CBLS {BivRegBLS}

Correlated Bivariate Least Square regression (CBLS)

Description

Estimate the Correlated Bivariate Least Square regression with replicated data (in a (M,D) plot) where M=(X+Y)/2 and D=Y-X.

Usage

CBLS(data = NULL, xcol = 1, ycol = 2, var.x = NULL, var.y = NULL,
     df.var.x = Inf, df.var.y = Inf, ratio.var = NULL, conf.level = 0.95,
     pred.level = 0.95, npoints = 1000, qx = 1, qy = 1, xpred = NULL)

Arguments

data

a data set (data frame or matrix).

xcol

a numeric vector to specify the X column(s) or a character vector with the column names.

ycol

a numeric vector to specify the Y column(s) or a character vector with the column names.

var.x

a numeric variable for the variance of the measurement error of device X if known.

var.y

a numeric variable for the variance of the measurement error of device Y if known.

df.var.x

a numeric variable for the degrees of freedom of the variance of the measurement error of device X if known.

df.var.y

a numeric variable for the degrees of freedom of the variance of the measurement error of device Y if known.

ratio.var

a numeric value for λ, the ratio of the measurement error variances (Y over X) if known.

conf.level

a numeric value for the confidence level (expressed between 0 and 1).

pred.level

a numeric value for the predictive level (expressed between 0 and 1).

npoints

an integer (at least 10) for the number of points to smooth the hyperbolic curves.

qx

an integer to predict the mean of qy Y future values from the mean of qx X values (generalized interval).

qy

an integer to predict the mean of qy Y future values from the mean of qx X values (generalized interval).

xpred

a numeric vector for customized predictions at given M values.

Details

The data argument is mandatory. If the data are unreplicated, then the measurement error variances must be given or their ratio (λ) in order to calculate the correlation, ρ_{MD}, between the measurement errors of the differences (on the Y-axis) and the measurement errors of the means (on the X-axis). The confidence level is used for the confidence intervals of the parameters (ρ_{MD}, β (slope), α (intercept)), the hyperbolic confidence intervals (the prediction of the expectation of Y for a given X) and the hyperbolic confidence bands. The predictive level is used for the hyperbolic predictive intervals (the prediction of a future Y for a given X) and the hyperbolic generalized intervals (the prediction of the mean of q future Y values for a given X).

Value

A CBLS class object, a list including the following elements:

Xij

a table with the (replicated) X measurements (replicates are in columns).

Yik

a table with the (replicated) Y measurements (replicates are in columns).

Xi

a vector with the means of the X measurements.

Yi

a vector with the means of the Y measurements.

Mi

a vector with the means ((X+Y)/2) measurements.

Di

a vector with the differences (Y-X) measurements.

nxi

a vector with the number of X replicates per sample (patient).

nyi

a vector with the number of Y replicates per sample (patient).

variances_x

a vector with the variances calculated on the X replicates per sample (patient).

variances_y

a vector with the variances calculated on the Y replicates per sample (patient).

Rho.MD

a table with the value of ρMD (the correlation between the measurement errors of the means and the differences) and its confidence interval.

Ellipse.CBLS

a two columns matrix with the coordinates of the joint confidence interval (confidence region, ellipse) for the parameters (β, α).

Estimate.CBLS

a table (data frame) with the estimates of the intercept and the slope, standard error, confidence interval and pvalue (null hypothesis: slope = 0, intercept = 0).

Pred.CBLS

a data frame with npoints rows (from the minimum to the maximum of the observed X values) and the following columns: the X values where the predictions are calculated (X0), the Y predicted values (Ypred), the lower and upper bounds of the confidence interval, predictive interval, generalized interval and confidence bands.

xpred.CBLS

a data frame with the customized predictions and the same columns than Pred.CBLS.

Author(s)

Bernard G FRANCQ

References

Francq BG, Govaerts BB. How to regress and predict in a Bland-Altman plot? Review and contribution based on tolerance intervals and correlated-errors-in-variables models. Statistics in Medicine, 2016; 35:2328-2358.

See Also

BLS

Examples

library(BivRegBLS)
data(SBP)
# CBLS regression on replicated data
res.CBLS1=CBLS(data=SBP,xcol=c("J1","J2","J3"),ycol=8:10,qx=3,qy=3,xpred=c(100,120,140,160))
# CBLS regression on unreplicated data with measurement error variances previously estimated
res.CBLS2=CBLS(data=SBP,xcol=c("J1"),ycol="S1",var.x=80,var.y=50,df.var.x=100,df.var.y=100)