analysis-ror.Rmd

---
title: "Base Ranker: Reporting Odds Ratio (ROR)"
author:
  - name: Nan Xiao
    url: https://nanx.me/
    affiliation: Seven Bridges
    affiliation_url: https://www.sevenbridges.com/
  - name: Soner Koc
    url: https://github.com/skoc
    affiliation: Seven Bridges
    affiliation_url: https://www.sevenbridges.com/
  - name: Kaushik Ghose
    url: https://kaushikghose.wordpress.com/
    affiliation: Seven Bridges
    affiliation_url: https://www.sevenbridges.com/
date: "`r Sys.Date()`"
output: distill::distill_article
bibliography: rankv.bib
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, eval = TRUE, cache = TRUE)
```

Beside PRR, ROR is yet another commonly used metric for safety signal detection. Let's denote the vaccine-symptom pairs from the VAERS database as many $2 \times 2$ contingency tables:

| Target vaccine | Target symptom | All other symptoms       | Total     |
| :------------- | :------------- | :----------------------- | :-------- |
| Yes            | $n_{ij}$       | $n_i - n_{ij}$           | $n_i$      |
| No             | $n_j - n_{ij}$ | $n - n_i - n_j + n_{ij}$ | $n - n_i$ |
| Total          | $n_j$          | $n - n_j$                | $n$       |

In the table, $n_i = \sum_j n_{ij}$, $n_j = \sum_i n_{ij}$. The reporting odds ratio (ROR) [@van2002comparison] for each vaccine-symptom pair is defined as

$$
ROR_{ij} = \frac{n_{ij}}{\tilde{E}_{ij}}
$$

where

$$
\tilde{E}_{ij} = \frac{(n_i - n_{ij})(n_j - n_{ij})}{n - n_i - n_j + n_{ij}}.
$$

Similar to PRR, a relatively higher ROR indicates stronger association between the vaccine and the symptom.

Load the packages for ROR-based singal detection and ranking:

```{r}
suppressMessages(library("PhViD"))
library("kableExtra")
```

Load the preprocessed VAERS data and transform it into the analyzable format:

```{r}
df_p <- readRDS("data-processed/df_p.rds")
df_p <- df_p[, 1:3]
df_v <- as.PhViD(df_p, MARGIN.THRES = 10)
```

Calculate the Reporting Odds Ratio (ROR) [@van2002comparison] and the ranking statistic --- lower bound of the 95% two-sided confidence interval of log(ROR):

```{r}
lst_ror <- ROR(df_v, MIN.n11 = 10, DECISION = 3, RANKSTAT = 2)
df_ror <- lst_ror$SIGNALS[order(lst_ror$SIGNALS$`LB95(log(ROR))`, decreasing = TRUE), 1:6]
row.names(df_ror) <- NULL
```

View the top ranked vaccine-adverse event pairs:

```{r}
head(df_ror) %>% kable() %>% kable_styling()
```

```{r,echo=FALSE}
saveRDS(df_ror, file = "data-processed/df_ror.rds")
```