Package 'clikcorr'

Censoring data and LIKelihood-based CORRelation estimation and inference

Description

A profile likelihood based method of estimation and hypothesis testing on the correlation coefficient of bivariate data with different types of cencoring.

Usage

clikcorr(data, lower1, upper1, lower2, upper2, cp = 0.95, dist = "n", 
 df = 4, sv = NA, nlm = FALSE, ...)
## Default S3 method:
clikcorr(data, lower1, upper1, lower2, upper2, cp = 0.95, dist = "n", 
 df = 4, sv = NA, nlm = FALSE, ...)
## S3 method for class 'clikcorr'
print(x, ...)
## S3 method for class 'clikcorr'
summary(object, ...)

Arguments

data	a data frame name.
lower1	the lower bound of the first of the two variables whose correlation coefficient to be calculated.
upper1	the upper bound of the first of the two variables whose correlation coefficient to be calculated.
lower2	the lower bound of the second of the two variables whose correlation coefficient to be calculated.
upper2	the upper bound of the second of the two variables whose correlation coefficient to be calculated.
cp	confidence level for the confidence interval.
dist	working distribution. By default, dist="n" assuming the data from a bivariate normal distribution. Set dist="t" if the data are assumed generated from a bivariate t-distribution.
df	degree of freedom of the bivariate t-distribution when dist="t". By default df=4.
sv	user specified starting values for the vector of (mean1, mean2, var1, corr, var2).
nlm	use nlm as the optimization method to minimize the negative log (profile) likelihood. By default nlm=FALSE and optim is used to maximize the log (profile) likelihood.
x	an object of class "clikcorr", i.e., a fitted model.
object	an object of class "clikcorr", i.e., a fitted model.
...	not used.

Details

clikcorr conducts point estimation and hypothesis testing on the correlation coefficient of bivariate data with different types of cencoring.

Value

A list with components:

pairName	variable names for the input paired data structure in the clikcorr class.
pairData	a paired data structure in the clikcorr class.
dist	Normal or t distribution.
df	degree of freedom for t distribution.
coefficients	maximum likelihood estimate (MLE) of the correlation coefficient.
Cov	estimated variance covariance matrix.
Mean	estimated means.
CI	unsymmetric profile confidence interval for the estimated correlation coefficient.
P0	p-value for likelihood ratio test with null hypothesis says that the true correlation coefficient equals zero.
logLik	the value of the log likelihood at MLE.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)
logND1 <- logND[51:90,]

obj <- clikcorr(logND1, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678")

## Not run: 
clikcorr(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678")

clikcorr(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678",
 nlm=TRUE)

clikcorr(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678",
 method="BFGS")

clikcorr(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678",
 sv=c(5,-0.5,0.6,0.5,0.6))

clikcorr(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678",
 dist="t", df=10, nlm=TRUE)

## End(Not run)

print(obj)
summary(obj)

---

censoring data and likelihood-based correlation estimation

Description

Provides point estimation and confidence interval for the correlation coefficient.

Usage

est(data, lower1, upper1, lower2, upper2, cp = 0.95, dist = "n", df = 4, sv = NA, 
nlm = FALSE, ...)

Arguments

data	data frame name.
lower1	the lower bound of the first of the two variables whose correlation coefficient to be calculated.
upper1	the upper bound of the first of the two variables whose correlation coefficient to be calculated.
lower2	the lower bound of the second of the two variables whose correlation coefficient to be calculated.
upper2	the upper bound of the second of the two variables whose correlation coefficient to be calculated.
cp	confidence level for the confidence interval.
dist	working distribution. By default, dist="n" assuming the data from a bivariate normal distribution. Set dist="t" if the data are assumed generated from a bivariate t-distribution.
df	degree of freedom of the bivariate t-distribution when dist="t". By default df=4.
sv	user specified starting values for the vector of (mean1, mean2, var1, corr, var2).
nlm	use nlm as the optimization method to minimize the negative log (profile) likelihood. By default nlm=FALSE and optim is used to maximize the log (profile) likelihood.
...	not used.

Value

Cor	maximum likelihood estimate (MLE) of the correlation coefficient.
Cov	estimated variance covariance matrix.
Mean	estimated means.
LCL	lower bound of the profile confidence interval.
UCL	upper bound of the profile confidence interval.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)
logND1 <- logND[51:90,]

est(logND1, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678")

## Not run: 
est(logND, "t1_TCDD", "t2_TCDD", "t1_PeCDD", "t2_PeCDD")

est(logND, "t1_TCDD", "t2_TCDD", "t1_PeCDD", "t2_PeCDD", dist="t",
 nlm=TRUE)

## End(Not run)

---

censoring data and likelihood-based correlation estimation inference

Description

Provides likelihood ratio tests for making statistical inference about the correlation coefficient from bivariate censored/missing data.

Usage

lrt(data, lower1, upper1, lower2, upper2, dist = "n", df = 4, 
 sv = NA, r0 = 0, nlm = FALSE, ...)

Arguments

data	a data frame name.
lower1	the lower bound of the first of the two variables whose correlation coefficient to be calculated.
upper1	the upper bound of the first of the two variables whose correlation coefficient to be calculated.
lower2	the lower bound of the second of the two variables whose correlation coefficient to be calculated.
upper2	the upper bound of the second of the two variables whose correlation coefficient to be calculated.
dist	working distribution. By default, dist="n" assuming the data from a bivariate normal distribution. Set dist="t" if the data are assumed generated from a bivariate t-distribution.
df	degree of freedom of the bivariate t-distribution when dist="t". By default df=4.
sv	user specified starting values for the vector of (mean1, mean2, var1, corr, var2).
r0	correlation coefficient value under the null hypothesis. By default is 0.
nlm	use nlm as the optimization method to minimize the negative log (profile) likelihood. By default nlm=FALSE and optim is used to maximize the log (profile) likelihood.
...	not used.

Value

Cor	maximum likelihood estimate (MLE) of the correlation coefficient.
m1llk	value of the log likelihood function evaluated at the MLE.
m0llk	value of the log likelihood function evaluated at the r0.
P0	p-value for likelihood ratio test with null hypothesis says that the true correlation coefficient equals r0.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)

lrt(logND, "t1_TCDD", "t2_TCDD", "t1_PeCDD", "t2_PeCDD")

## Not run: 
lrt(logND, "t1_TCDD", "t2_TCDD", "t1_PeCDD", "t2_PeCDD", dist="t")

## End(Not run)

---

an NEHANSE data example

Description

ND is an example data set extracted from National Health and Nutrition Examination Survey (NHANSE). The data set contains 100 samples and IDs and upper and lower bounds for 22 chemical compounds, including 7 dioxins, 9 furans, and 6 PCBs.

Usage

data(ND)

Format

A data frame with 1643 observations and 45 variables. Variables contain SEQN: ID; t1_TCDD: lower bound for dioxin TCDD; t2_TCDD: upper bound for dioxin TCDD; ... t1_PCB_189: lower bound for PCB_189 and t2_PCB_189: upper bound for PCB_189.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)

---

Graphical function for visualizing bivariate profile likelihood.

Description

Produces a plot of the profile log likelihood function.

Usage

## S3 method for class 'clikcorr'
plot(x, type = "l", lwd = 2, col = "red", ...)

Arguments

x	a "clikcorr" object.
type	line type.
lwd	line weight.
col	line color.
...	not used.

Details

produces a plot of the profile log likelihood function.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)
logND1 <- logND[51:90,]

obj <- clikcorr(logND1, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678")
plot(obj, type="o")

## Not run: 
obj <- clikcorr(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678", "t2_HxCDF_234678")
plot(obj, type="o", col="blue", lwd=1)

## End(Not run)

---

Graphical function for visualizing bivariate censored and/or missing data

Description

Generates matrix of scatter plots for bivariate data with different types of censoring and missing.

Usage

splot(data, lower.list, upper.list, ti =ifelse(length(lower.list)>2, 
paste("Scatter plots of", lower.list[1], "to", lower.list[length(lower.list)]), 
paste("Scatter plot of", lower.list[1], "and", lower.list[2])),
 legend = TRUE, cex = 1.5, ...)

Arguments

data	a data frame name.
lower.list	the lower bounds names in the data frame of the variables between which the scatter plots are to be generated.
upper.list	the upper bounds names in the data frame of the variables between which the scatter plots are to be generated.
ti	figure title.
legend	figure legend.
cex	simbol sizes.
...	not used.

Details

Generates matrix of scatter plots for bivariate data with different types of censoring and missing.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)

splot(logND, c("t1_OCDD", "t1_TCDF", "t1_HxCDF_234678"),
 c("t2_OCDD", "t2_TCDF", "t2_HxCDF_234678"), ti="scatter plot matrix")

splot(logND, c("t1_OCDD", "t1_TCDF", "t1_HxCDF_234678"),
 c("t2_OCDD", "t2_TCDF", "t2_HxCDF_234678"), ti="scatter plot matrix", bg="gold")

---

Graphical function 2 for visualizing bivariate censored and/or missing data.

Description

Generates scatter plot for bivariate data with different types of censoring and missing.

Usage

splot2(data, lower1, upper1, lower2, upper2, pch = 21, bg = "cyan", 
xlab = lower1, ylab = lower2, ...)

Arguments

data	a data frame name.
lower1	the lower bound name in the data frame of the first of the two variables for whose pairwise correlation to be calculated.
upper1	the upper bound name in the data frame of the first of the two variables for whose pairwise correlation to be calculated.
lower2	the lower bound name in the data frame of the second of the two variables for whose pairwise correlation to be calculated.
upper2	the upper bound name in the data frame of the second of the two variables for whose pairwise correlation to be calculated.
pch	point character.
bg	point background color.
xlab	x axis label.
ylab	y axis label.
...	not used.

Details

Generates scatter plot for bivariate data with different types of censoring and missing.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)

splot2(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678",
 "t2_HxCDF_234678", xlab="OCDD", ylab="HxCDF234678")

x <- logND[which(!is.na(logND[,14]) & !is.na(logND[,15])),14]
y <- logND[which(!is.na(logND[,26]) & !is.na(logND[,27])),26]
xhist = hist(x, plot=FALSE, breaks=10)
yhist = hist(y, plot=FALSE, breaks=10)
  
zones=matrix(c(2,0,1,3), ncol=2, byrow=TRUE)
layout(zones, widths=c(5/6,1/6), heights=c(1/6,5/6))
top = max(c(xhist$counts, yhist$counts))
par(mar=c(5,5,1,1))
splot2(logND, "t1_OCDD", "t2_OCDD", "t1_HxCDF_234678",
 "t2_HxCDF_234678", xlab="OCDD", ylab="HxCDF234678", cex=1.5)  

par(mar=c(0,6,2,4))
barplot(xhist$counts, axes=FALSE, ylim=c(0, max(xhist$counts)), space=0)
par(mar=c(6,0,4,2))
barplot(yhist$counts, axes=FALSE, xlim=c(0, max(yhist$counts)), space=0, horiz=TRUE)

---

Calculating starting values for the vector of (mean1, mean2, var1, corr, var2) from completely observed data.

Description

Calculates starting values for the vector of (mean1, mean2, var1, corr, var2) from completely observed data.

Usage

sv(data, lower1, upper1, lower2, upper2)

Arguments

data	a data frame name.
lower1	the lower bound of the first variable of the two variables whose correlation coefficient to be calculated.
upper1	the upper bound of the first variable of the two variables whose correlation coefficient to be calculated.
lower2	the lower bound of the second variable of the two variables whose correlation coefficient to be calculated.
upper2	the upper bound of the second variable of the two variables whose correlation coefficient to be calculated.

Details

function sv calculates starting values for the vector of (mean1, mean2, var1, corr, var2) from completely observed data.

Value

mu1	starting value for the mean parameter of the first variable.
mu2	starting value for the mean parameter of the second variable.
var1	starting value for the variance parameter of the first variable.
cor	starting value for the correlation coefficient.
var2	starting value for the variance parameter of the second variable.

Author(s)

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie.

References

Yanming Li, Kerby Shedden, Brenda W. Gillespie and John A. Gillespie (2016). Calculating Profile Likelihood Estimates of the Correlation Coefficient in the Presence of Left, Right or Interval Censoring and Missing Data.

Examples

data(ND)
logND <- log(ND)

sv(logND, "t1_TCDD", "t2_TCDD", "t1_PeCDD", "t2_PeCDD")

---