In fpaskali/LFApp: Shiny Apps for Lateral Flow Assays

knitr::opts_chunk$set(echo = TRUE)

Import of Data

We import the data and select the variables needed for the analysis.

tmp <- strsplit(FORMULA, "~")[[1]]
y.var <- names(unlist(sapply(colnames(CalibrationData), 
                             grep, x = tmp[1])))
x.vars <- names(unlist(sapply(colnames(CalibrationData), 
                              grep, x = tmp[2])))
if(SUBSET != ""){
  calData <- eval(call("subset", x =  CalibrationData,
                       subset = parse(text = SUBSET)))
}else{
  calData <- CalibrationData
}
calData <- calData[,c(y.var, x.vars)]
calData

Model

We will apply the following model.

FORMULA

Analysis

We now fit (simple) linear model.

fit <- lm(as.formula(FORMULA), data = calData)
summary(fit)

We determine the inverse of the fitted model.

ab <- coef(fit)
names(ab) <- NULL
predFunc <- function(newdata){}
body(predFunc) <- substitute({ with(newdata, (eval(y)-a)/b) }, 
                             list(y = parse(text = respVar), 
                                a = ab[1], 
                                b = ab[2]))

We plot the given concentrations against the fitted values.

library(ggplot2)
modelPlot <- ggplot(calData, aes_string(x = concVar, y = respVar)) +
            geom_point() + geom_smooth(method = "lm") +
            annotate("text",  x=-Inf, y = Inf,
            label = substitute(paste(R^2, " = ", R2, ", adj. ", R^2, " = ", adj.R2), 
                              list(R2 = summary(fit)$r.squared, adj.R2 = summary(fit)$adj.r.squared)), 
            vjust=1, hjust=0, size = 5)
modelPlot

Computation of LOB, LOD and LOQ

We compute limit of blank (LOB), limit of detection (LOD) and limit of quantification (LOQ) by inverting the regression fit. We get the LOB by inverting the upper bound of the one-sided 95\% confidence interval at concentration $0$. In caso of the LOD, the upper-bound of the 99.95\% confidence interval at concentration $0$ is inverted. LQQ we define as $3\times\textrm{LOD}$.

LOB <- (confint(fit, parm = 1, level = 0.90)[2]-ab[1])/ab[2]
names(LOB) <- "LOB"
LOB
LOD <- (confint(fit, parm = 1, level = 0.999)[2]-ab[1])/ab[2]
names(LOD) <- "LOD"
LOD
LOQ <- 3*LOD
names(LOQ) <- "LOQ"
LOQ