PhViD (version 1.0.2)

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 $\lambda$

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()).

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-Reglat A, Thiessard F, Kreft-Jais C, Miremont-Salame G, Begaud B, Tubert-Bitter P. Bayesian Pharmacovigilance Signal Detection Methods Revisited in a Multiple Comparison Setting, Statistics in Medicine, accepted.

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