Predict median and 95% credible interval of the x% Lethal Concentration.
The function LCx, \(x\)% Lethal Concentration (\(LC_x\)), is use to compute
the dose required to kill \(x\)% of the members of a tested population
after a specified test duration (time_LCx) (default is the maximum
time point of the experiment).
Mathematical definition of \(x\)% Lethal Concentration at time \(t\), denoted \(LC(x,t)\), is:
\(S(LC(x,t), t) = S(0, t)*(1- x/100)\),
where \(S(LC(x,t), t)\) is the survival probability at concentration \(LC(x,t)\) at time \(t\), and \(S(0,t)\) is the survival probability at no concentration (i.e. concentration is \(0\)) at time \(t\) which reflect the background mortality \(h_b\):
\(S(0, t) = exp(-hb* t)\).
In the function LCx, we use the median of \(S(0,t)\) to rescale the
\(x\)% Lethal Concentration at time \(t\).
LCx(object, ...)# S3 method for survFit
LCx(object, X, time_LCx = NULL, conc_range = NULL, npoints = 100, ...)
returns an object of class LCx.
The function returns an object of class LCx, which is a list
with the following information:
Survival probability of individuals surviving considering the median of the background mortality (i.e. \(S(0, t)*(1- x/100)\))
Survival probability of individuals surviving as provided in arguments (i.e. \((100-X)/100)\)
A number giving the time at which \(LC_{x}\) has to be estimated as provided in arguments or if NULL, the latest time point of the experiment is used.
A data.frame with quantiles (median, 2.5% and 97.5%)
of \(LC_{X}\) at time time_LCx for \(X\)% of individuals
A data.frame with four columns: concentration, and median q50 and 95% credible interval
(qinf95 and qsup95) of the survival probability at time time_LCx
An object of class survFit
Further arguments to be passed to generic methods
Percentage of individuals dying (e.g., \(50\) for \(LC_{50}\), \(10\) for \(LC_{10}\), ...)
A number giving the time at which \(LC_{x}\) has to be estimated. If NULL, the latest time point of the experiment is used.
A vector of length 2 with minimal and maximal value of the range of concentration. If NULL, the range is define between 0 and the highest tested concentration of the experiment.
Number of time point in conc_range between 0 and the maximal concentration. 100 by default.
When class of object is survFit, see LCx.survFit.