ny_u

Conditional negative log-likelihood \(-l(y \vert u)\) of y given the random effects u

internal

A random-effects stochastic model that allows quick detection of
clonal dominance events from clonal tracking data collected in gene therapy studies. Starting from the Ito-type equation describing the dynamics of cells duplication, death and differentiation at clonal level, we first considered its local linear approximation as the base model.
The parameters of the base model, which are inferred using a maximum likelihood approach,
are assumed to be shared across the clones. Although this assumption makes inference easier,
in some cases it can be too restrictive and does not take into account possible scenarios of clonal dominance.
Therefore we extended the base model by introducing random effects for the clones.
In this extended formulation the dynamic parameters are estimated using a tailor-made
expectation maximization algorithm. Further details on the methods can be found in L. Del Core et al., (2022) <doi:10.1101/2022.05.31.494100>.

Luca Del Core

RestoreNet

Random-Effects Stochastic Reaction Networks

Marco Grzegorczyk

Ernst Wit

ny_u function

<dl><dt>theta</dt>
<dd>p-dimensional vector parameter.</dd>
<dt>Z</dt>
<dd>A\(n \times Jp\) dimensional block-diagonal design matrix.</dd>
<dt>X</dt>
<dd>A \(n \times K\) dimensional (design) matrix.
Each j-th block (\(j = 1,\dots,J\)) is a \(n_j \times p\) dimensional design matrix for the j-th clone.</dd>
<dt>y</dt>
<dd>n-dimensional vector of the time-adjacent cellular increments</dd>
<dt>V</dt>
<dd>A \(p \times K\) dimensional net-effect matrix.</dd>
<dt>VCNs</dt>
<dd>A n-dimensional vector including values of the vector copy number corresponding to the cell counts of y.</dd>
<dt>nObs</dt>
<dd>A K-dimensional vector including the frequencies of each clone k (\(k = 1,\dots,K\)).</dd></dl>

Arguments

Conditional negative log-likelihood — ny_u

<dl>

<dt>theta</dt>
<dd>p-dimensional vector parameter.</dd>


<dt>Z</dt>
<dd>A\(n \times Jp\) dimensional block-diagonal design matrix.</dd>


<dt>X</dt>
<dd>A \(n \times K\) dimensional (design) matrix.
Each j-th block (\(j = 1,\dots,J\)) is a \(n_j \times p\) dimensional design matrix for the j-th clone.</dd>


<dt>y</dt>
<dd>n-dimensional vector of the time-adjacent cellular increments</dd>


<dt>V</dt>
<dd>A \(p \times K\) dimensional net-effect matrix.</dd>


<dt>VCNs</dt>
<dd>A n-dimensional vector including values of the vector copy number corresponding to the cell counts of y.</dd>


<dt>nObs</dt>
<dd>A K-dimensional vector including the frequencies of each clone k (\(k = 1,\dots,K\)).</dd>

</dl>

ny_u: Conditional negative log-likelihood

Description

Usage

Value

Arguments