CIpvBayes {bdpv}

Confidence intervals for negative and positive predictive values in a case-control setting by simulation from the posterior distribution.

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

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

# 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))