As mentioned in the other vignettes, the openEBGM package is capable of calculating \(EBGM\) and quantile scores from the posterior distribution. openEBGM makes it easy to calculate such quantities using a class and object system. While creation of objects of class openEBGM is not necessary (see previous vignette), it provides access to methods for some common generic functions and reduces the number of function calls needed.
To create the object, we first need to calculate the hyperparameter estimates.
library(openEBGM) data(caers) proc <- processRaw(caers, stratify = FALSE, zeroes = FALSE) squashed <- squashData(proc) theta_init <- data.frame(alpha1 = c(0.2, 0.1, 0.3, 0.5, 0.2), beta1 = c(0.1, 0.1, 0.5, 0.3, 0.2), alpha2 = c(2, 10, 6, 12, 5), beta2 = c(4, 10, 6, 12, 5), p = c(1/3, 0.2, 0.5, 0.8, 0.4) ) hyper_estimate <- autoHyper(squashed, theta_init = theta_init, zeroes = FALSE, squashed = TRUE, N_star = 1)
Once we have the hyperparameter estimates and the processed data, we can calculate the \(EBGM\) scores and any desired quantile(s) from the posterior distribution.
As seen above, we can calculate the \(EBGM\) scores with or without adding quantiles. If using quantiles, we can specifying any number of quantiles.
Once the object has been created, we can use class-specific methods for some of R’s generic functions (namely,
#We can print an openEBGM object to get a quick look at the contents print(ebout) #> #> There were 131 var1-var2 pairs with a QUANT_05 greater than 2 #> #> Top 5 Highest QUANT_05 Scores #> var1 var2 N #> 13924 REUMOFAN PLUS WEIGHT INCREASED 16 #> 8187 HYDROXYCUT REGULAR RAPID RELEASE CAPLETS EMOTIONAL DISTRESS 19 #> 13886 REUMOFAN PLUS IMMOBILE 6 #> 7793 HYDROXYCUT HARDCORE CAPSULES CARDIO-RESPIRATORY DISTRESS 8 #> 8220 HYDROXYCUT REGULAR RAPID RELEASE CAPLETS INJURY 11 #> E QUANT_05 #> 13924 0.40643623 15.68 #> 8187 0.89690107 11.65 #> 13886 0.07866508 10.16 #> 7793 0.30482718 8.99 #> 8220 0.56317044 8.98 print(ebout_noquant, threshold = 3) #> #> There were 556 var1-var2 pairs with an EBGM score greater than 3 #> #> Top 5 Highest EBGM Scores #> var1 var2 N #> 13924 REUMOFAN PLUS WEIGHT INCREASED 16 #> 13886 REUMOFAN PLUS IMMOBILE 6 #> 8187 HYDROXYCUT REGULAR RAPID RELEASE CAPLETS EMOTIONAL DISTRESS 19 #> 4093 EMERGEN-C (ASCORBIC ACID, B-COMPLEX, ELECTROLYTE, COUGH 6 #> 7832 HYDROXYCUT HARDCORE CAPSULES MULTIPLE INJURIES 5 #> E EBGM #> 13924 0.40643623 23.26 #> 13886 0.07866508 18.28 #> 8187 0.89690107 16.78 #> 4093 0.14481526 16.03 #> 7832 0.09237187 15.63
When quantiles are present, simply printing the object shows, by default, how many var1-var2 pairs exist that have QUANT\(>x\), where \(x\) is the minimum quantile threshold used for the data (default 2). In the absence of quantiles, it simply outputs the number of var1-var2 pairs that have an \(EBGM\) score greater than the specified threshold. In both cases, it also shows a quick look at the var1-var2 pairs with the highest \(x\) or \(EBGM\), depending on whether quantiles were calculated or not.
One can also use the
summary() function on an openEBM object to get further information about the calculations.
#> #> Summary of the EB-Metrics #> EBGM QUANT_05 QUANT_95 #> Min. : 0.200 Min. : 0.0700 Min. : 0.51 #> 1st Qu.: 2.010 1st Qu.: 0.4800 1st Qu.:12.19 #> Median : 2.390 Median : 0.5100 Median :14.73 #> Mean : 2.356 Mean : 0.5377 Mean :13.31 #> 3rd Qu.: 2.580 3rd Qu.: 0.5200 3rd Qu.:15.73 #> Max. :23.260 Max. :15.6800 Max. :33.48
As seen above, by default the
summary() function, when called on an openEBGM object, outputs some descriptive statistics on the \(EBGM\) and quantile scores, and a histogram of the \(EBGM\) scores. There are options to disable plot output, or to calculate the log2 transform of the scores, which provides a Bayesian information statistic (when applied to the \(EBGM\) score).
summary(ebout, plot.out = FALSE, log.trans = TRUE) #> #> Summary of the EB-Metrics #> EBGM QUANT_05 QUANT_95 #> Min. :-2.322 Min. :-3.8365 Min. :-0.9714 #> 1st Qu.: 1.007 1st Qu.:-1.0589 1st Qu.: 3.6076 #> Median : 1.257 Median :-0.9714 Median : 3.8807 #> Mean : 1.161 Mean :-0.9833 Mean : 3.6316 #> 3rd Qu.: 1.367 3rd Qu.:-0.9434 3rd Qu.: 3.9754 #> Max. : 4.540 Max. : 3.9709 Max. : 5.0652
Finally, openEBGM provides a method for the
plot() function that can produce a variety of different plots. These are shown below.
As seen, by default, the
plot() function shows the top \(EBGM\) scores by var1-var2 combinations (only var1 is shown for space preservation) and “error bars” using the lowest and highest quantiles calculated. The sample size for each var1-var2 combination is also plotted.
A specific event from var2 may also be selected, and only the var1-var2 combinations that include this particular event will be shown. An example is shown below.
In addition to the bar chart, the
plot() function can also create a histogram of the \(EBGM\) scores.
Again, one may choose an event from var2 by which to subset the data when plotting.
Finally, the last type of plot included with the
plot() function shows the shrinkage performed by the algorithm. It is called the “Chirtel Squid Plot”, titled after its creator, Stuart Chirtel.
While a specific event may be selected by which to subset the data, it can lead to a less informative plot due to smaller sample size.
openEBGM was designed to give the user a high level of control over data analysis choices (stratification, data squashing, etc.) using DuMouchel’s Gamma-Poisson Shrinkage (GPS) method (1999,
https://doi.org/10.1145/502512.502526). The GPS method applies to any large contingency table, so openEBGM can be used to mine a variety of databases in which the rate of co-occurrence of two variables or items is of interest (sometimes known as the “market basket problem”). U.S. FDA products and adverse events is just one of many possible applications.