Since the Laplace distribution recently justified to represent jitter in the CNA breakpoints is not sufficiently accurate to estimate small changes, we propose a more accurate approximation based on the modified Bessel function of the second kind and zeroth order.
Bayesian estimates of the magnitude of the change tend to estimate small shifts almost precisely.
In addition, complex models of this type, even if correctly specified, are fraught with statistical uncertainty, which severely limits their usefulness in making estimates of small changes in response that are needed in risk assessments to support exposure standards.
Further research should also be conducted to assess other aspects of responsiveness including the minimal important difference (MID), a concept related to estimating the smallest change in score that can be regarded as important [ 10].
Our approach to estimating biosynthetic cost simulates small changes in the demand for an amino acid in cell growth (as part of the biomass producing reaction) then analyses the corresponding response in the supply of three nutrients: glucose, ammonium and sulphate.
This theory estimates whether any small change in the equilibrium state of the stress field in the mining region provokes a sudden release of energy or induces a large change in the geometry of the mine system.
Although we used questions that have previously been validated with nicotine measures [ 40], and we estimated a relatively small change in SHS smoking status during follow-up in the cohort, we cannot exclude the possibility that our finding for no association with duration of SHS exposure was due, in part, to non-differential misclassification.
Nevertheless, our sensitivity analyses suggested robustness of our results, as there were relatively small changes in estimated rates from the addition of an incremental case of leiomyosarcoma to one large or small trial previously reporting no cases.
Weaknesses have been identified with this methodology in modeling disease progression, obtaining good quality information on costs for patients treated in the community, and sensitivity to small changes in estimated incremental costs.
Statistical estimates are obtained for small changes in the coupling stiffness based on the information derived from the ensemble of damage patterns.
