Simulate a marked point pattern from the DenMark data-generating process

Cells of the analyzed type follow an inhomogeneous Poisson process with log lambda1(s) = beta0 + a11 w1(s), and each cell's count for gene k is Poisson with log mu_k(s) = beta1 + sigma2 * (rho_k w1(s) + sqrt(1 - rho_k^2) w2k(s)).

Usage

denmark_simulate(
  rho = c(geneA = 0.6, geneB = 0, geneC = -0.6),
  width = 6,
  height = 4,
  n_cells = 5000,
  ell1 = 1,
  ell2 = 1,
  a11 = 1,
  sigma2 = 0.8,
  beta1 = 0.5,
  seed = 1,
  tissue = c("rectangle", "irregular"),
  n_other = 0,
  celltype = "Target"
)

Arguments

rho: Named vector of true correlations, one gene per element.
width, height: Size of the window [0, width] x [0, height].
n_cells: Number of cells of the analyzed type: the thinned point pattern is subsampled to n_cells cells when it has more.
ell1, ell2: Length-scales of the density and expression fields.
a11: Standard deviation of the log cell intensity.
sigma2: Standard deviation of the log expression.
beta1: Intercept of the log expression.
seed: Random seed, set with set.seed(); this resets the global random number stream.
tissue: "rectangle" (cells fill the window) or "irregular" (cells lie in a lobed tissue section).
n_other: Number of cells of other types; together with the analyzed cells they define the tissue boundary.
celltype: Label of the analyzed cell type (used when n_other > 0; the other cells are labeled "Other").

Value

Data frame with the columns x, y, celltype (when n_other > 0) and one count column per gene; the true values are stored in attr(, "truth"), including the true tissue outline for tissue = "irregular".

Details

The fields are smooth, zero-mean, unit-variance Gaussian fields with approximately Matern-3/2 covariance, drawn by random Fourier features. The fields are standardized, and each w2k is orthogonalized against w1, on a regular lattice over the tissue (that is, over space rather than over the cells), so that the spatial correlation of the two fields equals rho_k, which is what rho measures in the model.

With tissue = "irregular", the cells lie in a lobed tissue section inside the window, so that the analysis needs a tissue boundary (see denmark_alpha_shape()). The cells of other types are drawn from the candidate locations that the thinning rejected, so they are densest where the analyzed cells are sparse; their gene counts are Poisson with mean 0.3.

Examples

sim <- denmark_simulate(rho = c(up = 0.5, down = -0.5), n_cells = 500)
head(sim)
#>           x        y up down
#> 1 5.7341203 1.897406  1    1
#> 2 4.9010699 2.176218  0    2
#> 3 4.8743040 2.718039  3    0
#> 4 0.2315825 1.722756  0    4
#> 5 5.5570991 3.673129  3    3
#> 6 5.7925512 0.500681  5    5
attr(sim, "truth")$rho
#>   up down 
#>  0.5 -0.5 

sec <- denmark_simulate(n_cells = 1000, tissue = "irregular", n_other = 800,
                        celltype = "Tumor")
table(sec$celltype)
#> 
#> Other Tumor 
#>   800  1000