Appendix S5 — Model Mis-specification (Description Only)
Planned experiments — not yet implemented
Source:vignettes/supp-S5-misspecification.qmd
Overview
The DeCovarT model assumes that bulk expression arises from a Gaussian mixture:
\boldsymbol{y} \sim \sum_{j=1}^{J} p_j \, \mathcal{N}(\boldsymbol{\mu}_j,\, \boldsymbol{\Sigma}_j).
Real bulk RNA-seq violates this assumption in at least five ways:
- Observation noise model: counts follow a negative binomial (NB) or Poisson-log-normal (PLN) distribution rather than Gaussian.
- Heavy-tailed or contaminated bulk: outlier samples (technical artefacts, cell doublets) inflate tails.
- Missing reference component: an unmodelled cell type contributes to the bulk; all estimated proportions are redistributed.
- Inter-sample (copula) correlations: genes share latent batch structure, inducing correlation across observations.
- Wrong covariance reference: the within-cell-type covariance \boldsymbol{\Sigma}_j is estimated from a different cohort or technology, introducing systematic bias.
Planned experiments
S5a — Observation noise model
| Factor | Levels |
|---|---|
| Data-generating law | Gaussian (baseline); t_\nu (\nu = 3); log-normal/PLN; contaminated Gaussian (\varepsilon = 0.05) |
| Algorithm | NNLS, DeconRNASeq, Marquardt–Levenberg (full \boldsymbol{\Sigma}) |
| G, J | 50 genes, 3 cell types |
Hypothesis: DeCovarT should retain lower bias under log-normal noise than NNLS because the covariance captures more of the signal geometry, but may be more sensitive than NNLS to heavy-tail contamination.
Connection to HADACA3 (Barbot and Richard 2026): the SDC5 dataset uses a copula + NB noise model; SDE5 uses an EM-based noise model. These represent the practical domain of mis-specification most relevant to pancreatic tumour deconvolution.
see also use of a multivariate Student t_\nu or simple Gaussian noise.
S5b — Missing reference component
| Factor | Levels |
|---|---|
| Missing-type fraction | None (0%); rare (2%); moderate (10%) |
| Detection strategy | None (ignore); re-normalise; add null cell type |
| Metric | RMSE of remaining types; false inclusion rate |
Hypothesis: closure forces the missing mass onto the J modelled cell types; the distribution of the error across types depends on the mean-collinearity structure. DeCovarT may exhibit a different redistribution pattern than NNLS because the second-order term couples the proportions estimation.
S5c — Model complex dependencies
Copula-correlated NB samples
| Factor | Levels |
|---|---|
| Copula family | Gaussian; Clayton (positive tail dependence) |
| Marginal | NB (r = 5, \mu = \bar{\mu}_g) |
| Correlation strength | \tau_K \in \{0, 0.2, 0.5\} |
This directly mirrors the SDC5 HADACA3 scenario (Barbot and Richard 2026).
Poisson-log-normal samples
| Factor | Levels |
|---|---|
| Marginal | PLN (\mu = \bar{\mu}_g) |
| Correlation strength | \tau_K \in \{0, 0.2, 0.5\} |
Can be simulated with splatter (Zappia et al. 2017) or SymSim).
S5d : Spillover effect and missing reference component
The full factorial plan (detailled_siulation_code.md) includes these additional factors that touch on mis-specification and are also out of scope:
| Factor | Planned levels | Notes |
|---|---|---|
| spillover strength | \alpha \in \{0, 0.2, 0.5\} | |
| Missing-reference component | None; 2%; 10% | S5b above |
| Reference covariance sample size | Oracle; 20; 50; 200 donors | See Appendix S4 |
We may also consider an alternative model using a linear mixed model to add correlations between cell types.
S5e : Add outlier genes to test the robustness of the estimation
| Factor | Planned levels | Notes |
|---|---|---|
| Outlier genes | 10% of genes; 20% of genes; 30% of genes | |
| Outlier strength | \sigma \in \{0, 0.2, 0.5\} |