1D Pooling theory.Rmd

---
title: '1D Pooling: Theory'
author: "Xianbin Cheng"
date: "December 18, 2018"
output: html_document
---

# Objective  

  1. We want to calculate the sensitivity, specificity and cost of one-dimensional pooling using combination theories.
  
# Method  

1. Load necessary libraries and files.

```{r, message=FALSE, warning = FALSE}
library(tidyverse)
source("1D_pooling_theory.R")
```

2. Set input parameters

  * `n` = the total number of kernels in a plate (48 by default).
  * `n_pool` = the number of pools. When pooling by rows, `n_pool` = 6. When pooling by columns, `n_pool` = 8.

```{r}
n = 48
```

3. Calculate the sensitivity, specificity, and cost under theoretical assumptions. We assume the following scenario does not exist: a pool is flagged as positive when all the kernels are negative just because the pooled concentration reaches the pool limit. For example, when we pool by rows, any pool exceeding `r 20/8`ppb should be flagged as a positive pool. Even if all the kernels have 5 ppb aflatoxin, the pooled concentration would still exceed the limit, resulting in a lot of false positive kernels.

```{r}
# Pool by rows
pool_row = gen_1d_data_theo(n = n, n_pool = 6)
metrics_pbr = calc_metrics_1d_theo(df = pool_row)
cost_pbr = calc_cost_1d_theo(df = pool_row, n_pool = 6)

# Pool by columns
pool_col = gen_1d_data_theo(n = n, n_pool = 8)
metrics_pbc = calc_metrics_1d_theo(df = pool_col)
cost_pbc = calc_cost_1d_theo(df = pool_col, n_pool = 8) 
```

# Result

1. Visualization of expected sensitivity and specificity with different number of positive kernels.

```{r}
# Pool by rows
draw_metrics_1d_theo(data = metrics_pbr, n = n)

# Pool by columns
draw_metrics_1d_theo(data = metrics_pbc, n = n)
```

2. Visualization of expected cost

```{r}
# Pool by rows
draw_cost_1d_theo(data = cost_pbr, n = 48)
# Pool by columns
draw_cost_1d_theo(data = cost_pbc, n = 48)
```