safety scientists such as Steve Taylor, Rene Crevel and others.

The statistical approach used is interesting. They use an interval-censored survival analysis where dose is the time variable. They estimate the proportion responding at each dose and fit survival models, such as the Weibull, to obtain a smooth distribution. The interval-censoring allows for different dosing across different individuals.

This seems to be a clever approach, but it seems unusual for a dose-response analysis. I haven’t seen it used in other fields. I’m just curious if anyone else has encountered this or has any other insight into the question.

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Nancy Cook
Brigham & Women's Hospital
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While their approach is interesting, even if it is valid it seems to me a bit like using a hammer to kill a fly.  I also wonder whether they are getting information that has clinical interpretability (e.g. a confidence interval for that first percentile).  

This sounds to me like a case where you could just use an approach that estimates, with confidence, that first percentile.  I think this would be the more straight forward and standard approach, and for the first percentile it would require that you know the lowest few data points (but if people at the upper end are censored that would be ok).

You would need fairly large samples to do this with much precision (in the 100s), no matter how you do it.  So if they are using small samples here I would question the value of their results in any case.  

I haven't vetted the accuracy, but this resource looks like it might have some helpful information:  http://people.stat.sfu.ca/~cschwarz/Stat-650/Notes/PDF/ChapterPercentiles.pdf

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Joe Nolan
Associate Professor of Statistics
Director, Burkardt Consulting Center
Northern Kentucky University
Department of Mathematics & Statistics

I've never seen anyone else do what you're describing, but I did something very much like that when I was a graduate student back in the '90s. The task set to our class was, find a colleague's problem, and apply Survival Analysis to it. My colleague had mosquitoes, treated in independent groups at different dose levels of a chemical. The outcome was death. I treated dose as the time variable. To the best of my memory, observations were right-censored for dead mosquitoes, and left-censored for alive mosquitoes. It seemed to work well. Sadly, I did not re-analyze via more traditional methods for comparison purposes.

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Eric Siegel
Biostatistician
Univ of Arkansas for Medical Sciences, Department of Biostatistics

Nancy,

Did the toxicologist/researchers come up with this approach? If so, where did they develop the idea? 

I've read through many tox texts dealing with dose/responce curves and tox testing. Many of the ideas I read "look good" until you think about it for a while. If you compare it back to what you know and are familiar with, and it doesn't stack up, don't be afraid to call it out. 

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Andrew Ekstrom

I agree that this sounds a bit unusual for dose-response modeling. If you were interested in the whole dose-response curve then I think this corresponds to a situation for a dose-titration model (also known as optional titration design, flexible dose titration and others).

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Martin Kappler
statalpha