fit_coef: Fit coefficients
In alstat/Radica: Radiation Induced Chromosome Aberrations

Description Usage Arguments Details References Examples

Fit coefficients to the chromosomal aberration data.

1 2	fit_coef(x, cells, aberrations, doses, cell.dist, model = "lq", level = 0.95, dist = NULL, curve = FALSE, na.rm = FALSE)

`x`	a data frame consisting the total number of cells, number of aberrations detected, doses and cell distribution of chromosomal aberration;
`cells`	column name of the total number of cells in x;
`aberrations`	column name of the aberrations detected in x;
`doses`	column name of the doses in x;
`cell.dist`	a vector of length 2 for the starting and end column of the cell distribution;
`model`	a character for type of regression model, default is set to `"lq"`, for linear-quadratic model. And `"l"` for linear model;
`level`	a numeric for the confidence level of the fitted values.
`dist`	if set to `NULL`, then the data is considered as non-overdispersed, and thus uses the Poisson family with dispersion = 1. But if set to `"overdispersed"`, then quassi-Possoin family is considered with the dispersion not restricted to 1, but is estimated.
`curve`	logical option for plot of the calibration curve. If set to `TRUE`, calibration curve is generated.
`na.rm`	logical switch, if set to TRUE, missing values are ommitted from the computation.

The function fits the coefficient into the data using the linear-quadratic model:

Y = C + α*D + β*D ^ 2

where Y is the yields of the chromosome aberrations; C, α and β are the coefficients need to be estimated; and D is the dose.

or, for high LET radiation, the α-term becomes large and eventually the β-term becomes biologically less relevant and also statistically ‘masked’ and the dose response is approximated by the linear equation

Y = C + α*D

For dicentrics, irradiation with X or gamma rays produces a distribution of damage which is very well represented by the Poisson distribution. In contrast, neutrons and other types of high LET radiation produce distributions which display overdispersion, where the variance (σ^2) exceeds the mean (y).

Because curve fitting methods are based on Poisson statistics, the dicentric cell distribution should be tested for compliance with the Poisson distribution for each dose used to construct the calibration curve. Nowadays, the most widely used test is the u test. The u test statistic is a normalized unit of the dispersion index (σ^2/y), which for a Poisson distribution should be unity. u values higher than 1.96 indicate overdispersion (with a two-sided significance level, α = 0.025).

The function returns a list:

preliminary a data frame of the original data but with new columns, for disp_idx (dispersion index) and u_test (Poisson u test);
summary a summary of the GLM model.

EPR-Biodosimetry (2011).

Quick-R. Generalized Linear Models. Retrieved June 4, 2014.

library(Radica) 

cobalt1 <- fit_coef(Cobalt60, cells = cell, aberrations = aberr,
  doses = doses, cell.dist = c(4, 9), curve = TRUE)

# for overdispersion (see if residual deviance is much larger than degrees
# of freedom) consider quasi-Poisson family.
cobalt2 <- fit_coef(Cobalt60, cells = cell, aberrations = aberr,
  doses = doses, cell.dist = c(4, 9), dist = "over-dispersed", curve = TRUE)
  
# For high Linear Energy Transfer (LET) data, we consider the linear model
# with over-dispersed distribution
mevhe <- fit_coef(Mev4He, cells = cell, aberrations = aberr, model = "l",
  doses = doses, cell.dist = c(4, 11), dist = "over-dispersed", curve = TRUE)