Base Ranker: Proportional Reporting Ratio (PRR)

PRR is a commonly used metric for safety signal detection. We can 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, \(n_i = \sum_j n_{ij}\), \(n_j = \sum_i n_{ij}\). They are the marginal sums over all other symptoms or vaccines for each unique vaccine \(i\) and symptom \(j\). The proportional reporting ratio (PRR) (Evans, Waller, and Davis 2001) for each vaccine-symptom pair is defined as

\[ PRR_{ij} = \frac{n_{ij}}{E_{ij}} \]

where

\[ E_{ij} = \frac{n_j (n_i - n_{ij})}{n - n_{ij}}. \]

\(PRR_{ij}\) measures the disproportionality in rates of the target symptom \(j\) to all other symptoms for exposure to vaccine \(i\) in the contingency table. It assumes that the reports of symptom \(j\) are independent to all other symptoms on vaccine \(i\), while this can turned out to be a quite strong assumption in reality. A relatively higher value of PRR indicates stronger association between the vaccine and the symptom.

Load the packages for PRR-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)

We calculate the Proportional Reporting Ratio (PRR) (Evans, Waller, and Davis 2001) and the ranking statistic — lower bound of the 95% two-sided confidence interval of log(PRR):

lst_prr <- PRR(df_v, MIN.n11 = 10, DECISION = 3, RANKSTAT = 2)
df_prr <- lst_prr$SIGNALS[order(lst_prr$SIGNALS$"LB95(log(PRR))", decreasing = TRUE), 1:8]
row.names(df_prr) <- NULL

View the top ranked vaccine-adverse event pairs:

head(df_prr) %>% kable() %>% kable_styling()

drug code	event effect	count	expected count	LB95(log(PRR))	PRR	drug margin	event margin
INFLUENZA (SEASONAL) (FLUCELVAX)	Product use issue	57	0.0863973	6.873915	1410.7090	2765	107
INFLUENZA (SEASONAL) (AFLURIA)	Multiple use of single-use product	49	0.3842040	6.772886	6327.8212	26313	50
HPV (CERVARIX)	Product use issue	22	0.0236538	6.601841	1170.5511	757	107
SMALLPOX (DRYVAX)	Cow pox	125	0.6461921	6.443733	922.3838	14005	158
INFLUENZA (SEASONAL) (AFLURIA)	HIV antigen negative	48	0.4149403	6.091730	1033.1137	26313	54
SMALLPOX (ACAM2000)	Pericardial disease	64	0.2820515	5.936602	555.5036	8943	108

Evans, Stephen JW, Patrick C Waller, and S Davis. 2001. “Use of Proportional Reporting Ratios (Prrs) for Signal Generation from Spontaneous Adverse Drug Reaction Reports.” Pharmacoepidemiology and Drug Safety 10 (6): 483–86.