epi.betabuster {epiR} | R Documentation |

A function to return shape1 and shape2 parameters for a beta distribution, based on expert elicitation.

epi.betabuster(mode, conf, greaterthan, x, conf.level = 0.95, max.shape1 = 100, step = 0.001)

`mode` |
scalar, the mode of the variable of interest. Must be a number between 0 and 1. |

`conf` |
level of confidence (expressed on a 0 to 1 scale) that the true value of the variable of interest is greater or less than argument |

`greaterthan` |
logical, if |

`x` |
scalar, value of the variable of interest (see above). |

`conf.level` |
magnitude of the returned confidence interval for the estimated beta distribution. Must be a single number between 0 and 1. |

`max.shape1` |
scalar, maximum value of the shape1 parameter for the beta distribution. |

`step` |
scalar, step value for the shape1 parameter. See details. |

The beta distribution has two parameters: `shape1`

and `shape2`

, corresponding to `a`

and `b`

in the original verion of BetaBuster. If `r`

equals the number of times an event has occurred after `n`

trials, `shape1`

= `(r + 1)`

and `shape2`

= `(n - r + 1)`

.

A list containing the following:

`shape1` |
the |

`shape2` |
the |

`mode` |
the mode of the estimated beta distribution. |

`mean` |
the mean of the estimated beta distribution. |

`median` |
the median of the estimated beta distribution. |

`lower` |
the lower bound of the confidence interval of the estimated beta distribution. |

`upper` |
the upper bound of the confidence interval of the estimated beta distribution. |

`variance` |
the variance of the estimated beta distribution. |

Simon Firestone (Faculty of Veterinary and Agricultural Sciences, The University of Melbourne, Australia) with acknowledgements to Wes Johnson and Chun-Lung Su for the original standalone software.

Christensen R, Johnson W, Branscum A, Hanson TE (2010). Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. Chapman and Hall, Boca Raton.

## EXAMPLE 1: ## If a scientist is asked for their best guess for the diagnostic sensitivity ## of a particular test and the answer is 0.90, and if they are also willing ## to assert that they are 80% certain that the sensitivity is greater than ## 0.75, what are the shape1 and shape2 parameters for a beta distribution ## satisfying these constraints? rval.beta01 <- epi.betabuster(mode = 0.90, conf = 0.80, greaterthan = TRUE, x = 0.75, conf.level = 0.95, max.shape1 = 100, step = 0.001) rval.beta01$shape1; rval.beta01$shape2 ## The shape1 and shape2 parameters for the beta distribution that satisfy the ## constraints listed above are 9.875 and 1.986, respectively. ## This beta distribution reflects the probability distribution obtained if ## there were 9 successes, r: r <- rval.beta01$shape1 - 1; r ## from 10 trials, n: n <- rval.beta01$shape2 + rval.beta01$shape1 - 2; n dat.df01 <- data.frame(x = seq(from = 0, to = 1, by = 0.001), y = dbeta(x = seq(from = 0, to = 1,by = 0.001), shape1 = rval.beta01$shape1, shape2 = rval.beta01$shape2)) ## Density plot of the estimated beta distribution: ## Not run: library(ggplot2) ggplot(data = dat.df01, aes(x = x, y = y)) + geom_line() + scale_x_continuous(name = "Test sensitivity") + scale_y_continuous(name = "Density") ## End(Not run)

[Package *epiR* version 2.0.31 Index]