The BCPNN method leverages the information component (IC) to measure the association between the vaccine and symptom. IC is widely used to measure the mutual information between two random variables.
Let \(p_i\) be the probability of a target vaccine \(i\) exposure being reported, \(p_j\) be the the probability of the target symptom \(j\) being reported, and \(p_{ij}\) be the joint probability of a report on the target symptom \(j\) under exposure to the target vaccine \(i\). Bate et al. (Bate et al. 1998) defines the metric \(\text{IC}_{ij}\) as
\[ \text{IC}_{ij} = \log_2\frac{p_{ij}}{p_i p_j}. \]
Recall the contingency table for target vaccine \(i\) and target symptom \(j\):
| 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 | \(n_j\) | \(n - n_j\) | \(n\) |
Let the cell counts for vaccine-symptom pairs \((i, j)\) be \(n_{ij}\). The BCPNN data model assumes
\[ n_{ij} | p_{ij} \sim \text{Binomial}(n, p_{ij}),\\ p_{ij} \sim \text{Beta}(\alpha_{ij}, \beta_{ij}) \]
where
\[ \alpha_{ij} = 1,\\ \beta_{ij} = \frac{1}{E(p_i | n_i) + E(p_j | n_j)} - 1. \]
Under the assumption of independence, the marginal sums over the rows and columns of the \(i \times j\) contingency table are:
\[ n_i | p_i \sim \text{Binomial}(n, p_i),\\ n_j | p_j \sim \text{Binomial}(n, p_j) \]
where
\[ p_i \sim \text{Beta}(1, 1),\\ p_j \sim \text{Beta}(1, 1). \]
The IC estimate is
\[ \hat{\text{IC}_{ij}} = \log_2 \frac{(n_{ij} + 1) (n + 2)^2}{(n_{ij} + 1) (n+2)^2 + n(n_i + 1) (n_j + 1)}. \]
The variance estimation is given by
\[ \hat{\sigma_{ij}}^2 = \frac{1}{(\log 2)^2} (\frac{n - n_{ij} + \gamma - 1}{(n_{ij} + 1)(n+\gamma+1)} + \frac{n-n_{i} + 1}{(n_i + 1) (n+3)} + \frac{n - n_j + 1}{(n_j + 1)(n+3)}) \]
where
\[ \gamma = \frac{(n+2)^2}{(n_i + 1)(n_j + 1)}. \]
Load the packages for BCPNN-based singal detection and ranking:
suppressMessages(library("PhViD"))
library("kableExtra")Load the preprocessed VAERS data and transform it into the analyzable format:
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 Information Component derived by the Bayesian neural network model (Bate et al. 1998), (Norén et al. 2006) and the ranking statistic — 2.5% quantile of the posterior distribution of IC:
lst_bcpnn <- BCPNN(df_v, MIN.n11 = 10, DECISION = 3, RANKSTAT = 2)
df_bcpnn <- lst_bcpnn$SIGNALS[order(lst_bcpnn$SIGNALS$`Q_0.025(log(IC))`, decreasing = TRUE), 1:5]
row.names(df_bcpnn) <- NULLView the top ranked vaccine-adverse event pairs:
head(df_bcpnn) %>% kable() %>% kable_styling()| drug code | event effect | count | expected count | Q_0.025(log(IC)) |
|---|---|---|---|---|
| SMALLPOX (ACAM2000) | Troponin I increased | 161 | 0.9218906 | 6.122739 |
| SMALLPOX (DRYVAX) | Cow pox | 125 | 0.6461921 | 5.914686 |
| INFLUENZA (SEASONAL) (FLUBLOK QUADRIVALENT) | Product administered to patient of inappropriate age | 141 | 0.9689921 | 5.911459 |
| INFLUENZA (SEASONAL) (FLUCELVAX) | Drug administered to patient of inappropriate age | 350 | 4.4240284 | 5.848871 |
| MENINGOCOCCAL CONJUGATE (MENVEO) | Incorrect product formulation administered | 204 | 2.0229991 | 5.838318 |
| ROTAVIRUS (ROTASHIELD) | Gastrointestinal haemorrhage | 94 | 0.3269645 | 5.834576 |
Bate, Andrew, Marie Lindquist, I Ralph Edwards, Sten Olsson, Roland Orre, Anders Lansner, and R Melhado De Freitas. 1998. “A Bayesian Neural Network Method for Adverse Drug Reaction Signal Generation.” European Journal of Clinical Pharmacology 54 (4): 315–21.
Norén, G Niklas, Andrew Bate, Roland Orre, and I Ralph Edwards. 2006. “Extending the Methods Used to Screen the Who Drug Safety Database Towards Analysis of Complex Associations and Improved Accuracy for Rare Events.” Statistics in Medicine 25 (21): 3740–57.
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