---
title: "Interactions"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{interactions}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
options(rmarkdown.html_vignette.check_title = FALSE)
```

```{r setup}
library(vigicaen)
library(rlang)
library(dplyr)
```

# Introduction

It is possible to explore interactions between drugs on
an adr reporting.

This tutorial does not aim at covering the concepts underlying
interactions in pharmacovigilance. It is about running them 
in practice.

In particular, we will not cover the differences between additive
interactions, statistical/synergistic interactions.

`compute_interaction()` use is shown [at the end of the vignette](#compute_int).

We use built-in example dataset.

```{r interaction_dm}

# ---- Tables ---- ####

demo <- demo_
drug <- drug_

# ---- Dictionary step ---- ####

d_drecno <- ex_$d_drecno
a_llt <- ex_$a_llt

# #### Data management #### ####

# ---- Drugs ---- ####

demo <-
    demo |>
    add_drug(
      d_code = d_drecno,
      drug_data = drug_
    ) 

# ---- Adrs ---- ####

demo <- 
  demo |>
    add_adr(
      a_code = a_llt,
      adr_data = adr_
    )

# ---- Sex ---- ####

demo <- 
  demo |> 
  mutate(
    sex = case_when(Gender == "1" ~ 1,
                    Gender == "2" ~ 2,
                    TRUE ~ NA_real_)
    )
```

# Additive interactions

## Multivariate analysis

Additive effect of two covariates can be obtained by multiplying 
the Odds-Ratio of each.

```{r mod_inter}
mod3 <- glm(a_colitis ~ ipilimumab + sex,
            data = demo,
            family = "binomial")

mod_or <- 
  compute_or_mod(
  summary(mod3)$coefficients,
      estimate = Estimate,
    std_er = Std..Error
  ) |> select(rn, orl, ci, up_ci)

mod_or
```

```{r echo=FALSE}
ror_ipi <- mod_or[rn == "ipilimumab", orl]
ror_sex <- mod_or[rn == "sex", orl]
```
With reporting Odds-Ratio of ipilimumab being `r ror_ipi`
and the reporting Odds-Ratio of sex being `r ror_sex`, 
the additive effect of both is `r ror_ipi` * `r ror_sex`.

## Subgroup comparisons

Some way to approach multiplicative interactions is to compare
the disproportionality signal in subgroups.

The `compute_dispro()` function can be used for these analyses,
assuming the initial dataset is filtered on the appropriate
subgroup.

Say we want to investigate the interaction between ipilimumab
and nivolumab and colitis reporting.

```{r}
demo |> 
  filter(nivolumab == 1) |> 
  compute_dispro(
    y = "a_colitis",
    x = "ipilimumab"
    )
```
The overall analysis implies to perform additional analysis in
different settings.

In our example:

-   If ipilimumab alone leads to an overreporting of colitis
-   If nivolumab, among ipilimumab cases, leads to an overreporting of colitis
-   If the combination ipilimumab + nivolumab versus any control
(or the whole dataset) increases the notifications of colitis.

Both IC and ROR can be used here.

# Statistical interactions {#inter_stat}

## Logistic regression model

The true statistical interaction is obtained with the following
model

```{r}
mod4 <- glm(a_colitis ~ ipilimumab + sex + ipilimumab * sex,
            data = demo,
            family = "binomial")

compute_or_mod(
  summary(mod4)$coefficients,
  estimate = Estimate,
  std_er = Std..Error
)
```

## Bayesian Information Component, `compute_interaction()` {#compute_int}

The formula for the interaction between 3 variables 
($y$, the event of interest, $x1$ and $x2$,
two potential explanatory factors) 
in information component is

$log_2\frac{n_{y, x1, x2}}{n.expected_{interaction}}$

with $n.expected_{interaction}$ equal to

$\frac{n_{x1, x2} * n_{y, x1} * n_{y, x2} * n.total}{n_{x1} * n_{x2} * n_y}$

The parameters are read as follows

| Parameter       | Case                                                                      |
|-----------------|-------------------------------------------------------|
| $n_{x1}$        | number of cases reporting x1                                              |
| $n_{x1, x2}$    | number of cases reporting x1 **AND** x2                                    |
| $n_{y, x1, x2}$ | number of cases reporting x1 **AND** x2 **AND** y                           |
| $n.total$       | total number of cases in the study population  |

The credibility interval is calculated as for the usual IC.

`compute_interaction()` produces this interaction statistic.

```{r compute_int}

demo |>
  compute_interaction(
    y = "a_colitis",
    x = "ipilimumab",
    z = "nivolumab"
  )

```