PhViD (version 1.0.3)

GPS: Gamma Poisson Shrinkage

Description

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

Usage

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)

Arguments

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 $\log_2(\lambda)$

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.THRES

See TRONC

PRIOR.INIT

Vector of initialization of the prior parameters $(\alpha_1, \beta_1, \alpha_2, \beta_2, w)$. By default, PRIOR.INIT $= c(\alpha_1 = 0.2, \beta_1 = 0.06, \alpha_2 = 1.4, \beta_2 = 1.8, w = 0.1)$, ie the prior parameters found in DuMouchel (19

PRIOR.PARAM

Chosen hyper parameters. By default, PRIOR.PARAM = NULL which means that the hyperparameters are calculated by maximising the marginal likelihood.

Value

• 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()).

encoding

UTF-8

Details

Each observed count $n_{11}$ is assumed to be drawn from a Poisson distribution with parameters $e_{11}$ where $e_{11}$ is the expected count under the hypothesis of independence between the adverse events and the drugs ($n1. \times n.1 / N$, see as.PhViD). $\lambda$ is a priori assumed to be distributed according to a mixture of two gamma distributions: $\lambda \sim w \: \Gamma(\alpha_1,\beta_1) + (1-w) \: \Gamma(\alpha_2,\beta_2)$.

References

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.

Examples

## 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