ppwdeming (version 1.0.6)

PWD_RL: Weighted Deming -- Rocke-Lorenzato - known sigma, kappa

Description

This code fits the weighted Deming regression on predicate readings (X) and test readings (Y), with user-supplied Rocke-Lorenzato ("RL") parameters sigma (\(\sigma\)) and kappa (\(\kappa\)).

Usage

PWD_RL(X, Y, sigma, kappa, lambda=1, epsilon=1e-6)

Value

A list containing the following components:

alpha

the fitted intercept

beta

the fitted slope

fity

the vector of predicted Y

mu

the vector of estimated latent true values

resi

the vector of residuals

like

the -2 log likelihood L

innr

the number of inner refinement loops executed

error

an error code if the iteration fails

Arguments

X

the vector of predicate readings,

Y

the vector of test readings,

sigma

the RL sigma parameter,

kappa

the RL kappa parameter,

lambda

optional (default of 1) - the ratio of the X to the Y precision profile,

epsilon

optional - convergence tolerance limit.

Author

Douglas M. Hawkins, Jessica J. Kraker

Details

The Rocke-Lorenzato precision profile model assumes the following forms for the variances, with proportionality constant \(\lambda\):

• predicate precision profile model: \(g_i = var(X_i) = \lambda\left(\sigma^2 + \left[\kappa\cdot \mu_i\right]^2\right)\) and

• test precision profile model: \(h_i = var(Y_i) = \sigma^2 + \left[\kappa\cdot (\alpha + \beta\mu_i)\right]^2\).

The algorithm uses maximum likelihood estimation. Proportionality constant \(\lambda\) is assumed to be known or estimated externally.

References

Hawkins DM and Kraker JJ. Precision Profile Weighted Deming Regression for Methods Comparison, on Arxiv (2025) doi:10.48550/arXiv.2508.02888

Hawkins DM (2014). A Model for Assay Precision. Statistics in Biopharmaceutical Research, 6, 263-269. doi:10.1080/19466315.2014.899511

Examples

# library
library(ppwdeming)

# parameter specifications
sigma <- 1
kappa <- 0.08
alpha <- 1
beta  <- 1.1
true  <- 8*10^((0:99)/99)
truey <- alpha+beta*true
# simulate single sample - set seed for reproducibility
set.seed(1039)
# specifications for predicate method
X     <- sigma*rnorm(100)+true *(1+kappa*rnorm(100))
# specifications for test method
Y     <- sigma*rnorm(100)+truey*(1+kappa*rnorm(100))

# fit RL with given sigma and kappa
RL_results <- PWD_RL(X,Y,sigma,kappa)
cat("\nWith given sigma and kappa, the estimated intercept is",
    signif(RL_results$alpha,4), "and the estimated slope is",
    signif(RL_results$beta,4), "\n")