Profile-likelihood confidence intervals for cellular ratios

Inverts the likelihood-ratio test of lrt_decovart() coordinate by coordinate: the interval collects every \(c\) with \(2\{\ell(\hat{\boldsymbol{p}})-\ell^{\mathrm{prof}}_j(c)\} \le\chi^{2}_{1,1-\alpha}\). Because likelihood ratios are invariant under reparametrisation, the interval respects \(0\le p_j\le 1\) without the delta-method linearisation that makes Wald intervals unreliable near a simplex face.

Usage

confint_profile_decovart(
  y = NULL,
  mean_signature_matrix,
  Sigma,
  bulk_expression = NULL,
  level = 0.95,
  celltypes = NULL,
  epsilon = 10^-8,
  itmax = 500L
)

Arguments

y

Numeric vector (or one-column matrix) \(\boldsymbol{y}\in\mathbb{R}^{G}\).

mean_signature_matrix

Numeric matrix \(\boldsymbol{\mu}\in\mathcal{M}_{G\times J}\) (plug-in means).

Sigma

Array of cell-type covariances in \(\mathcal{M}_{G\times G\times J}\).

bulk_expression

Numeric matrix \(\boldsymbol{Y}\in \mathcal{M}_{G\times N}\) of replicate bulk profiles sharing one composition, used instead of y for the pooled (population) test.

level

Confidence level \(1-\alpha\).

celltypes

Cell types to profile; defaults to all.

epsilon, itmax

Relative convergence tolerance and iteration budget passed to stats::optim().

Value

A matrix with one row per cell type and columns estimate, lower, upper.

See also

confint.decovart_fit() for the Wald analogue, lrt_decovart()

Other decovart_inference: bootstrap_decovart(), boundary_diagnostics(), chi_bar_square_pvalue(), equivariance_check_decovart(), lrt_decovart(), multistart_decovart(), profile_loglik_decovart(), reference_bootstrap_decovart(), restricted_mle_decovart()

Examples

mu <- matrix(c(20, 40, 15, 40, 20, 25), nrow = 3)
colnames(mu) <- paste0("ct", 1:2)
Sigma <- array(c(diag(3), diag(3)), dim = c(3, 3, 2))
y <- drop(mu %*% c(0.6, 0.4))
confint_profile_decovart(y, mu, Sigma)
#>     estimate     lower     upper
#> ct1 0.599338 0.5530429 0.6473202
#> ct2 0.400662 0.3526798 0.4469571