---
title: "Screening: Screen-T-Rex and the biobank screening"
output:
  rmarkdown::html_vignette:
    toc: true
    css: vignette_styles.css
bibliography: references.bib
csl: ieee.csl
link-citations: true
vignette: >
  %\VignetteIndexEntry{Screening: Screen-T-Rex and the biobank screening}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.align = "center",
                      fig.width = 6, fig.height = 4)
options(width = 80)
library(TRexSelector)
old_threads <- trex_set_num_threads(min(2L, trex_get_max_threads()))
```

# Screening before selecting

A genomics biobank holds hundreds of thousands of variables and hundreds of phenotypes. Running the full
T-Rex calibration on every phenotype is costly, and for most phenotypes the answer is that nothing is
selected. Screen-T-Rex [@machkour2023screen] is a single-pass version of the random experiments without
the L-loop and the T-loop: $K$ experiments with $p$ dummies each, stopped at the first dummy, and an FDR
estimate read off the vote. It reports an estimated FDR instead of controlling a target, so it is a fast
first pass. The biobank screening wraps it in a decision rule per phenotype: when the estimated FDR of the
screening falls into an acceptance window, the screening result is kept, otherwise the full T-Rex selector
runs as a fallback.

# Screen-T-Rex

The screening selector takes no target FDR.

```{r data}
set.seed(2024)
n <- 100
p <- 300
true_support <- c(3, 50, 120, 200, 280)
beta <- numeric(p)
beta[true_support] <- 2
X <- matrix(rnorm(n * p), n, p)
y <- as.numeric(X %*% beta + rnorm(n))
```

```{r screen}
scr <- TRexScreeningSelector$new(X, y, seed = 3, verbose = FALSE,
                                 control = trex_control(K = 20))
scr$select()
scr$selected_indices
scr$estimated_FDR
```

`beta_mat` holds the coefficients of the original variables at the stop of each experiment (one column
per experiment) and `dummy_betas` those of the dummies, the material the estimate is read off. The
L-loop strategy is forced to `"STANDARD"` here, fresh dummies per experiment.

```{r mats}
dim(scr$beta_mat)
dim(scr$dummy_betas)
```

## A bootstrap confidence interval

`use_bootstrap_CI = TRUE` resamples the experiments `R_boot` times and reports the upper confidence bound
of the estimated FDR instead of the point estimate, at `confidence_level`. `ci_grid_step` is the
resolution of the bound.

```{r boot}
boot <- TRexScreeningSelector$new(X, y, seed = 3, verbose = FALSE,
                                  screen_control = trex_screen_control(use_bootstrap_CI = TRUE,
                                                                       R_boot = 200),
                                  control = trex_control(K = 20))
boot$select()
boot$used_bootstrap
boot$confidence_level
boot$estimated_FDR
boot$selected_indices
```

## Dependent variables

`trex_method` switches the screening to dependency-aware dummies: `"TREX_DA_AR1"`, `"TREX_DA_EQUI"`
and `"TREX_DA_BLOCK_EQUI"` draw autoregressive, equi-correlated and block equi-correlated dummies.
`estimated_correlation` reports the correlation the dummies were drawn with.

```{r da}
ar <- TRexScreeningSelector$new(X, y, seed = 3, verbose = FALSE,
                                screen_control = trex_screen_control(trex_method = "TREX_DA_AR1"),
                                control = trex_control(K = 20))
ar$select()
round(ar$estimated_correlation, 3)
```

# The biobank screening

`TRexBiobankScreeningSelector` screens one or many phenotypes against one genotype matrix. `Y` is a
vector for one phenotype or a matrix with one column per phenotype. The acceptance window of the
estimated FDR is `trex_biobank_control(lower_bound_FDR, upper_bound_FDR)`, and `tFDR` is the target
of the fallback selector.

```{r biobank}
Y <- cbind(y, as.numeric(X %*% (0.5 * beta) + rnorm(n)), rnorm(n))
colnames(Y) <- c("strong", "weak", "null")
bio <- TRexBiobankScreeningSelector$new(X, Y, tFDR = 0.1, seed = 3, verbose = FALSE,
                                        biobank_control = trex_biobank_control(0.05, 0.15),
                                        control = trex_control(K = 20))
res <- bio$select()
length(res)
```

Each record names the phenotype, the method that produced the result and whether the fallback ran.

```{r records}
summary_tab <- do.call(rbind, lapply(res, function(r)
  data.frame(phenotype = r$phenotype_index, selected = length(r$selected_indices),
             estimated_FDR = round(r$estimated_FDR, 3), method = r$method_used,
             fallback = r$used_fallback_trex)))
summary_tab
res[[1]]$selected_indices
```

The record also keeps the ordinary and the bootstrap screening results
(`selected_indices_screen_ordinary`, `estimated_FDR_screen_bootstrap`, ...), so the decision can be
audited. For a single phenotype `select()` returns one record instead of a list.

# Large designs

Both screening selectors accept a memory-mapped design (`mem_matrix()`), which the memory-mapping page
describes. The combination of the screening and a mapped design is what solved sparse regression
problems with five million variables on a laptop [@scheidt2023bigtrex].

```{r teardown, include = FALSE}
trex_set_num_threads(old_threads)
```

# References