---
title: "Robust inference"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{OmicsBraid robust inference}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", eval = FALSE)
```


## Recommended empirical procedures

OmicsBraid v0.2.2 provides resampling-calibrated alternatives for settings where chi-square approximations may be sensitive to non-Gaussian data.

### Global omnibus

`omnibus_method = "permutation"` permutes the two-group labels at the **biological-subject level**, leaving each subject's cross-omic measurement vector linked.

### Heterogeneity

`heterogeneity_method = "null_shift_bootstrap"` imposes a fitted equal-effect null while retaining residual distributions, missingness, and matched-subject structure, then calibrates the covariance-aware heterogeneity statistic by stratified bootstrap.

```{r}
emp <- empirical_omics_tests(
  data = obj,
  group = "group",
  reference = "Control",
  comparison = "Disease",
  effects = fit$effects,
  entities = candidate_entities,
  B = 1999,
  seed = 1,
  omnibus_method = "permutation",
  heterogeneity_method = "null_shift_bootstrap",
  p_adjust = "BH"
)
```

## Confidence intervals

Analytic intervals remain the v0.2.2 default. BCa layer intervals can be used as a sensitivity analysis when heavy tails/non-normality are a concern. Percentile bootstrap intervals are not the preferred robust sensitivity option based on the completed validation.

## Genome-wide p-value resolution

A finite empirical procedure with $B$ resamples cannot provide arbitrarily small p-values. If thousands of entities are screened, ensure the empirical resolution is compatible with the desired multiplicity correction. In the manuscript applications, continuous asymptotic p-values were used for genome-wide BH-FDR and empirical methods were pre-declared secondary robustness checks on selected candidates.