bpAcc (version 0.0-2)

PAccept: Probability of acceptance - ANSI/AAMI-SP10 standard.

Description

Probability of acceptance - ANSI/AAMI-SP10 standard.

Usage

PAccept(xbar,sd,N,distribution = "normal", criteria = "SP10:2006")

Value

It returns the probability of a device meeting the SP10 criteria

Arguments

xbar, sd

mean and standar deviation of the average errors distribution (normal).

N

Sample size (number of participants).

distribution

Underlying distribution the errors \(\delta\) are pulled from. The default is normal, i.e. a normal distribution.

criteria

SP10 criteria used.

Author

Tanvi Chandel, Tet-Chuan Lee, Andrew Lowe, Victor Miranda.

Details

Computes the acceptance probability of a device D for blood pressure measuring under the ANSI/AAMI-SP10 standards for a size-n sample of average errors from an asymptotically normal distribution with mean xbar and stadard deviation sd.

$$1-\frac{1}{2}[1+erf(\frac{0.78-\hat{p}}{\sqrt(2)(\frac{\hat{p}(1-\hat{p})}{N})})]$$

The distribution is of the true probability of tolerable error p where the tolerable error according to the ANSI/AAMI-SP10, is an error between -10 mmHg to 10 mmHg on a single person, using average of that person's readings. Using the sampling distribution of sampling proportion, the probabilty of p>=0.78 is evaluated, which is called as the probabilty of acceptance or probability that for a given sample size n, sample mean xbar and sample standard deviation sd, the device is meeting the SP10 criteria.

Complete details in Chandel, et al. (2023). The paper outlines the mathematical and statistical aspects behind PAccept. The threshold probability for acceptance according to ANSI/AAMI-SP10 is 95% i.e.,Prob(p>=0.78) >= 0.95

References

Chandel, T. and Lee, TC. and Lowe, A. and Miranda, V. (2023) Blood Pressure Device Accuracy Evaluation: Statistical Considerations with an Implementarion in R, Statistics in Medicine (under review).

Examples

## Probability of acceptance of a device for a sample size (N) = 30 with sample 
## mean (xbar) = 5, standard deviation = 5.
PAccept(xbar=5,sd=5,N=30,distribution = "normal", criteria = "SP10:2006")


## Probability of acceptance of a device for a sample size (N) = 60 with sample 
## mean (xbar) = 2, standard deviation = 7.
PAccept(xbar=2,sd=7,N=60,distribution = "normal", criteria = "SP10:2006")