-Effi.Rhistory

category = c("nha", "nhanesyrsfu", "nhanesother"),  # replaced nhanesna with nha in the category
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank"
)
v=draw.triple.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
category = c("Missing BP", "No follow-up", "Other Ethnicity"),
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank"
)
v=draw.triple.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
category = c("Missing BP", "No follow-up", "Other Ethnicity"),
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank"
)
v=draw.triple.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
category = c("Missing BP", "No follow-up", "Other Ethnicity"),
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank",
cat.pos = c(-40, 0,180)
)
v=draw.triple.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
category = c("Missing BP", "No follow-up", "Other Ethnicity"),
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank",
cat.pos = c(-40, 0,180)
)
grid.draw(v)
draw.triple.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
category = c("Missing BP", "No follow-up", "Other Ethnicity"),
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank",
cat.pos = c(-40, 0,180)
)
v <- draw.triple.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
category = c("Missing BP", "No follow-up", "Other Ethnicity"),
fill = c("skyblue", "pink1", "mediumorchid"),
lty = "blank",
cat.pos = c(-40, 0,180),
cex = 2
)
bprange <- nhanessysrange | nhanesdiasrange
v <- draw.quad.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
area4 = sum(bprange), # BP out of range
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n14 = sum(!nhanesna & bprange),
n24 = sum(nhanes$yrsfu==0 & bprange),
n34 = sum(nhanes$other==1 & bprange),
n124 = sum(!nhanesna & nhanes$yrsfu==0 & bprange),
n134 = sum(!nhanesna & nhanes$other==1 & bprange),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
n234=sum(nhanes$yrsfu==0 & nhanes$other==1 & bprange),
n1234=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1 & bprange),
category = c("Missing BP", "No follow-up", "Other Ethnicity","BP out of range"),
fill = c("skyblue", "pink1", "mediumorchid", "orange"),
lty = "blank",
cat.pos = c(180, 0,180,0),
cex = 1
)
sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1 & bprange)
sum(nhanes$yrsfu==0 & nhanes$other==1 & bprange)
sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1)
sum(!nhanesna & nhanes$other==1 & bprange)
sum(bprange)
bprange <- nhanessysrange | nhanesdiasrange
bprange[is.na(bprange)] <- FALSE
v <- draw.quad.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
area4 = sum(bprange), # BP out of range
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n14 = sum(!nhanesna & bprange),
n24 = sum(nhanes$yrsfu==0 & bprange),
n34 = sum(nhanes$other==1 & bprange),
n124 = sum(!nhanesna & nhanes$yrsfu==0 & bprange),
n134 = sum(!nhanesna & nhanes$other==1 & bprange),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
n234=sum(nhanes$yrsfu==0 & nhanes$other==1 & bprange),
n1234=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1 & bprange),
category = c("Missing BP", "No follow-up", "Other Ethnicity","BP out of range"),
fill = c("skyblue", "pink1", "mediumorchid", "orange"),
lty = "blank",
cat.pos = c(180, 0,180,0),
cex = 1
)
v <- draw.quad.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
area4 = sum(bprange), # BP out of range
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n14 = sum(!nhanesna & bprange),
n24 = sum(nhanes$yrsfu==0 & bprange),
n34 = sum(nhanes$other==1 & bprange),
n124 = sum(!nhanesna & nhanes$yrsfu==0 & bprange),
n134 = sum(!nhanesna & nhanes$other==1 & bprange),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
n234=sum(nhanes$yrsfu==0 & nhanes$other==1 & bprange),
n1234=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1 & bprange),
category = c("Missing BP", "No follow-up", "Other Ethnicity","BP out of range"),
fill = c("skyblue", "pink1", "mediumorchid", "orange"),
lty = "blank",
cat.pos = c(180, 0,180,0),
cex = 1
)
v <- draw.quad.venn(
area1=sum(!nhanesna), # Missing BP
area2=sum(nhanes$yrsfu==0), # No follow-up
area3=sum(nhanes$other==1), # Other ethnicity
area4 = sum(bprange), # BP out of range
n12=sum(!nhanesna & nhanes$yrsfu==0),
n23=sum(nhanes$yrsfu==0 & nhanes$other==1),
n13=sum(!nhanesna & nhanes$other==1),
n14 = sum(!nhanesna & bprange),
n24 = sum(nhanes$yrsfu==0 & bprange),
n34 = sum(nhanes$other==1 & bprange),
n124 = sum(!nhanesna & nhanes$yrsfu==0 & bprange),
n134 = sum(!nhanesna & nhanes$other==1 & bprange),
n123=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1),
n234=sum(nhanes$yrsfu==0 & nhanes$other==1 & bprange),
n1234=sum(!nhanesna & nhanes$yrsfu==0 & nhanes$other==1 & bprange),
category = c("Missing BP", "No follow-up", "Other Ethnicity","BP out of range"),
fill = c("skyblue", "pink1", "mediumorchid", "orange"),
lty = "blank",
cat.pos = c(220, 0,0,0),
cex = 1
)
knitr::opts_chunk$set(echo = TRUE)
options(tinytex.verbose = TRUE)
library(tidyverse)
library(formatR)
library(magrittr)
library(knitr)
library(tinytex)
library(kableExtra)
library(VennDiagram)
# Load data
nhanes_old=read.csv('Data_raw/nh3bpdat290716.csv')
# Update mortality with 2017 public release
nhanes_update=read.csv('Data_raw/NHANES_ML_update.csv',colClasses = 'integer') %>%
mutate(yrsfuExam = round(permth_exm/12,2), yrsfuHome = round(permth_int/12, 2)) %>%
filter(eligstat == 1)
nhanes_old %<>% mutate(yrsfuExam = round(yrsfuExam, 2), yrsfuHome = round(yrsfuHome,2), permth_exm = round(yrsfuExam *12), permth_int = round(yrsfuHome*12))
# Compare old and new mortality
old_dead <- sort(nhanes_old$SEQN[nhanes_old$dead==1])
new_dead <- sort(nhanes_update$seqn[nhanes_update$mortstat==1])
conflict_dead <- old_dead[ !(old_dead %in% new_dead)] # Tested: No resurrections
missing_update <- nhanes_old$SEQN[!(nhanes_old$SEQN %in% nhanes_update$seqn)] #Tested: No one from old data set missing from followup
missing_old <- !(nhanes_update$seqn %in% nhanes_old$SEQN) # 6 subjects in the updated data set with mortality data (all alive) who were not in the old data set.
nhanes_update %<>% filter(!missing_old) # remove them
identical(nhanes_old$SEQN,nhanes_update$seqn) # Sequence of ids now identical
fu_diff <- nhanes_update$permth_int - nhanes_update$permth_exm
fu_diff_update <- nhanes_update$permth_int - nhanes_old$permth_int
identical(nhanes_old$UCOD_LEADING[!is.na(nhanes_old$UCOD_LEADING)], nhanes_update$ucod_leading[!is.na(nhanes_old$UCOD_LEADING)])
#TRUE, so cause-of-death codes for all individuals who were dead in the first data set are identical
conflict_old <- subset(nhanes_old, nhanes_old$SEQN %in% conflict_dead)
conflict_new <- subset(nhanes_update, nhanes_update$seqn %in% conflict_dead)
nhanes <- nhanes_old
nhanes$UCOD_LEADING <- nhanes_update$ucod_leading
nhanes$yrsfuExam <- nhanes_update$yrsfuExam
nhanes$yrsfuHome <- nhanes_update$yrsfuHome
nhanes$dead <- nhanes_update$mortstat
nhanes$mrtHrt <- as.integer(nhanes$UCOD_LEADING==1)  # 1 codes for Heart
nhanes$mrtNeo <- as.integer(nhanes$UCOD_LEADING==2)  # 2 codes for Neoplasm
nhanes$mrtInj <- as.integer(nhanes$UCOD_LEADING==4)  # 4 codes for Injury
nhanes$mrtOtherCVD <- as.integer(nhanes$UCOD_LEADING==5)  # 5 codes for other CVD
# Change NAs to 0
nhanes$mrtHrt[is.na(nhanes$mrtHrt)] <- 0
nhanes$mrtNeo[is.na(nhanes$mrtNeo)] <- 0
nhanes$mrtInj[is.na(nhanes$mrtInj)] <- 0
nhanes$mrtOtherCVD[is.na(nhanes$mrtOtherCVD)] <- 0
nhanes$eventhrt <- with(nhanes, mrtOtherCVD+mrtHrt)
nhanes$eventother <- with(nhanes, dead-eventhrt)
nhanes$yrsfu=pmin(nhanes_update$yrsfuHome,nhanes$yrsfuExam, na.rm = TRUE)
# Note: The most recent examination (home or clinic) is a left truncation time,
#   so follow-up is the minimum. For some the clinic is missing.
#   We call the follow-up the home follow-up time, but it doesn't matter,
#   since those individuals will be excluded from analysis.
whichsys=match(c('systolicA','systolicB','systolicC'),names(nhanes))
whichdias=match(c('diastolicA','diastolicB','diastolicC'),names(nhanes))
whichsyshome=match(c('systolicAhome','systolicBhome','systolicChome'),names(nhanes))
whichdiashome=match(c('diastolicAhome','diastolicBhome','diastolicChome'),names(nhanes))
whichBP=c(whichsys,whichdias)
whichBPhome=c(whichsyshome,whichdiashome)
allBP=c(whichBP,whichBPhome)
allsys=c(whichsys,whichsyshome)
alldias=c(whichdias,whichdiashome)
### Means and variances
sys=nhanes[,whichsys]
dias=nhanes[,whichdias]
sysH=nhanes[,whichsyshome]
diasH=nhanes[,whichdiashome]
nhanes$meandias=apply(dias,1,mean)
nhanes$meansys=apply(sys,1,mean)
nhanes$sysDel=apply(sysH,1,mean)-apply(sys,1,mean)
nhanes$diasDel=apply(diasH,1,mean)-apply(dias,1,mean)
nhanes$vardias=apply(dias,1,var)
nhanes$varsys=apply(sys,1,var)
nhanes$sddias=sqrt(nhanes$vardias)
nhanes$sdsys=sqrt(nhanes$varsys)
nhanes$precdias=1/(nhanes$vardias+1/3)
nhanes$precsys=1/(nhanes$varsys+1/3)
race <- with(nhanes, ifelse(white==1, 2, ifelse(black==1, 1,ifelse(mexican==1,3, 0))))
nhanes$race <- as.factor(race)
type=factor(1+race+3*(1-nhanes$female)*(race>0)+6*(race==0)) # other race all type 7
levels(type)=c('female, black','female, white','female, Mex','male, black','male, white','male, Mex','other')
nhanes$type=type
nhanesna=!(is.na(apply(nhanes[,allBP],1,prod)))
diaslow <- apply(nhanes[,alldias],1,min)<40
diashigh <- apply(nhanes[,alldias],1,max)>140
syslow <- apply(nhanes[,allsys],1,min)<60
syshigh <- apply(nhanes[,allsys],1,max)>250
nhanessysrange=(syslow | syshigh)
nhanesdiasrange=(diaslow | diashigh)
dias0 <- apply(nhanes[,alldias],1,min) == 0
sys0 <- apply(nhanes[,allsys],1,min) == 0
nhanesgood=(nhanesna&(nhanes$yrsfu>0)&nhanes$other==0)
n_original <- dim(nhanes)[1]
n_no_other <- sum(nhanes$other==0)
n_followup <- sum(nhanes$yrsfu>0 & nhanesna & nhanes$other==0)
n_no_followup <- sum(nhanes$yrsfu==0 & nhanesna & nhanes$other==0)
frs=read.csv('Data_raw/FRS.csv')
whichfrs <- '1998' # 'ATP' or '1998'
#Choose versions of FRS
if(whichfrs=='ATP'){nhanes$FRS=frs$ATP.FRS[match(nhanes$SEQN,frs$SEQN)]} else{nhanes$FRS=frs$X1998.FRS[match(nhanes$SEQN,frs$SEQN)]}
#################################################
#
#			Add in observer data
#
#################################################
exm=read.csv('Data_raw/Examiners.csv')
nhanes$Exam=exm$PEPTECH[match(nhanes$SEQN,exm$SEQN)]
nhanes$Exam[nhanes$Exam>4000]=0  ## Combine the 88888 examiner with 0
nhanes$Exam[is.na(nhanes$Exam)]=0
#nhanesA=subset(nhanesA,Exam>0)
examname=sort(unique(nhanes$Exam))
examlist=lapply(examname,function(en) subset(nhanes,Exam==en)$nunq.dias)
examlists=lapply(examname,function(en) subset(nhanes,Exam==en)$nunq.sys)
nhanesA=nhanes[nhanesgood & !nhanessysrange&!nhanesdiasrange, ]
nhanesA$type=factor(nhanesA$type,exclude=7)
N=dim(nhanesA)[1]
k=3
BP_type_names <- c('Systolic','Diastolic')
BP_place_names <- c('Home','Clinic')
whichsys=match(c('systolicA','systolicB','systolicC'),names(nhanesA))
whichdias=match(c('diastolicA','diastolicB','diastolicC'),names(nhanesA))
whichsyshome=match(c('systolicAhome','systolicBhome','systolicChome'),names(nhanesA))
whichdiashome=match(c('diastolicAhome','diastolicBhome','diastolicChome'),names(nhanesA))
whichBP=c(whichsys,whichdias)
whichBPhome=c(whichsyshome,whichdiashome)
# Make BP measures into array
sys=data.matrix(nhanesA[,whichsys])
dias=data.matrix(nhanesA[,whichdias])
sysH=data.matrix(nhanesA[,whichsyshome])
diasH=data.matrix(nhanesA[,whichdiashome])
allBP <- list(Systolic = list(Home = sysH, Clinic = sys), Diastolic = list(Home = diasH, Clinic = dias))
L=length(sys)
gamma_dimnames <- list( c('alpha','theta','beta') , c('Clinic' , 'Home'))
norm_dimnames <- c('m_M','m_Delta', 'sigma2_M', 'sigma2_Delta')
demog.data <- data.frame(Ethnicity = droplevels(nhanesA$race) %>% fct_recode(Black = '1',White = '2',Mexican = '3'),
Sex = factor(nhanesA$female) %>% fct_recode(Male = '0', Female = '1') )
# Make a table of means for systolic home BP by ethnicity and sex
bp_table <- list()
bp.data <- data.frame()
which_diff <- function(x) { # for a vector with 3 entries, with two the same, return the one that is different
if (x[1] == x[2]) {return(3)} else {
if (x[1] == x[3]) {return(2)} else {return(1)}
}
}
for (BPtype in BP_type_names){
for (BPplace in BP_place_names){
bp.data %<>% rbind(cbind(demog.data, BPtype = factor(BPtype, levels = BP_type_names) , BPplace = factor(BPplace), Mean = apply(allBP[[BPtype]][[BPplace]],1,mean), SD = apply(allBP[[BPtype]][[BPplace]],1,sd),
Number = apply(allBP[[BPtype]][[BPplace]],1,function(x) length(unique(x))),
Which_Diff = apply(allBP[[BPtype]][[BPplace]],1,which_diff)))
}
}
mean_sd_summary <- mean_sd_summary <- bp.data %>%
group_by(BPplace,BPtype, Sex, Ethnicity) %>%
summarise(
Mean_of_Mean = mean(Mean, na.rm = TRUE),
Mean_of_SD = mean(SD, na.rm = TRUE)
)
bp.data.cor <- bp.data %>%
group_by(BPtype, BPplace) %>%
summarize(correlation = cor(Mean, SD, use = "complete.obs"))
# Make a table of last digit fractions for bp by type and place
bp_last_digit <- matrix(0,nrow=0,ncol=5)
for (BPtype in BP_type_names){
for (BPplace in BP_place_names){
digit_table <- unname(table(allBP[[BPtype]][[BPplace]]%%10))
digits=digit_table/sum(digit_table)
bp_last_digit %<>% rbind(digits)
}
}
bp_last_digit %<>% as_tibble
names(bp_last_digit) <- 2*(0:4)
bp_last_digit$Place <- rep(BP_place_names,each=2)
bp_last_digit$Type <- rep(BP_type_names,2)
bp_last_digit %<>% select(Place,Type,everything())
# Calculate expected number of all with same last digit given 3 observations of sd = S
prob_repeated3 <- function(S, intervalwidth=2){
# Assume overall mean is uniform
# so average over the interval [0,10]
# then probability of same is sum_j (Phi(10j+intervalwidth-x)-Phi(10j-x))^3
sum(sapply(seq(-1,1),function(j)
.1*integrate(function(x) #(1-x/intervalwidth)*dnorm(x,sd=S)*(pnorm(x,sd=S)-.5),0,intervalwidth)$value
(pnorm(10*j+intervalwidth-x,sd=S)-pnorm(10*j-x,sd=S))^3,-5,5)$value) )
}
# Calculate expected number of all with same last digit given 3 observations of sd = S
prob_repeated3 <- function(S, intervalwidth=2){
# Assume overall mean is uniform
# so average over the interval [0,10]
# then probability of same is sum_j (Phi(10j+intervalwidth-x)-Phi(10j-x))^3
sum(sapply(seq(-1,1),function(j)
.1*integrate(function(x) #(1-x/intervalwidth)*dnorm(x,sd=S)*(pnorm(x,sd=S)-.5),0,intervalwidth)$value
(pnorm(10*j+intervalwidth-x,sd=S)-pnorm(10*j-x,sd=S))^3,-5,5)$value) )
}
prob_repeated2 <- function(S, intervalwidth=2){
# Assume overall mean is uniform
# so average over the interval [0,10]
# then probability of same is sum_j 3*(Phi(10j+intervalwidth-x)-Phi(10j-x))^2 - 2*prob_repeated3
sum(sapply(seq(-1,1),function(j)
.1*integrate(function(x) #(1-x/intervalwidth)*dnorm(x,sd=S)*(pnorm(x,sd=S)-.5),0,intervalwidth)$value
3*(pnorm(10*j+intervalwidth-x,sd=S)-pnorm(10*j-x,sd=S))^2,-5,5)$value) ) + 2*prob_repeated3(S,intervalwidth)
}
sd_summary <- bp.data %>%
group_by(BPplace,BPtype) %>%
summarise(
Mean_of_SD = mean(SD, na.rm = TRUE),
# fraction with all three measurements equal
Fraction3 = mean(Number==1, na.rm = TRUE),
Fraction2 = mean(Number==2, na.rm = TRUE)
)
# Calculate probability of three measurements being equal given unequal interval lengths
prob_repeated3_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated(S,intervalwidth)))
}
prob_repeated2_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated2(S,intervalwidth)))
}
sd_summary$Prob_repeated3 <- sapply(sd_summary$Mean_of_SD,prob_repeated)
# Calculate expected number of all with same last digit given 3 observations of sd = S
prob_repeated3 <- function(S, intervalwidth=2){
# Assume overall mean is uniform
# so average over the interval [0,10]
# then probability of same is sum_j (Phi(10j+intervalwidth-x)-Phi(10j-x))^3
sum(sapply(seq(-1,1),function(j)
.1*integrate(function(x) #(1-x/intervalwidth)*dnorm(x,sd=S)*(pnorm(x,sd=S)-.5),0,intervalwidth)$value
(pnorm(10*j+intervalwidth-x,sd=S)-pnorm(10*j-x,sd=S))^3,-5,5)$value) )
}
prob_repeated2 <- function(S, intervalwidth=2){
# Assume overall mean is uniform
# so average over the interval [0,10]
# then probability of same is sum_j 3*(Phi(10j+intervalwidth-x)-Phi(10j-x))^2 - 2*prob_repeated3
sum(sapply(seq(-1,1),function(j)
.1*integrate(function(x) #(1-x/intervalwidth)*dnorm(x,sd=S)*(pnorm(x,sd=S)-.5),0,intervalwidth)$value
3*(pnorm(10*j+intervalwidth-x,sd=S)-pnorm(10*j-x,sd=S))^2,-5,5)$value) ) + 2*prob_repeated3(S,intervalwidth)
}
sd_summary <- bp.data %>%
group_by(BPplace,BPtype) %>%
summarise(
Mean_of_SD = mean(SD, na.rm = TRUE),
# fraction with all three measurements equal
Fraction3 = mean(Number==1, na.rm = TRUE),
Fraction2 = mean(Number==2, na.rm = TRUE)
)
# Calculate probability of three measurements being equal given unequal interval lengths
prob_repeated3_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated(S,intervalwidth)))
}
prob_repeated2_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated2(S,intervalwidth)))
}
sd_summary$Prob_repeated3 <- sapply(sd_summary$Mean_of_SD,prob_repeated3)
sd_summary$Prob_repeated2 <- sapply(sd_summary$Mean_of_SD,prob_repeated2)
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Fraction repeated", "Prob repeated"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Fraction all repeated", "Prob all repeated", "Fraction 2 repeated", "Prob 2 repeated"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
head(bp.data)
head(bp.data,15)
mean(bp.data$Number==2)
sd_summary
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Frac all rep", "Frac 2 rep", "Prob all rep",  "Prob 2 rep"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
prob_repeated3(2.8,2)*5
sd_summary$Prob_repeated3 <- sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j],unlist(bp_last_digit[j,3:7])]))
sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j],unlist(bp_last_digit[j,3:7])))
# Calculate probability of three measurements being equal given unequal interval lengths
prob_repeated3_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated3(S,intervalwidth)))
}
prob_repeated2_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated2(S,intervalwidth)))
}
sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j],unlist(bp_last_digit[j,3:7])))
j=1
sd_summary$Mean_of_SD[j]
unlist(bp_last_digit[j,3:7])
sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j],10*unlist(bp_last_digit[j,3:7])))
sapply(1:4, function(j) prob_repeated2_intervals(sd_summary$Mean_of_SD[j],10*unlist(bp_last_digit[j,3:7])))
sd_summary$Prob_repeated3 <- sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j],10*unlist(bp_last_digit[j,3:7])))
sd_summary$Prob_repeated2 <- sapply(1:4, function(j) prob_repeated2_intervals(sd_summary$Mean_of_SD[j],10*unlist(bp_last_digit[j,3:7])))
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Frac all rep", "Frac 2 rep", "Prob all rep",  "Prob 2 rep"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
prob_repeated2 <- function(S, intervalwidth=2){
# Assume overall mean is uniform
# so average over the interval [0,10]
# then probability of same is sum_j 3*(Phi(10j+intervalwidth-x)-Phi(10j-x))^2 - 2*prob_repeated3
sum(sapply(seq(-1,1),function(j)
.1*integrate(function(x)
3*(pnorm(10*j+intervalwidth-x,sd=S)-pnorm(10*j-x,sd=S))^2,-5,5)$value) ) - 2*prob_repeated3(S,intervalwidth)
}
sd_summary <- bp.data %>%
group_by(BPplace,BPtype) %>%
summarise(
Mean_of_SD = mean(SD, na.rm = TRUE),
# fraction with all three measurements equal
Fraction3 = mean(Number==1, na.rm = TRUE),
Fraction2 = mean(Number==2, na.rm = TRUE)
)
# Calculate probability of three measurements being equal given unequal interval lengths
prob_repeated3_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated3(S,intervalwidth)))
}
prob_repeated2_intervals <- function(S,intervals){
sum(sapply(intervals, function(intervalwidth) prob_repeated2(S,intervalwidth)))
}
sd_summary$Prob_repeated3 <- sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j],10*unlist(bp_last_digit[j,3:7])))
sd_summary$Prob_repeated2 <- sapply(1:4, function(j) prob_repeated2_intervals(sd_summary$Mean_of_SD[j],10*unlist(bp_last_digit[j,3:7])))
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Frac all rep", "Frac 2 rep", "Prob all rep",  "Prob 2 rep"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
sd_summary$Prob_repeated3 <- sapply(1:4, function(j) prob_repeated3_intervals(sd_summary$Mean_of_SD[j]+1/3,10*unlist(bp_last_digit[j,3:7])))
sd_summary$Prob_repeated2 <- sapply(1:4, function(j) prob_repeated2_intervals(sd_summary$Mean_of_SD[j]+1/3,10*unlist(bp_last_digit[j,3:7])))
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Frac all rep", "Frac 2 rep", "Prob all rep",  "Prob 2 rep"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
sd_summary$Prob_repeated3 <- sapply(1:4, function(j) prob_repeated3_intervals(sqrt(sd_summary$Mean_of_SD[j]^ 2+1/3),10*unlist(bp_last_digit[j,3:7])))
sd_summary$Prob_repeated2 <- sapply(1:4, function(j) prob_repeated2_intervals(sqrt(sd_summary$Mean_of_SD[j]^2+1/3),10*unlist(bp_last_digit[j,3:7])))
#Print table of sd_summary
cat(kable(sd_summary,format="latex", escape = F,booktabs = T, digits=3,
linesep = rep(c(rep("",5),"\\addlinespace"),4),
col.names=c("Place","Sys/Dias","Mean of SD","Frac all rep", "Frac 2 rep", "Prob all rep",  "Prob 2 rep"),caption = 'Summary data for repeated measures') %>%  kable_styling(latex_options = "hold_position") )
sqrt(2.739^2+1/3)
5*prob_repeated2(2.8)
5*prob_repeated3(2.8)
sqrt(3.775^2+1/3)
5*prob_repeated3(3.82)
sqrt(3.082^2+1/3)
5*prob_repeated3(3.136)