GPS: Gamma Poisson Shrinkage
In PhViD: PharmacoVigilance Signal Detection

Description Usage Arguments Details Value Author(s) References Examples

Gamma Poisson Shrinkage model proposed by DuMouchel (1999) extended to the multiple comparison framework.

GPS(DATABASE,  RR0 = 1, MIN.n11 = 1, DECISION = 1, DECISION.THRES = 0.05, 
RANKSTAT = 1, TRONC = FALSE, TRONC.THRES = 1,   
PRIOR.INIT = c(alpha1 = 0.2, beta1 = 0.06, alpha2 = 1.4,
beta2 = 1.8, w = 0.1), PRIOR.PARAM = NULL)

`DATABASE`	Object returned by the function `as.PhViD`.
`RR0`	Value of the tested risk. By default, `RR0=1`.
`MIN.n11`	Minimum number of notifications for a couple to be potentially considered as a signal. This option does not affect the calculation of the hyper parameters. By default, `MIN.n11 = 1`.
`DECISION`	Decision rule for the signal generation based on 1 = FDR (Default value) 2 = Number of signals 3 = Ranking statistic. See `RANKSTAT`
`DECISION.THRES`	Threshold for `DECISION`. Ex 0.05 for FDR (`DECISION`=1).
`RANKSTAT`	Statistic used for ranking the couples: 1 = Posterior probability of the null hypothesis 2 = 5% quantile of the posterior distribution of lambda 3 = Posterior Expectation of log(lambda,2)
`TRONC`	If TRUE, only the data with at least `TRONC.THRES` notifications are considered in the calculation of the hyper parameters and the likelihood is a product of mixture of two negative binomial truncated by `TRONC.THRES-1`. By default, `TRONC=F`
`TRONC.THRES`	See `TRONC`
`PRIOR.INIT`	Vector of initialization of the prior parameters (alpha1, beta1, alpha2, beta2, w). By default, `PRIOR.INIT` = c(alpha1 = 0.2, beta1 = 0.06, alpha2 = 1.4, beta2 = 1.8, w = 0.1), ie the prior parameters found in DuMouchel (1999).
`PRIOR.PARAM`	Chosen hyper parameters. By default, `PRIOR.PARAM` = NULL which means that the hyperparameters are calculated by maximising the marginal likelihood.

Each observed count n11 is assumed to be drawn from a Poisson distribution with parameters e11 where e11 is the expected count under the hypothesis of independence between the adverse events and the drugs (n1. * n.1 / N, see as.PhViD). lambda is a priori assumed to be distributed according to a mixture of two gamma distributions: lambda ~ w Ga(alpha1,beta1) + (1-w) Ga(alpha2,beta2).

`ALLSIGNALS`	Data.frame summarizing the results of all couples with at least `MIN.n11` notifications ordered by `RANKSTAT`. It contains notably the labels, the cell counts, the expected counts, `RANKSTAT`, the ratios(count/expected count), the marginal counts and the estimations of FDR, FNR, Se et Sp. If `RANKSTAT!=1`, the last column is the posterior probability of the null hypothesis.
`SIGNALS`	Same Data.frame as `ALLSIGNALS` but restricted to the list of generated signals.
`NB.SIGNALS`	Number of generated signals.
`INPUT.PARAM`	Parameters entered in the function.
`PARAM`	A list that contains the prior hyper parameters (`PRIOR.PARAM`). Additionally if `PRIOR.PARAM=NULL`, it also contains the prior hyper parameters initialization (`PRIOR.INIT`) and the convergence code (see `nlm()`).

Ismaïl Ahmed & Antoine Poncet

Ahmed I, Haramburu F, Fourrier-Réglat A, Thiessard F, Kreft-Jais C, Miremont-Salamé G, Bégaud B, Tubert-Bitter P. Bayesian pharmacovigilance signal detection methods revisited in a multiple comparison setting. Stat Med. 2009 Jun 15;28(13):1774-1792.

DuMouchel W, Bayesian Data Mining in Large Frequency Tables, with an Application to the FDA Spontaneous Reporting System, The American Statistician, 1999, 53, 177-190.

Szarfman A, Machado S, O'Neill R, Use of Screening Algorithms and Computer Systems to Efficiently Signal Higher-Than-Expected Combinations of Drugs and Events in the US FDA's Spontaneous Reports Database Drug Safety, 2002, 25, 381-392.

## start
#data(PhViDdata.frame)


#PhViDdata <- as.PhViD(PhViDdata.frame)
#res <- GPS(PhViDdata)

#List of signals generated by the decision rule proposed 
#by Szarfman et al. (2002)
#res2 <- GPS(PhViDdata, DECISION = 3, DECISION.THRES = 2, RANKSTAT = 2)
## end

Loading required package: LBE
Loading required package: MCMCpack
Loading required package: coda
Loading required package: MASS
##
## Markov Chain Monte Carlo Package (MCMCpack)
## Copyright (C) 2003-2020 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park
##
## Support provided by the U.S. National Science Foundation
## (Grants SES-0350646 and SES-0350613)
##