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analysisOfVariance.R
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analysisOfVariance.R
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# data = read.table("~/Documents/GitHub/BV/data/example_data.txt",
# header = T, sep = "\t")
# head(data)
#
# analyte = "Measurement"
# subject = "Subject"
# gender = "Gender"
# replicate = "Replicate"
# time = "Time"
# decimal = 3
#
# outlierS1 = "subjetcs"; outlierS2 = TRUE; outlierS3 = TRUE;
# showResult = "original"
#
# # data[,analyte] = log(data[,analyte])
#
#
#
#
#
# head(data)
#
#
# out = outlier(data = data, analyte=analyte, subject=subject, replicate=replicate,
# time=time, gender=gender, decimal =3, outlierS1 = "none", outlierS2 = F, outlierS3 = F,
# showResult = showResult)
#
# data = out$dataWithoutOutliers
#
# analyte = "value"
# subject = "subject"
# gender = "gender"
# replicate = "replicate"
# time = "time"
# alpha = 0.05
# CVresult = "original"
#
# head(data)
#
# aov = analysisOfVariance(data, gender, subject, replicate, time, CVresult, decimal, alpha = alpha)
# aov$resultsAllOriginalLme$rcvResult
analysisOfVariance <- function(data, gender, subject, replicate, time, CVresult, decimal, alpha = alpha){
library(nlme)
alpha = as.numeric(alpha)
lower_title = paste0("Lower Limit (",(1-alpha)*100,"%)")
upper_title = paste0("Upper Limit (",(1-alpha)*100,"%)")
lowerMean_title = paste0("Lower Limit (",(1-alpha)*100,"%)")
upperMean_title = paste0("Upper Limit (",(1-alpha)*100,"%)")
# if(CVresult == "lnTransformed" || CVresult == "transformBack"){
#
# data$value = log(data$value)
#
# }
data = data[,c("subject", "gender", "time", "replicate", "value")]
######################### CV-ANOVA ###################################
if(CVresult == "cv" || CVresult == "mom" || CVresult == "lnmom" ){
# if(CVresult == "cv"){
#
# #
# # means = tapply(data$value, data[,subject], mean, na.rm = TRUE)
# #
# # subjects = split(data, data[,subject])
# #
# #
# # for(i in 1:length(means)){
# #
# # subjects[[i]]$value = subjects[[i]]$value / means[i]
# #
# # }
# #
# #
# # data = do.call(rbind.data.frame, subjects)
# #
# dataGender = split(data, data[,"gender"])
#
# }
#
# if(CVresult == "mom"){
#
#
# # data = momTransformation(data = data, time = time, measure = "value", method ="mom")
# dataGender = split(data, data[,"gender"])
#
# }
# if(CVresult == "lnmom"){
# data = momTransformation(data = data, time = time, measure = "value", method ="lnmom")
dataGender = split(data, data[,"gender"])
# }
data[,"subject"] = as.factor(data[,"subject"])
data[,"replicate"] = as.factor(data[,"replicate"])
data[,"time"] = as.factor(data[,"time"])
bv <- lme(value ~1, random=~1|subject/time, data=data)
N <- nrow(data)
r <- length(unique(data[,"subject"]))
ni <- as.numeric(table(data[ ,"subject"]))
sgConstant <- (1/(r - 1))*sum((ni^2)*(1/ni - 1/N))
ti = ni/2
replicateNumber = 2
w1List = list()
for(i in 1:length(ti)){
w1List[[i]] = rep(((replicateNumber^2)*((1/ni[i])-(1/sum(ni))))/(bv$dims$ngrps[[2]]-1),ti[i])
}
w3List = list()
for(i in 1:length(ti)){
w3List[[i]] = rep((replicateNumber^2)*((1/sqrt(replicateNumber^2)) - (1/ni[i]))/(bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]),ti[i])
}
w1uList1 = list()
for(i in 1:length(ti)){
w1uList1[[i]] = sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w3uList1 = list()
for(i in 1:length(ti)){
w3uList1[[i]] = ti[i]/sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w1 = do.call("sum", w1List)
w2 = sgConstant
w3 = do.call("sum", w3List)
w1u = sum((1/ti))/sum((1/(ti*(ti/unlist(w1uList1)))))
w2u = bv$dims$ngrps[[2]]/sum(1/(ti*(ti/(0.5*(ti)))))
w3u = (bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]) / sum((ti-1)/unlist(w3uList1))
c2u = (w2u-w1u)/(w3u)
c3u = w2u-1-c2u
c2 = w1u/w3u
c3 = 0
alpha = alpha
inf = 999999999
## lme model
anova = summary(aov(value ~ subject/time, data))
sigma2_analytical = anova[[1]][[2]][3]/anova[[1]][[1]][3]
sigma2_within = (anova[[1]][[2]][2]/anova[[1]][[1]][2]-anova[[1]][[2]][3]/anova[[1]][[1]][3])/w3
sigma2_between = (anova[[1]][[2]][1]/anova[[1]][[1]][1] - sigma2_analytical-w1*sigma2_within)/w2
grandMean = mean(data$value)
seGrandMean = sd(data$value)/sqrt(N)
llMean = grandMean-qnorm(1-alpha/2)*seGrandMean
ulMean = grandMean+qnorm(1-alpha/2)*seGrandMean
sigma_analytical = sqrt(sigma2_analytical)
sigma_within = sqrt(sigma2_within)
sigma_between = ifelse(sigma2_between > 0, sqrt(sigma2_between),0)
sigma_total = sqrt(sigma2_analytical + sigma2_within + sigma2_between)
CV_analytical = abs(sigma_analytical/grandMean)
CV_within = abs(sigma_within/grandMean)
CV_between = abs(sigma_between/grandMean)
CV_total = abs(sigma_total/grandMean)
ll_analytical = sqrt((sigma_analytical^2)/qf(alpha/2, bv$dims$ngrps[[1]], inf, lower.tail = F))
ul_analytical = sqrt((sigma_analytical^2)/qf(alpha/2, bv$dims$ngrps[[1]], inf, lower.tail = T))
lower_analytical = ll_analytical/grandMean
upper_analytical = ul_analytical/grandMean
if(CVresult == "cv"){msu_between = 0}else{
msu_between = sigma2_between*sgConstant + sigma2_analytical + sigma2_within*2
}
sigma2_within = sigma_within^2
sigma2_analytical = sigma_analytical^2
sigma2_between = (msu_between-sigma2_analytical-w1u*sigma2_within)#sigma_between^2
msu_within = 2*sigma2_within+sigma2_analytical
dfbetween = (bv$dims$ngrps[[2]]-1)
dfwithin = (bv$dims$ngrps[[1]]-bv$dims$ngrps[[2]])
dfanalytical = (bv$dims$ngrps[[1]])
g1 = 1-1/(qf(alpha/2, dfbetween, inf, lower.tail = F))
g2 = 1-1/(qf(alpha/2, dfwithin, inf, lower.tail = F))
g3 = 1-1/(qf(alpha/2, dfanalytical, inf, lower.tail = F))
h1 =1/(qf(1-alpha/2, dfbetween, inf, lower.tail = F))-1
h2 = 1/(qf(1-alpha/2, dfwithin, inf, lower.tail = F))-1
h3 = 1/(qf(1-alpha/2, dfanalytical, inf, lower.tail = F))-1
g12 = (((qf(alpha/2, dfbetween, dfwithin, lower.tail = F)-1)^2)-g1^2*(qf(alpha/2, dfbetween, dfwithin, lower.tail = F)^2)-h2^2)/(qf(alpha/2, dfbetween, dfwithin, lower.tail = F))
g13 = (((qf(alpha/2, dfbetween, dfanalytical, lower.tail = F)-1)^2)-g1^2*(qf(alpha/2, dfbetween, dfanalytical, lower.tail = F)^2)-h3^2)/(qf(alpha/2, dfbetween, dfanalytical, lower.tail = F))
g23 = (((qf(alpha/2, dfwithin, dfanalytical, lower.tail = F)-1)^2)-g2^2*(qf(alpha/2, dfwithin, dfanalytical, lower.tail = F))^2-h3^2)/(qf(alpha/2, dfwithin, dfanalytical, lower.tail = F))
g32 = (((qf(alpha/2, dfanalytical, dfwithin, lower.tail = F)-1)^2)-g3^2*(qf(alpha/2, dfanalytical, dfwithin, lower.tail = F))^2-h2^2)/(qf(alpha/2, dfanalytical, dfwithin, lower.tail = F))
h12 = (((1-qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))^2)-h1^2*(qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))^2-g2^2)/(qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))
h13 = (((1-qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))^2)-h1^2*(qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))^2-g3^2)/(qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))
h23 = (((1-qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))^2)-h2^2*(qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))^2-g3^2)/(qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))
h32 = (((1-qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))^2)-h3^2*(qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))^2-g2^2)/(qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))
VLba = (g2^2)*(msu_within^2)+(h3^2)*(sigma2_analytical^2)+g23*msu_within*sigma2_analytical
VUba = (h2^2)*(msu_within^2)+(g3^2)*(sigma2_analytical^2)+h23*msu_within*sigma2_analytical
VLa = g1^2*msu_between^2+h2^2*c2^2*msu_within^2+h3^2*c3^2*sigma2_analytical^2+g12*c2*msu_between*msu_within+g13*abs(c3)*msu_between*sigma2_analytical
VLa2 = h1^2*msu_between^2+g2^2*c2^2*msu_within^2+g3^2*c3^2*sigma2_analytical^2+h12*c2*msu_between*msu_within+h13*abs(c3)*msu_between*sigma2_analytical
ll_within = sqrt((msu_within-sigma2_analytical-sqrt(VLba))/2)
ul_within = sqrt((msu_within-sigma2_analytical+sqrt(VUba))/2)
lower_within = ll_within/grandMean
upper_within = ul_within/grandMean
ll_between = sqrt((msu_between - msu_within - sqrt(VLa))/sgConstant)
ul_between = sqrt((msu_between - msu_within + sqrt(VLa2))/sgConstant)
lower_between = ll_between/grandMean
upper_between = ul_between/grandMean
c34 = (sgConstant-2)/2
c35 = sgConstant-1-c34
vlTot = (g1^2)*(msu_between^2)+(g2^2)*(c2u^2)*(msu_within^2)+(g3^2)*(c3u^2)*(sigma2_analytical^2)
vuTot = (h1^2)*(msu_between^2)+(h2^2)*(c2u^2)*(msu_within^2)+(h3^2)*(c3u^2)*(sigma2_analytical^2)
ll_total = sqrt((msu_between + c34*msu_within + c35*sigma2_analytical- sqrt(vlTot))/sgConstant)
ul_total = sqrt((msu_between + c34*msu_within + c35*sigma2_analytical+ sqrt(vuTot))/sgConstant)
lower_total = ll_total/grandMean
upper_total = ul_total/grandMean
############# ALL subjects
CVTable = data.frame(matrix(NA,4,5))
colnames(CVTable) = c("Source", "sigma", "CV%", lower_title, upper_title)
CVTable[1,"Source"] = "Between"
CVTable[2,"Source"] = "Within"
CVTable[3,"Source"] = "Analytical"
CVTable[4,"Source"] = "Total"
CVTable[1, "sigma"] = round(sigma_between,decimal)
CVTable[2, "sigma"] = round(sigma_within,decimal)
CVTable[3, "sigma"] = round(sigma_analytical,decimal)
CVTable[4, "sigma"] = round(sigma_total,decimal)
CVTable[1, lower_title] = ifelse(sigma_between > 0, round(lower_between*100,decimal),0)
CVTable[2, lower_title] = round(lower_within*100,decimal)
CVTable[3, lower_title] = round(lower_analytical*100,decimal)
CVTable[4, lower_title] = round(lower_total*100,decimal)
CVTable[1, upper_title] = ifelse(sigma_between > 0, round(upper_between*100,decimal),0)
CVTable[2, upper_title] = round(upper_within*100,decimal)
CVTable[3, upper_title] = round(upper_analytical*100,decimal)
CVTable[4, upper_title] = round(upper_total*100,decimal)
CVTable[1, "CV%"] = round(CV_between*100,decimal)
CVTable[2, "CV%"] = round(CV_within*100,decimal)
CVTable[3, "CV%"] = round(CV_analytical*100,decimal)
CVTable[4, "CV%"] = round(CV_total*100,decimal)
CVa = CVTable[3,3] #in percentage
CVi = CVTable[2,3]#in percentage
CVg = CVTable[1,3] #in percentage
z = qnorm(1-alpha/2) #for alpha = 0.05
#z = 2.58 #for alpha = 0.01
### Calculation of Index of Individuality (II) ###
#II indicates the utility of population-based reference values
II = CVi/CVg
### Calculation of Reference Change Value (RCV) ###
#RCV is also called as ‘critical difference (CD)’, and indicates whether the difference between
#two consecutive measurements from the same individual is significant or not.
RCV = formatC(sqrt(2)*z*sqrt((CVa^2)+(CVi^2)), digits = decimal, format = "f")
k = z*sqrt(2)
t1 = w3u-1
t2 = w3u
VLrcv = (g2^2)*(msu_within^2)+(g3^2)*(t1^2)*(sigma2_analytical^2)
VUrcv = (h2^2)*(msu_within^2)+(h3^2)*(t1^2)*(sigma2_analytical^2)
lower_RCV = formatC(((k*(sqrt((msu_within+t1*sigma2_analytical-1*sqrt(VLrcv))/t2)))/grandMean)*100, digits = decimal, format = "f")
upper_RCV = formatC(((k*(sqrt((msu_within+t1*sigma2_analytical+1*sqrt(VUrcv))/t2)))/grandMean)*100, digits = decimal, format = "f")
rcvResult = cbind.data.frame(RCV, lower_RCV, upper_RCV)
colnames(rcvResult) = c("RCV (%)", "Lower limit (%)", "Upper limit (%)")
CVresults = data.frame(matrix(NA,1,9))
colnames(CVresults) = c("Group", "Mean", lowerMean_title, upperMean_title, "CV_A%", "CV_I%", "CV_G%", "II", "n")
CVresults[1,1] = "All Subjects"
CVresults[1,2] = round(grandMean,decimal)
CVresults[1,3] = round(llMean,decimal)
CVresults[1,4] = round(ulMean,decimal)
CVresults[1,5] = round(CVa,decimal)
CVresults[1,6] = round(CVi,decimal)
CVresults[1,7] = round(CVg,decimal)
CVresults[1,8] = round(II,decimal)
# CVresults[1,9] = NA
CVresults[1,9] = nrow(data)
errorTable = matrix(NA,3,3)
rownames(errorTable) = c("Optimal","Desirable","Minimal")
colnames(errorTable) = c("Imprecision,%", "Bias,%","TEa,%")
errorTable[1,1] = paste("<",round(0.25*CVi,decimal))
errorTable[2,1] = paste("<",round(0.50*CVi,decimal))
errorTable[3,1] = paste("<",round(0.75*CVi,decimal))
errorTable[1,2] = paste("<",round(0.125*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[2,2] = paste("<",round(0.250*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[3,2] = paste("<",round(0.375*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[1,3] = paste("<",round(1.65*(0.25*CVi)+0.125*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[2,3] = paste("<",round(1.65*(0.50*CVi)+0.250*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[3,3] = paste("<",round(1.65*(0.75*CVi)+0.375*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable = cbind.data.frame("Quality Levels" = row.names(errorTable), errorTable)
resultsAllCvAnova = list(CVTable = CVTable, CVresults = CVresults, errorTable = errorTable, rcvResult=rcvResult)
################### Subset Original ###############
gender1 = names(dataGender)[1]
############################# Gender = Gender 1 #######################################
dataGender1 = dataGender[[gender1]]
dataGender1[,"subject"] = as.factor(dataGender1[,"subject"])
dataGender1[,"replicate"] = as.factor(dataGender1[,"replicate"])
dataGender1[,"time"] = as.factor(dataGender1[,"time"])
bv <- lme(value ~1, random=~1|subject/time, data=dataGender1)
N <- nrow(dataGender1)
r <- length(unique(dataGender1[,"subject"]))
ni <- as.numeric(table(dataGender1[ ,"subject"]))
ni = ni[ni>0]
sgConstant <- (1/(r - 1))*sum((ni^2)*(1/ni - 1/N))
ti = ni/2
replicateNumber = 2
w1List = list()
for(i in 1:length(ti)){
w1List[[i]] = rep(((replicateNumber^2)*((1/ni[i])-(1/sum(ni))))/(bv$dims$ngrps[[2]]-1),ti[i])
}
w3List = list()
for(i in 1:length(ti)){
w3List[[i]] = rep((replicateNumber^2)*((1/sqrt(replicateNumber^2)) - (1/ni[i]))/(bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]),ti[i])
}
w1uList1 = list()
for(i in 1:length(ti)){
w1uList1[[i]] = sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w3uList1 = list()
for(i in 1:length(ti)){
w3uList1[[i]] = ti[i]/sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w1 = do.call("sum", w1List)
w2 = sgConstant
w3 = do.call("sum", w3List)
w1u = sum((1/ti))/sum((1/(ti*(ti/unlist(w1uList1)))))
w2u = ti[1]/sum(1/(ti*(ti/(0.5*(ti)))))
w3u = (bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]) / sum((ti-1)/unlist(w3uList1))
c2u = (w2u-w1u)/(w3u)
c3u = w2u-1-c2u
c2 = w1u/w3u
c3 = 0
alpha = alpha
inf = 999999999
anova = summary(aov(value ~ subject/time, dataGender1))
sigma2_analytical = anova[[1]][[2]][3]/anova[[1]][[1]][3]
sigma2_within = (anova[[1]][[2]][2]/anova[[1]][[1]][2]-anova[[1]][[2]][3]/anova[[1]][[1]][3])/w3
sigma2_between = (anova[[1]][[2]][1]/anova[[1]][[1]][1] - sigma2_analytical-w1*sigma2_within)/w2
grandMean = mean(dataGender1$value)
seGrandMean = sd(dataGender1$value)/sqrt(N)
llMean = grandMean-qnorm(1-alpha/2)*seGrandMean
ulMean = grandMean+qnorm(1-alpha/2)*seGrandMean
sigma_analytical = sqrt(sigma2_analytical)
sigma_within = sqrt(sigma2_within)
sigma_between = sqrt(sigma2_between)
sigma_total = sqrt(sigma2_analytical + sigma2_within + sigma2_between)
CV_analytical = abs(sigma_analytical/grandMean)
CV_within = abs(sigma_within/grandMean)
CV_between = abs(sigma_between/grandMean)
CV_total = abs(sigma_total/grandMean)
ll_analytical = sqrt((sigma_analytical^2)/qf(alpha/2, bv$dims$ngrps[[1]], inf, lower.tail = F))
ul_analytical = sqrt((sigma_analytical^2)/qf(alpha/2, bv$dims$ngrps[[1]], inf, lower.tail = T))
lower_analytical = ll_analytical/grandMean
upper_analytical = ul_analytical/grandMean
sigma2_between = sigma_between^2
sigma2_within = sigma_within^2
sigma2_analytical = sigma_analytical^2
msu_within = 2*sigma2_within+sigma2_analytical
if(CVresult == "cv"){msu_between = 0}else{
msu_between = sigma2_between*sgConstant + sigma2_analytical + sigma2_within*2
}
dfbetween = (bv$dims$ngrps[[2]]-1)
dfwithin = (bv$dims$ngrps[[1]]-bv$dims$ngrps[[2]])
dfanalytical = (bv$dims$ngrps[[1]])
g1 = 1-1/(qf(alpha/2, dfbetween, inf, lower.tail = F))
g2 = 1-1/(qf(alpha/2, dfwithin, inf, lower.tail = F))
g3 = 1-1/(qf(alpha/2, dfanalytical, inf, lower.tail = F))
h1 =1/(qf(1-alpha/2, dfbetween, inf, lower.tail = F))-1
h2 = 1/(qf(1-alpha/2, dfwithin, inf, lower.tail = F))-1
h3 = 1/(qf(1-alpha/2, dfanalytical, inf, lower.tail = F))-1
g12 = (((qf(alpha/2, dfbetween, dfwithin, lower.tail = F)-1)^2)-g1^2*(qf(alpha/2, dfbetween, dfwithin, lower.tail = F)^2)-h2^2)/(qf(alpha/2, dfbetween, dfwithin, lower.tail = F))
g13 = (((qf(alpha/2, dfbetween, dfanalytical, lower.tail = F)-1)^2)-g1^2*(qf(alpha/2, dfbetween, dfanalytical, lower.tail = F)^2)-h3^2)/(qf(alpha/2, dfbetween, dfanalytical, lower.tail = F))
g23 = (((qf(alpha/2, dfwithin, dfanalytical, lower.tail = F)-1)^2)-g2^2*(qf(alpha/2, dfwithin, dfanalytical, lower.tail = F))^2-h3^2)/(qf(alpha/2, dfwithin, dfanalytical, lower.tail = F))
g32 = (((qf(alpha/2, dfanalytical, dfwithin, lower.tail = F)-1)^2)-g3^2*(qf(alpha/2, dfanalytical, dfwithin, lower.tail = F))^2-h2^2)/(qf(alpha/2, dfanalytical, dfwithin, lower.tail = F))
h12 = (((1-qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))^2)-h1^2*(qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))^2-g2^2)/(qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))
h13 = (((1-qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))^2)-h1^2*(qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))^2-g3^2)/(qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))
h23 = (((1-qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))^2)-h2^2*(qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))^2-g3^2)/(qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))
h32 = (((1-qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))^2)-h3^2*(qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))^2-g2^2)/(qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))
VLba = (g2^2)*(msu_within^2)+(h3^2)*(sigma2_analytical^2)+g23*msu_within*sigma2_analytical
VUba = (h2^2)*(msu_within^2)+(g3^2)*(sigma2_analytical^2)+h23*msu_within*sigma2_analytical
VLa = g1^2*msu_between^2+h2^2*c2^2*msu_within^2+h3^2*c3^2*sigma2_analytical^2+g12*c2*msu_between*msu_within+g13*abs(c3)*msu_between*sigma2_analytical
VLa2 = h1^2*msu_between^2+g2^2*c2^2*msu_within^2+g3^2*c3^2*sigma2_analytical^2+h12*c2*msu_between*msu_within+h13*abs(c3)*msu_between*sigma2_analytical
ll_within = sqrt((msu_within-sigma2_analytical-sqrt(VLba))/2)
ul_within = sqrt((msu_within-sigma2_analytical+sqrt(VUba))/2)
lower_within = ll_within/grandMean
upper_within = ul_within/grandMean
ll_between = sqrt((msu_between - msu_within - sqrt(VLa))/sgConstant)
ul_between = sqrt((msu_between - msu_within + sqrt(VLa2))/sgConstant)
lower_between = ll_between/grandMean
upper_between = ul_between/grandMean
c34 = (sgConstant-2)/2
c35 = sgConstant-1-c34
vlTot = (g1^2)*(msu_between^2)+(g2^2)*(c2u^2)*(msu_within^2)+(g3^2)*(c3u^2)*(sigma2_analytical^2)
vuTot = (h1^2)*(msu_between^2)+(h2^2)*(c2u^2)*(msu_within^2)+(h3^2)*(c3u^2)*(sigma2_analytical^2)
ll_total = sqrt((msu_between + c34*msu_within + c35*sigma2_analytical- sqrt(vlTot))/sgConstant)
ul_total = sqrt((msu_between + c34*msu_within + c35*sigma2_analytical+ sqrt(vuTot))/sgConstant)
lower_total = ll_total/grandMean
upper_total = ul_total/grandMean
CVTable = data.frame(matrix(NA,4,5))
colnames(CVTable) = c("Source", "sigma", "CV%", lower_title, upper_title)
CVTable[1,"Source"] = "Between"
CVTable[2,"Source"] = "Within"
CVTable[3,"Source"] = "Analytical"
CVTable[4,"Source"] = "Total"
CVTable[1, "sigma"] = round(sigma_between,decimal)
CVTable[2, "sigma"] = round(sigma_within,decimal)
CVTable[3, "sigma"] = round(sigma_analytical,decimal)
CVTable[4, "sigma"] = round(sigma_total,decimal)
CVTable[1, lower_title] = round(lower_between*100,decimal)
CVTable[2, lower_title] = round(lower_within*100,decimal)
CVTable[3, lower_title] = round(lower_analytical*100,decimal)
CVTable[4, lower_title] = round(lower_total*100,decimal)
CVTable[1, upper_title] = round(upper_between*100,decimal)
CVTable[2, upper_title] = round(upper_within*100,decimal)
CVTable[3, upper_title] = round(upper_analytical*100,decimal)
CVTable[4, upper_title] = round(upper_total*100,decimal)
CVTable[1, "CV%"] = round(CV_between*100,decimal)
CVTable[2, "CV%"] = round(CV_within*100,decimal)
CVTable[3, "CV%"] = round(CV_analytical*100,decimal)
CVTable[4, "CV%"] = round(CV_total*100,decimal)
CVa = CVTable[3,3] #in percentage
CVi = CVTable[2,3]#in percentage
CVg = CVTable[1,3] #in percentage
z = qnorm(1-alpha/2) #for alpha = 0.05
#z = 2.58 #for alpha = 0.01
### Calculation of Index of Individuality (II) ###
#II indicates the utility of population-based reference values
II = CVi/CVg
### Calculation of Reference Change Value (RCV) ###
#RCV is also called as ‘critical difference (CD)’, and indicates whether the difference between
#two consecutive measurements from the same individual is significant or not.
RCV = formatC(sqrt(2)*z*sqrt((CVa^2)+(CVi^2)), digits = decimal, format = "f")
k = z*sqrt(2)
t1 = w3u-1
t2 = w3u
VLrcv = (g2^2)*(msu_within^2)+(g3^2)*(t1^2)*(sigma2_analytical^2)
VUrcv = (h2^2)*(msu_within^2)+(h3^2)*(t1^2)*(sigma2_analytical^2)
lower_RCV = formatC(((k*(sqrt((msu_within+t1*sigma2_analytical-1*sqrt(VLrcv))/t2)))/grandMean)*100, digits = decimal, format = "f")
upper_RCV = formatC(((k*(sqrt((msu_within+t1*sigma2_analytical+1*sqrt(VUrcv))/t2)))/grandMean)*100, digits = decimal, format = "f")
rcvResult = cbind.data.frame(RCV, lower_RCV, upper_RCV)
colnames(rcvResult) = c("RCV (%)", "Lower limit (%)", "Upper limit (%)")
CVresults = data.frame(matrix(NA,1,9))
colnames(CVresults) = c("Group", "Mean", lowerMean_title, upperMean_title, "CV_A%", "CV_I%", "CV_G%", "II", "n")
CVresults[1,1] = gender1
CVresults[1,2] = round(grandMean,decimal)
CVresults[1,3] = round(llMean,decimal)
CVresults[1,4] = round(ulMean,decimal)
CVresults[1,5] = round(CVa,decimal)
CVresults[1,6] = round(CVi,decimal)
CVresults[1,7] = round(CVg,decimal)
CVresults[1,8] = round(II,decimal)
# CVresults[1,9] = NA
CVresults[1,9] = nrow(dataGender1)
errorTable = matrix(NA,3,3)
rownames(errorTable) = c("Optimal","Desirable","Minimal")
colnames(errorTable) = c("Imprecision,%", "Bias,%","TEa,%")
errorTable[1,1] = paste("<",round(0.25*CVi,decimal))
errorTable[2,1] = paste("<",round(0.50*CVi,decimal))
errorTable[3,1] = paste("<",round(0.75*CVi,decimal))
errorTable[1,2] = paste("<",round(0.125*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[2,2] = paste("<",round(0.250*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[3,2] = paste("<",round(0.375*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[1,3] = paste("<",round(1.65*(0.25*CVi)+0.125*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[2,3] = paste("<",round(1.65*(0.50*CVi)+0.250*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[3,3] = paste("<",round(1.65*(0.75*CVi)+0.375*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable = cbind.data.frame("Quality Levels" = row.names(errorTable), errorTable)
resultsCvAnovaGender1 = list(CVTable = CVTable, CVresults = CVresults, errorTable = errorTable, rcvResult=rcvResult)
#################################### Gender = Gender 2 ############################
gender2 = names(dataGender)[2]
datagender2 = dataGender[[gender2]]
datagender2[,"subject"] = as.factor(datagender2[,"subject"])
datagender2[,"replicate"] = as.factor(datagender2[,"replicate"])
datagender2[,"time"] = as.factor(datagender2[,"time"])
bv <- lme(value ~1, random=~1|subject/time, data=datagender2)
N <- nrow(datagender2)
r <- length(unique(datagender2[,"subject"]))
ni <- as.numeric(table(datagender2[ ,"subject"]))
ni = ni[ni>0]
sgConstant <- (1/(r - 1))*sum((ni^2)*(1/ni - 1/N))
ti = ni/2
replicateNumber = 2
w1List = list()
for(i in 1:length(ti)){
w1List[[i]] = rep(((replicateNumber^2)*((1/ni[i])-(1/sum(ni))))/(bv$dims$ngrps[[2]]-1),ti[i])
}
w3List = list()
for(i in 1:length(ti)){
w3List[[i]] = rep((replicateNumber^2)*((1/sqrt(replicateNumber^2)) - (1/ni[i]))/(bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]),ti[i])
}
w1uList1 = list()
for(i in 1:length(ti)){
w1uList1[[i]] = sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w3uList1 = list()
for(i in 1:length(ti)){
w3uList1[[i]] = ti[i]/sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w1 = do.call("sum", w1List)
w2 = sgConstant
w3 = do.call("sum", w3List)
w1u = sum((1/ti))/sum((1/(ti*(ti/unlist(w1uList1)))))
w2u = ti[1]/sum(1/(ti*(ti/(0.5*(ti)))))
w3u = (bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]) / sum((ti-1)/unlist(w3uList1))
c2u = (w2u-w1u)/(w3u)
c3u = w2u-1-c2u
c2 = w1u/w3u
c3 = 0
alpha = alpha
inf = 999999999
anova = summary(aov(value ~ subject/time, datagender2))
sigma2_analytical = anova[[1]][[2]][3]/anova[[1]][[1]][3]
sigma2_within = (anova[[1]][[2]][2]/anova[[1]][[1]][2]-anova[[1]][[2]][3]/anova[[1]][[1]][3])/w3
sigma2_between = (anova[[1]][[2]][1]/anova[[1]][[1]][1] - sigma2_analytical-w1*sigma2_within)/w2
grandMean = mean(datagender2$value)
seGrandMean = sd(datagender2$value)/sqrt(N)
llMean = grandMean-qnorm(1-alpha/2)*seGrandMean
ulMean = grandMean+qnorm(1-alpha/2)*seGrandMean
sigma_analytical = sqrt(sigma2_analytical)
sigma_within = sqrt(sigma2_within)
sigma_between = sqrt(sigma2_between)
sigma_total = sqrt(sigma2_analytical + sigma2_within + sigma2_between)
CV_analytical = abs(sigma_analytical/grandMean)
CV_within = abs(sigma_within/grandMean)
CV_between = abs(sigma_between/grandMean)
CV_total = abs(sigma_total/grandMean)
ll_analytical = sqrt((sigma_analytical^2)/qf(alpha/2, bv$dims$ngrps[[1]], inf, lower.tail = F))
ul_analytical = sqrt((sigma_analytical^2)/qf(alpha/2, bv$dims$ngrps[[1]], inf, lower.tail = T))
lower_analytical = ll_analytical/grandMean
upper_analytical = ul_analytical/grandMean
sigma2_between = sigma_between^2
sigma2_within = sigma_within^2
sigma2_analytical = sigma_analytical^2
msu_within = 2*sigma2_within+sigma2_analytical
if(CVresult == "cv"){msu_between = 0}else{
msu_between = sigma2_between*sgConstant + sigma2_analytical + sigma2_within*2
}
dfbetween = (bv$dims$ngrps[[2]]-1)
dfwithin = (bv$dims$ngrps[[1]]-bv$dims$ngrps[[2]])
dfanalytical = (bv$dims$ngrps[[1]])
g1 = 1-1/(qf(alpha/2, dfbetween, inf, lower.tail = F))
g2 = 1-1/(qf(alpha/2, dfwithin, inf, lower.tail = F))
g3 = 1-1/(qf(alpha/2, dfanalytical, inf, lower.tail = F))
h1 =1/(qf(1-alpha/2, dfbetween, inf, lower.tail = F))-1
h2 = 1/(qf(1-alpha/2, dfwithin, inf, lower.tail = F))-1
h3 = 1/(qf(1-alpha/2, dfanalytical, inf, lower.tail = F))-1
g12 = (((qf(alpha/2, dfbetween, dfwithin, lower.tail = F)-1)^2)-g1^2*(qf(alpha/2, dfbetween, dfwithin, lower.tail = F)^2)-h2^2)/(qf(alpha/2, dfbetween, dfwithin, lower.tail = F))
g13 = (((qf(alpha/2, dfbetween, dfanalytical, lower.tail = F)-1)^2)-g1^2*(qf(alpha/2, dfbetween, dfanalytical, lower.tail = F)^2)-h3^2)/(qf(alpha/2, dfbetween, dfanalytical, lower.tail = F))
g23 = (((qf(alpha/2, dfwithin, dfanalytical, lower.tail = F)-1)^2)-g2^2*(qf(alpha/2, dfwithin, dfanalytical, lower.tail = F))^2-h3^2)/(qf(alpha/2, dfwithin, dfanalytical, lower.tail = F))
g32 = (((qf(alpha/2, dfanalytical, dfwithin, lower.tail = F)-1)^2)-g3^2*(qf(alpha/2, dfanalytical, dfwithin, lower.tail = F))^2-h2^2)/(qf(alpha/2, dfanalytical, dfwithin, lower.tail = F))
h12 = (((1-qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))^2)-h1^2*(qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))^2-g2^2)/(qf(1-alpha/2, dfbetween, dfwithin, lower.tail = F))
h13 = (((1-qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))^2)-h1^2*(qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))^2-g3^2)/(qf(1-alpha/2, dfbetween, dfanalytical, lower.tail = F))
h23 = (((1-qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))^2)-h2^2*(qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))^2-g3^2)/(qf(1-alpha/2, dfwithin, dfanalytical, lower.tail = F))
h32 = (((1-qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))^2)-h3^2*(qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))^2-g2^2)/(qf(1-alpha/2, dfanalytical, dfwithin, lower.tail = F))
VLba = (g2^2)*(msu_within^2)+(h3^2)*(sigma2_analytical^2)+g23*msu_within*sigma2_analytical
VUba = (h2^2)*(msu_within^2)+(g3^2)*(sigma2_analytical^2)+h23*msu_within*sigma2_analytical
VLa = g1^2*msu_between^2+h2^2*c2^2*msu_within^2+h3^2*c3^2*sigma2_analytical^2+g12*c2*msu_between*msu_within+g13*abs(c3)*msu_between*sigma2_analytical
VLa2 = h1^2*msu_between^2+g2^2*c2^2*msu_within^2+g3^2*c3^2*sigma2_analytical^2+h12*c2*msu_between*msu_within+h13*abs(c3)*msu_between*sigma2_analytical
ll_within = sqrt((msu_within-sigma2_analytical-sqrt(VLba))/2)
ul_within = sqrt((msu_within-sigma2_analytical+sqrt(VUba))/2)
lower_within = ll_within/grandMean
upper_within = ul_within/grandMean
ll_between = sqrt((msu_between - msu_within - sqrt(VLa))/sgConstant)
ul_between = sqrt((msu_between - msu_within + sqrt(VLa2))/sgConstant)
lower_between = ll_between/grandMean
upper_between = ul_between/grandMean
c34 = (sgConstant-2)/2
c35 = sgConstant-1-c34
vlTot = (g1^2)*(msu_between^2)+(g2^2)*(c2u^2)*(msu_within^2)+(g3^2)*(c3u^2)*(sigma2_analytical^2)
vuTot = (h1^2)*(msu_between^2)+(h2^2)*(c2u^2)*(msu_within^2)+(h3^2)*(c3u^2)*(sigma2_analytical^2)
ll_total = sqrt((msu_between + c34*msu_within + c35*sigma2_analytical- sqrt(vlTot))/sgConstant)
ul_total = sqrt((msu_between + c34*msu_within + c35*sigma2_analytical+ sqrt(vuTot))/sgConstant)
lower_total = ll_total/grandMean
upper_total = ul_total/grandMean
CVTable = data.frame(matrix(NA,4,5))
colnames(CVTable) = c("Source", "sigma", "CV%", lower_title, upper_title)
CVTable[1,"Source"] = "Between"
CVTable[2,"Source"] = "Within"
CVTable[3,"Source"] = "Analytical"
CVTable[4,"Source"] = "Total"
CVTable[1, "sigma"] = round(sigma_between,decimal)
CVTable[2, "sigma"] = round(sigma_within,decimal)
CVTable[3, "sigma"] = round(sigma_analytical,decimal)
CVTable[4, "sigma"] = round(sigma_total,decimal)
CVTable[1, lower_title] = round(lower_between*100,decimal)
CVTable[2, lower_title] = round(lower_within*100,decimal)
CVTable[3, lower_title] = round(lower_analytical*100,decimal)
CVTable[4, lower_title] = round(lower_total*100,decimal)
CVTable[1, upper_title] = round(upper_between*100,decimal)
CVTable[2, upper_title] = round(upper_within*100,decimal)
CVTable[3, upper_title] = round(upper_analytical*100,decimal)
CVTable[4, upper_title] = round(upper_total*100,decimal)
CVTable[1, "CV%"] = round(CV_between*100,decimal)
CVTable[2, "CV%"] = round(CV_within*100,decimal)
CVTable[3, "CV%"] = round(CV_analytical*100,decimal)
CVTable[4, "CV%"] = round(CV_total*100,decimal)
CVa = CVTable[3,3] #in percentage
CVi = CVTable[2,3]#in percentage
CVg = CVTable[1,3] #in percentage
z = qnorm(1-alpha/2) #for alpha = 0.05
#z = 2.58 #for alpha = 0.01
### Calculation of Index of Individuality (II) ###
#II indicates the utility of population-based reference values
II = CVi/CVg
### Calculation of Reference Change Value (RCV) ###
#RCV is also called as ‘critical difference (CD)’, and indicates whether the difference between
#two consecutive measurements from the same individual is significant or not.
RCV = formatC(sqrt(2)*z*sqrt((CVa^2)+(CVi^2)), digits = decimal, format = "f")
k = z*sqrt(2)
t1 = w3u-1
t2 = w3u
VLrcv = (g2^2)*(msu_within^2)+(g3^2)*(t1^2)*(sigma2_analytical^2)
VUrcv = (h2^2)*(msu_within^2)+(h3^2)*(t1^2)*(sigma2_analytical^2)
lower_RCV = formatC(((k*(sqrt((msu_within+t1*sigma2_analytical-1*sqrt(VLrcv))/t2)))/grandMean)*100, digits = decimal, format = "f")
upper_RCV = formatC(((k*(sqrt((msu_within+t1*sigma2_analytical+1*sqrt(VUrcv))/t2)))/grandMean)*100, digits = decimal, format = "f")
rcvResult = cbind.data.frame(RCV, lower_RCV, upper_RCV)
colnames(rcvResult) = c("RCV (%)", "Lower limit (%)", "Upper limit (%)")
CVresults = data.frame(matrix(NA,1,9))
colnames(CVresults) = c("Group", "Mean", lowerMean_title, upperMean_title, "CV_A%", "CV_I%", "CV_G%", "II", "n")
CVresults[1,1] = gender2
CVresults[1,2] = round(grandMean,decimal)
CVresults[1,3] = round(llMean,decimal)
CVresults[1,4] = round(ulMean,decimal)
CVresults[1,5] = round(CVa,decimal)
CVresults[1,6] = round(CVi,decimal)
CVresults[1,7] = round(CVg,decimal)
CVresults[1,8] = round(II,decimal)
# CVresults[1,9] = NA
CVresults[1,9] = nrow(datagender2)
errorTable = matrix(NA,3,3)
rownames(errorTable) = c("Optimal","Desirable","Minimal")
colnames(errorTable) = c("Imprecision,%", "Bias,%","TEa,%")
errorTable[1,1] = paste("<",round(0.25*CVi,decimal))
errorTable[2,1] = paste("<",round(0.50*CVi,decimal))
errorTable[3,1] = paste("<",round(0.75*CVi,decimal))
errorTable[1,2] = paste("<",round(0.125*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[2,2] = paste("<",round(0.250*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[3,2] = paste("<",round(0.375*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[1,3] = paste("<",round(1.65*(0.25*CVi)+0.125*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[2,3] = paste("<",round(1.65*(0.50*CVi)+0.250*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable[3,3] = paste("<",round(1.65*(0.75*CVi)+0.375*sqrt((CVi^2)*(CVg^2)),decimal))
errorTable = cbind.data.frame("Quality Levels" = row.names(errorTable), errorTable)
resultsCvAnovaGender2 = list(CVTable = CVTable, CVresults = CVresults, errorTable = errorTable, rcvResult = rcvResult)
}else{
resultsAllCvAnova = NULL
resultsCvAnovaGender1 = NULL
resultsCvAnovaGender2 = NULL
}
######################### Original ###################################
if(CVresult != "transformBack" && CVresult != "cv"){
data[,"subject"] = as.factor(data[,"subject"])
data[,"replicate"] = as.factor(data[,"replicate"])
data[,"time"] = as.factor(data[,"time"])
dataGender = split(data, data[,"gender"])
## lme model
bv <- lme(value ~1, random=~1|subject/time, data=data, method = "REML")
N <- nrow(data)
r <- length(unique(data[,"subject"]))
ni <- as.numeric(table(data[ ,"subject"]))
sgConstant <- (1/(r - 1))*sum((ni^2)*(1/ni - 1/N))
ti = ni/2
replicateNumber = 2
w1List = list()
for(i in 1:length(ti)){
w1List[[i]] = rep(((replicateNumber^2)*((1/ni[i])-(1/sum(ni))))/(bv$dims$ngrps[[2]]-1),ti[i])
}
w3List = list()
for(i in 1:length(ti)){
w3List[[i]] = rep((replicateNumber^2)*((1/sqrt(replicateNumber^2)) - (1/ni[i]))/(bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]),ti[i])
}
w1uList1 = list()
for(i in 1:length(ti)){
w1uList1[[i]] = sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
w3uList1 = list()
for(i in 1:length(ti)){
w3uList1[[i]] = ti[i]/sum(rep(1/sqrt(replicateNumber^2), ti[i]))
}
# CI
w1 = do.call("sum", w1List)
w2 = sgConstant
w3 = do.call("sum", w3List)
w1u = sum((1/ti))/sum((1/(ti*(ti/unlist(w1uList1)))))
w2u = ti[1]/sum(1/(ti*(ti/(0.5*(ti)))))
w3u = (bv$dims$ngrps[["time"]]-bv$dims$ngrps[["subject"]]) / sum((ti-1)/unlist(w3uList1))
c2u = (w2u-w1u)/(w3u)
c3u = w2u-1-c2u
c2 = w1u/w3u
c3 = 0
alpha = alpha
inf = 999999999
# bv <- lmer(data=data, REML = TRUE, value ~ 1 + (1|subject) + (1|subject:time))
# bv <- lmer(data=data, REML = TRUE, value ~ 1 + (1|subject) + (1|subject:time))
summary = summary(bv)
grandMean = summary$coefficients$fixed[[1]]
seGrandMean = sqrt(summary$varFix)[[1]]/sqrt(N)
llMean = grandMean-1.96*seGrandMean
ulMean = grandMean+1.96*seGrandMean
table= nlme::VarCorr(bv)
sigma_between = as.numeric(table[2,2])
sigma_within = as.numeric(table[4,2])
sigma_analytical = as.numeric(table[5,2])
# sigma_total = sqrt(sigma2_analytical + sigma2_within + sigma2_between)
sigma2_between = sigma_between^2
sigma2_within = sigma_within^2
sigma2_analytical = sigma_analytical^2
llMean = grandMean-qnorm(1-alpha/2)*seGrandMean
ulMean = grandMean+qnorm(1-alpha/2)*seGrandMean
sigma_analytical = sqrt(sigma2_analytical)
sigma_within = sqrt(sigma2_within)
sigma_between = sqrt(sigma2_between)