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A new inverse regression model applied to radiation biodosimetry.

Higueras M, Puig P, Ainsbury EA, Rothkamm K - Proc. Math. Phys. Eng. Sci. (2015)

Bottom Line: For compound Poisson responses, complete and simplified models are provided.The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions.We provide R and SAS codes which reproduce these examples.

View Article: PubMed Central - PubMed

Affiliation: Centre for Radiation, Chemical and Environmental Hazards, Public Health England , Chilton, Oxfordshire OX11 0RQ, UK ; Departament de Matemàtiques , Universitat Autònoma de Barcelona , Bellaterra, Barcelona 08193, Spain.

ABSTRACT

Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by means of Hermite and negative binomial (NB) distributions. For compound Poisson responses, complete and simplified models are provided. The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions. Three examples of applications are given that demonstrate the usefulness of these methodologies in cytogenetic radiation biodosimetry and in radiotherapy. We provide R and SAS codes which reproduce these examples.

No MeSH data available.


Related in: MedlinePlus

Observed means (dots), plus/minus twice their standard errors (error bars), and predicted means (solid line) of the number of dicentrics for Poisson fitting, based on the data in table 1, omitting the 1.5 Gy test data. (Online version in colour.)
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RSPA20140588F1: Observed means (dots), plus/minus twice their standard errors (error bars), and predicted means (solid line) of the number of dicentrics for Poisson fitting, based on the data in table 1, omitting the 1.5 Gy test data. (Online version in colour.)

Mentions: In this example, for high-dose rate gamma-radiation exposure, an appropriate dose–response curve, i.e. the regression model, is a second degree polynomial without intercept [3], f(x,β)=β2x2+β1x (figure 1). In biodosimetry, this is called the linear-quadratic dose–response curve. The intercept has been removed because we assume that for a dose x=0 the expected number of dicentrics will be zero (for the 0 Gy sample there was only 1 dicentric in a total of 2592 blood cells). In general regression modelling, to analyse count data using a second degree polynomial mean response is not common, and a log-link mean response is the usual approach. However, in biodosimetry, the linear-quadratic dose–response curve has a biophysical interpretation [3] and is one of the most frequently employed in practice. Some problems could occur maximizing the likelihood function because β1 and β2 have to be necessarily positive. To ensure this, it is sometimes necessary to use numerical algorithms allowing constrains in the parameter domain.Figure 1.


A new inverse regression model applied to radiation biodosimetry.

Higueras M, Puig P, Ainsbury EA, Rothkamm K - Proc. Math. Phys. Eng. Sci. (2015)

Observed means (dots), plus/minus twice their standard errors (error bars), and predicted means (solid line) of the number of dicentrics for Poisson fitting, based on the data in table 1, omitting the 1.5 Gy test data. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4309124&req=5

RSPA20140588F1: Observed means (dots), plus/minus twice their standard errors (error bars), and predicted means (solid line) of the number of dicentrics for Poisson fitting, based on the data in table 1, omitting the 1.5 Gy test data. (Online version in colour.)
Mentions: In this example, for high-dose rate gamma-radiation exposure, an appropriate dose–response curve, i.e. the regression model, is a second degree polynomial without intercept [3], f(x,β)=β2x2+β1x (figure 1). In biodosimetry, this is called the linear-quadratic dose–response curve. The intercept has been removed because we assume that for a dose x=0 the expected number of dicentrics will be zero (for the 0 Gy sample there was only 1 dicentric in a total of 2592 blood cells). In general regression modelling, to analyse count data using a second degree polynomial mean response is not common, and a log-link mean response is the usual approach. However, in biodosimetry, the linear-quadratic dose–response curve has a biophysical interpretation [3] and is one of the most frequently employed in practice. Some problems could occur maximizing the likelihood function because β1 and β2 have to be necessarily positive. To ensure this, it is sometimes necessary to use numerical algorithms allowing constrains in the parameter domain.Figure 1.

Bottom Line: For compound Poisson responses, complete and simplified models are provided.The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions.We provide R and SAS codes which reproduce these examples.

View Article: PubMed Central - PubMed

Affiliation: Centre for Radiation, Chemical and Environmental Hazards, Public Health England , Chilton, Oxfordshire OX11 0RQ, UK ; Departament de Matemàtiques , Universitat Autònoma de Barcelona , Bellaterra, Barcelona 08193, Spain.

ABSTRACT

Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by means of Hermite and negative binomial (NB) distributions. For compound Poisson responses, complete and simplified models are provided. The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions. Three examples of applications are given that demonstrate the usefulness of these methodologies in cytogenetic radiation biodosimetry and in radiotherapy. We provide R and SAS codes which reproduce these examples.

No MeSH data available.


Related in: MedlinePlus