# CIpvBayes: Confidence intervals for negative and positive predictive... In bdpv: Inference and Design for Predictive Values in Diagnostic Tests

## Description

Computes confidence intervals for negative and positive predictive values by simulation from the posterior beta-distribution (Stamey and Holt, 2010), assuming a case-control design to estimate sensitivity and specificity, while prevalence estimates of an external study and/or prior knowledge concerning prevalence may be introduced additionally.

## Usage

 ```1 2 3 4 5 6 7``` ```CIpvBI(x1, x0, pr, conf.level = 0.95, alternative = c("two.sided", "less", "greater"), B=5000, shapes1=c(1,1), shapes0=c(1,1), ...) CIpvBII(x1, x0, xpr, conf.level = 0.95, alternative = c("two.sided", "less", "greater"), B=5000, shapes1=c(1,1), shapes0=c(1,1), shapespr=c(1,1), ...) ```

## Arguments

 `x1` A vector of two (integer) values, specifying the observed number of positive (`x1[1]`) and negative (`x1[2]`) test results in the group of true positives. `x0` A vector of two (integer) values, specifying the observed number of positive (`x0[1]`) and negative (`x0[2]`) test results in the group of true negatives. `pr` A single numeric value between 0 and 1, defining an assumed fixed (known) prevalence (for `CIpvBI`), where prevalence is the proportion of positives in the population. `xpr` An optional vector of two (integer) values, specifying the observed number of positive (`xpr[1]`) and negative (`xpr[2]`) outcomes from an external study that allows to estimate the prevalence of positives in the population of interest. `conf.level` The confidence level, a single numeric value between 0 and 1, defaults to 0.95 `alternative` A character string specifying whether two-sided (`"two.sided"`), only lower bounds (`"greater"`) or only upper bounds (`"less"`) shall be calculated. `B` A single integer, the number of samples from the posterior to be drawn. `shapes1` Two positive numbers, the shape parameters (a,b) of the beta prior for the sensitivity, by default a flat beta prior (a=1, b=1) is used. `shapes0` Two positive numbers, the shape parameters (a,b) of the beta prior for (1-specificity), by default a flat beta prior (a=1, b=1) is used. Note, that this definition differs from that in Stamey and Holt(2010), where the prior is defined for the specificity directly. `shapespr` Two positive numbers, the shape parameters (a,b) of the beta prior for the prevalence, by default a flat beta prior (a=1, b=1) is used. For `CIpvBII` only. `...` Arguments to be passed to `quantile(), other arguments are ignored without warning. `.

## Details

`CIpvBI` implements the method refered to as Bayes I in Stamey and Holt (2010), `CIpvBI` implements the method refered to as Bayes II in Stamey and Holt (2010), Equation (2) and following description (p. 103-104).

## Value

A list with elements

 `conf.int ` the confidence bounds `estimate ` the point estimate `tab ` a 2x2 matrix showing how the input data in terms of true positives and true negatives

## Author(s)

Frank Schaarschmidt

## References

Stamey JD and Holt MM (2010). Bayesian interval estimation for predictive values for case-control studies. Communications in Statistics - Simulation and Computation. 39:1, 101-110.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34``` ```# example data: Stamey and Holt, Table 8 (page 108) # Diseased # Test D=1 D=0 # T=1 240 87 # T=0 178 288 #n1,n0: 418 375 # reproduce the results for the Bayes I method # in Stamey and Holt (2010), Table 9, page 108 # assuming known prevalence 0.03 # ppv 0.0591, 0.0860 # npv 0.9810, 0.9850 CIpvBI( x1=c(240,178), x0=c(87,288), pr=0.03) # assuming known prevalence 0.04 # ppv 0.0779, 0.1111 # npv 0.9745, 0.9800 CIpvBI( x1=c(240,178), x0=c(87,288), pr=0.04) # compare with standard logit intervals tab <- cbind( x1=c(240,178), x0=c(87,288)) tab BDtest(tab, pr=0.03) BDtest(tab, pr=0.04) # reproduce the results for the Bayes II method # in Stamey and Holt (2010), Table 9, page 108 CIpvBII( x1=c(240,178), x0=c(87,288), shapespr=c(16,486)) CIpvBII( x1=c(240,178), x0=c(87,288), shapespr=c(21,481)) ```

bdpv documentation built on May 2, 2019, 1:08 p.m.