Dear colleagues:

 

Thanks very much for the replies related to my e-mail below.  Following the e-mail I have summarized the key replies received.

 

B. R. Scott

 

-----Original Message-----
From: Scott, Bobby
Sent: Monday, September 08, 2003 4:04 PM
To: [log in to unmask]
Subject: Help on interpretation of WinBUGS output

 

Colleagues:

 

We have used WinBUGS to implement fitting of a biological-based model to data for low-dose radiation induced stochastic biological effects (neoplastic transformation) in cells.  The mechanistic model involves four parameters which I will simply refer to here as A, B, C, and D and can yield hormetic-type dose-response relationships.  When A and B both equal zero, the model is identical to the linear, no-threshold (LNT) model used in low-dose cancer risk assessment.  In implementing our Bayesian analysis with WinBUGS, we have counted by iteration the posterior data sets (after discarding the burn-in) generated for which both A and B were zero.  This occurred 2 out of each 1000 iterations (total 20000 iterations).  We interpret these results to favor a dose-response shape other than associated with the LNT model.  Are we correct to assign a p value =2/1000 (or p < 0.01) for rejecting the LNT model?

 

Any comments you may have would be appreciated.

 

B. R. Scott

LRRI, Albuquerque, NM, USA

 

Key Replies to Above E-mail:

 

1. "A very fundamental question!" The indicated frequency of occurrence of the combination A=0, B=0 is not a p value.  It is a posterior probability that depends on the prior assumptions (probabilities).
2. The "step(x)" function can be used to count the occurrences of events of interest.
3. "With only 40 iterations having A=B=0, the estimate of the probability isn't great.  It may be that the chains are auto-correlated, so that these are not independent draws from the posterior, in which case the estimate could be way off (especially if all 40 iterations occurred together).  The only real way to check this is to run longer chains (or more chains) and see if the probabilities converge."
4. Define the LNT model in some formal graphical way that includes values near zero for A and B (i.e., close to the LNT model) and then use the LNT criteria to evaluate the posterior probability for the LNT model.  Otherwise one has to assign a "posterior probability for exactly LNT" = 0.002.

 

Comment related to 4 above: not all linear models are of the LNT type.  Linear-threshold (LT) models are considered different from LNT models with respect to assessing cancer risk to humans from exposure to toxic agents.  With LT models, doses below the threshold are considered not to cause cancer.  With the LNT model, any exposure to a genotoxic agent (one that damages DNA) of interest is considered to increase the cancer risk.  Neither the LNT nor LT model allows for risk to decrease after exposure.  Our recent publication (reference provided below) shows evidence that low-dose gamma radiation can turn on a protective process that leads to a decrease in the risk for stochastic biological effects.  Our current research indicates low doses of other agents (e.g. genotoxic chemicals) may also turn on the protective process.

 

 

Reference:  B. R. Scott et al. 2003.  Mechanistic basis for nonlinear dose-response relationships for low-dose radiation-induced stochastic effects."  Nonlinearity in Biology Toxicology and Medicine, Vol.1, No 1, pp. 93-122. [Available by request from B. Scott in pdf fomat]