In YiyiLiu1/bdChemo: Cell birth and death rates estimation

In this vignette, we give an example illustrating the usage of R package bdChemo.

Function bdChemo requires the following input:

z: compound concentrations (in log10 scale); a vector
x0: initial cell population sizes corresponding to concentrations in z; a vector (same length as z)
xt: cell population sizes at follow-up time corresponding to concentrations in z; a vector (same length as z)
x0c: control group (without compound treatment) initial cell population size; a scaler; for computing GI50
xtc: control group (without compound treatment) cell population size at follow-up time; a scaler; for computing GI50
bk: background noise measurements
curve.plot: whether to produce cell growth, birth and death rates plots
sample.return: whether posterior samples of \lambda and \lambda should be returned

Other arguments with default values are:

N: number of iterations
sa2l: prior normal distribution variance for \alpha_\lambda; sa2l controls the scale of \phi_\lambda in prior
sa2m: prior normal distribution variance for \alpha_\mu; controls the scale of \phi_\mu in prior
at: prior inverse-gamma distribution shape parameter for \tau_\lambda^2 and \tau_\mu^2
bt: prior inverse-gamma distribution rate parameter for \tau_\lambda^2 and \tau_\mu^2; at and bt together control the scale of \tau^2 in prior, which affects the fluctuation amplitude of the estimated curve (\tau is called amplitude parameter of the Gaussian kernel and the larger \tau^2 is, the larger the amplitude tends to be)
al: prior gamma distribution shape parameter for l_\lambda^2 and l_\mu^2
bl: prior gamma distribution rate parameter for l_\lambda^2 and l_\mu^2; al and bl together control the scale of l^2 in prior, which affects the smoothness of the estimated curve (l is called the length scale parameter of the Gaussian kernel, the larger l^2 is, the smoother the curve tends to be)
ql: lower bound of credible interval intended to output
qu: upper bound of credible interval intended to output

library("bdChemo")
data(example)
bd.example = bdChemo(example$z, example$x0, example$xt, example$x0c, example$xtc, example$bk, curve.plot = TRUE, sample.return = FALSE, N = 1e5)

The above code will plot cell growth, birth and death rate curves, similar to the one shown in Figure 3 of the manuscript (except that in the cell growth curve we plot cell counts normalized by initial cell population sizes since we allow the initial cell population sizes to be different across compound concentrations here). In addition, it also return a list "bd.example" with the following elements as described in users' manual. We will show the usage of these elements in the following code.

## log concentrations where mu and lambda are returned
znew = bd.example$znew

## means and credible intervals of mu, lambda and Kendall Process at znew
lambda.mean = bd.example$lambdas[1,]
lambda.lower.bound = bd.example$lambdas[2,]
lambda.upper.bound = bd.example$lambdas[3,]
mu.mean = bd.example$mus[1,]
mu.lower.bound = bd.example$mus[2,]
mu.upper.bound = bd.example$mus[3,]
kmean.mean = bd.example$kmean[1,]
kmean.lower.bound = bd.example$kmean[2,]
kmean.upper.bound = bd.example$kmean[3,]

## means and credible intervals of GI50, TGI, LC50 and IC50
gi50.mean = bd.example$summary[1,1]
gi50.lower.bound = bd.example$summary[2,1]
gi50.upper.bound = bd.example$summary[3,1]

tgi.mean = bd.example$summary[1,2]
tgi.lower.bound = bd.example$summary[2,2]
tgi.upper.bound = bd.example$summary[3,2]

lc50.mean = bd.example$summary[1,3]
lc50.lower.bound = bd.example$summary[2,3]
lc50.upper.bound = bd.example$summary[3,3]

## posterior samples of mu and lambda (can be used to calculate other summary statistics of interest)
lambda.sample = bd.example$post.lambda
mu.sample = bd.example$post.mu