View source: R/epi.betabuster.R

epi.betabuster | R Documentation |

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

```
epi.betabuster(mode, conf, imsure, 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 |

`imsure` |
a character string, 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 version of BetaBuster. If `r`

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

trials, `shape1`

= `(r + 1)`

and `shape2`

= `(n - r + 1)`

.

Take care when you're parameterising probability estimates that are at the extremes of the 0 to 1 bounds. If the returned `shape1`

parameter is equal to the value of `max.shape1`

(which, by default is 100) consider increasing the value of the `max.shape1`

argument. The `epi.betabuster`

functions issues a warning if these conditions are met.

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. |

`exp` |
a statement of the arguments used for this instance of the function. |

Simon Firestone (Melbourne Veterinary School, Faculty of Science, The University of Melbourne, Parkville Victoria 3010, 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.

Su C-L, Johnson W (2014) Beta Buster. Software for obtaining parameters for the Beta distribution based on expert elicitation. URL: `https://cadms.vetmed.ucdavis.edu/diagnostic/software`

.

```
## 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, imsure = "greater than",
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)) +
theme_bw() +
geom_line() +
scale_x_continuous(name = "Test sensitivity") +
scale_y_continuous(name = "Density")
## End(Not run)
## EXAMPLE 2:
## The most likely value of the specificity of a PCR for coxiellosis in
## small ruminants is 1.00 and we're 97.5% certain that this estimate is
## greater than 0.99. What are the shape1 and shape2 parameters for a beta
## distribution satisfying these constraints?
epi.betabuster(mode = 1.00, conf = 0.975, imsure = "greater than", x = 0.99,
conf.level = 0.95, max.shape1 = 100, step = 0.001)
## The shape1 and shape2 parameters for the beta distribution that satisfy the
## constraints listed above are 100 and 1, respectively. epi.betabuster
## issues a warning that the value of shape1 equals max.shape1. Increase
## max.shape1 to 500:
epi.betabuster(mode = 1.00, conf = 0.975, imsure = "greater than", x = 0.99,
conf.level = 0.95, max.shape1 = 500, step = 0.001)
## The shape1 and shape2 parameters for the beta distribution that satisfy the
## constraints listed above are 367.04 and 1, respectively.
```

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