Description Usage Arguments Details Value Author(s) Examples

Bayesian Detection of Risk using Inference on Blinded Safety data

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`y` |
observed pooled events (combined active and control group) e.g., y = 20 |

`pyr` |
total payr exposure (combined active and control group) e.g., pyr = 2000 |

`bg.events` |
background (historical) events for the control group e.g., bg.events = 5 |

`bg.pyr` |
background (historical) pyr exposure for the control group e.g., bg.pyr = 1000 |

`bg.rate` |
when specified used as the true background rate for the control group and ignores bg.events and bg.pyr, default: bg.rate=NULL |

`k` |
allocation ratio of treatment vs. control group, default: k=1 |

`p.params` |
paramaters of beta prior of p (used only when inf.type = 1 or = 2); default: p.param= list(a=1,b=1). See details below. |

`r.params` |
paramaters of log-normal prior of r (used only when p.params=NULL); default: r.param= list(mu=0,sd=2). See details below. |

`adj.k` |
when TRUE adjusts the prior specification for k >1 (or for k <1), default: adj.k = FALSE . See deatil below. |

`mc.params` |
contains detials of MCMC parameters, default: mc.params=list(burn=1000, iter=10000, nc=2) |

`inf.type` |
indicate inference type, default: inf.type =1 (gives conditional inference for fixed background rate). See deatil below. |

`plots` |
indicates whether standard plots to be generated, default: plots= TRUE |

`prnt` |
indicates whether inputs to be printed, default: prnt= TRUE |

This 'bdribs' package obtains Bayesian inferences on blinded pooled safety data ...

Values of p.params are used to specify a beta prior for p - default is Jeffreys non-informative prior: Beta(a=0.5,b=0.5).

If inf.type=1, then conditional posterior inference on r is obtained for a given fixed values of del0 = bg.rate = bg.events/bg.pyr.

If inf.type=2, then an average (marginal) Bayesian inference on r is obtained with respect to a prior on del0, where del0 ~ Gamma(bg.events, bg.pyr).

If prior on r must be specified directly it can be done by using a log-normal prior. To do that, p.params must be set to NULL and and then r.params should be specifed as a list to supply mean and sd of the lognormal. For example, to have a lognormal prior with log-mean 0 and log-sd = 2, we should set r.params = list(mu=0, sd=2) and p.params=NULL.

when adj.k = TRUE, and k is not 1 (that is, allocation ratio is not 1:1), then a non-informative prior such as (beta(.5, .5) is first specified on p, assuming equal allocation ratio and then adjusted for the give k. When adj.k = F, then no such adjustment is made on the prior for p. Note that no such adjustments needed if prior on r is directly specified (as discussed above). However, it is always difficult to specify a non-informative prior on r and therefore a a prior on p with adj.k =T is recommended in most cases.

returns a dataframe of MCMC output from the posterior distribution for parameters of interests

Saurabh Mukhopadhyay

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## Sample calls
#run 1: simple case with a fixed background rate of 0.45 per 100 pyr.
bdribs(y=5,pyr=500, bg.rate=0.0045,k=2)
#run 2: same as run 1; here bg.rate gets computed as bg.events/bg.pyr
bdribs(y=5,pyr=500, bg.events = 18, bg.pyr = 4000, k=2)
# run3: when inf.type = 2, uses a Gamma distribution for del0; e.g. here Gamma(18, 4000)
bdribs(y=5,pyr=500, bg.events = 18, bg.pyr = 4000, k=2, inf.type = 2)
#run4: similar to run1, but instead of default p~u(0,1) using p~beta(.5,.5)
bdribs(y=5,pyr=500, , bg.rate=0.0045,k=2, p.params=list(a=.5,b=.5))
#run5: similar to run1, but instead of default p ~ beta(.5,.5) using r ~ lognormal(mu=0,sd=2)
bdribs(y=5,pyr=500, , bg.rate=0.0045,k=2, p.params= NULL, r.params=list(mu=0,sd=2))
``` |

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