Sorry for the delay in answering your request for clarification. Before I start I may mention that I was a member of the Peer Review committee for the Hanford dose reconstruction project. My task was to look at the uncertainty and sensitivity analysis of the reconstructed dose values. The computation of 100 replicates is due to my initiative. This explains my concern about the misuse of these replicates.

There are two kinds of uncertainty involved in the estimation of the dose response parameter using reconstructed dose values and an observed disease vector:
a) The uncertainty of the dose response parameter, given an observed
disease vector and the dose vector;
b) The uncertainty of the dose vector.

All that is given with respect to b) is a random sample of size K of dose vectors drawn according to an N-dimensional subjective probability distribution quantifying what the analysts’ believe to know about the true dose vector. Since b) is necessarily quantified by subjective probability (the degree of belief interpretation of “probability” – a Bayesian concept) you cannot expect to have confidence limits (a concept from classical statistics) for the dose response parameter that account for a) and b).

There are only two options:
1) A fully Bayesian analysis, i.e. also for the uncertainty under a), which gives subjective probability limits but not confidence limits for the dose response parameter.
or
2) The computation of a q% confidence limit for the dose response parameter with each replicated dose vector used as if it were the true dose vector. The uncertainty under b) is then taken care of by estimating a u% subjective probability limit for the q% confidence limit. This was the approach mentioned in the last paragraph of my comment.


With respect to your remarks concerning the hypothesis test I would like to answer as follows:
If the test is performed with each of the K replicated dose vectors and the hypothesis is rejected for m out of the K tests then the subjective probability for rejection of the hypothesis test can be estimated and a confidence interval or limit obtained for this subjective probability. I am sure you do not want to deny this.

The problem of the classical “measurement” error is well known and a state of the art dose reconstruction study would treat it at the source namely for the input data that are subject to classical “measurement” error.

I hope I succeeded in providing the requested clarification.