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Parametric bootstrap for DeCovarT proportions and boundary tests

Source: R/03_06_decovart_inference.R
bootstrap_decovart.Rd

The conditional law of the bulk profile is fully specified, so the asymptotic calibrations of lrt_decovart() can be replaced by simulation. Given plug-in moments and a composition \(\boldsymbol{p}\), the function draws \(\boldsymbol{Y}^{(b)}\sim \mathcal{N}_{G}(\boldsymbol{\mu}\boldsymbol{p}, \boldsymbol{\Sigma}(\boldsymbol{p}))\), refits DeCovarT, and returns the empirical distribution of \(\hat{\boldsymbol{p}}^{(b)}\) together with percentile intervals.

Usage

bootstrap_decovart(
  y = NULL,
  mean_signature_matrix,
  Sigma,
  bulk_expression = NULL,
  p = NULL,
  null_value = NULL,
  n_boot = 500L,
  level = 0.95,
  n_replicates = 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.

p

Composition to simulate from. Defaults to the MLE computed from y / bulk_expression.

null_value

Named numeric vector of hypothesised ratios, e.g. c(celltype_2 = 0).

n_boot

Number of bootstrap replicates.

level

Confidence level for percentile intervals.

n_replicates

Number of bulk columns simulated per replicate; defaults to the number of observed columns.

epsilon, itmax

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

Value

A list with estimates (\(J\times\) n_boot matrix), interval (percentile bounds), p_simulated, and, when null_value is supplied, statistic (observed \(D\)), null_statistics, and p_value.

Details

Supplying null_value switches to a restricted bootstrap: replicates are generated under the restricted MLE and the likelihood-ratio statistic is recomputed on each, giving a Monte Carlo p-value that does not rely on the \(50{:}50\) asymptotic weights. For a composite null the remaining nuisance proportions are profiled at their restricted estimate, so the procedure is a plug-in (approximate) rather than an exact bootstrap.

Reference uncertainty is not propagated here: \(\boldsymbol{\mu}\) and \(\boldsymbol{\Sigma}_j\) are treated as known, exactly as in the frequentist likelihood. To resample the purified observations that produced those plug-in moments, use reference_bootstrap_decovart().

See also

lrt_decovart(), chi_bar_square_pvalue(), reference_bootstrap_decovart()

Other decovart_inference: boundary_diagnostics(), chi_bar_square_pvalue(), confint_profile_decovart(), 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))
set.seed(1)
bootstrap_decovart(y, mu, Sigma, n_boot = 20)$interval
#>          2.5%     97.5%
#> ct1 0.5647988 0.6266519
#> ct2 0.3733481 0.4352012